Session S00: Poster Session III (4pm-6pm CDT)

Determining bound states of Krypton in the range 22-32eV using the Dirac B-Spline atomic R-Matrix code

While the bound-states of Krypton below the first ionization threshold have been well-studied, there is little information in the literature regarding higher-energy states, typically corresponding to single-excitations from the 4s subshell, or double-excitations from the 4p subshell. Some of these high-energy states have been observed experimentally [1,2] but remain unassigned, while many more have yet to be discovered. In this work, we seek to determine bound-state energies of Krypton in the energy range 22-32eV using the Dirac B-Spline atomic R-Matrix suite of codes [3,4]. Of particular interest are the states of character 4s^-1np, and 4p⁴nln’l’. An initial atomic structure description of Kr⁺ is generated using DBSR_HF, a B-Spline Dirac-Hartree-Fock program [5]. Bound-state energies in a fully-relativistic coupling scheme are then determined using the DBSR suite.

 

 

 

[1] K. Coddling and R. P. Madden, J. Res. Natl. Bur. Stand. A Phys. Chem. 76A(1) (1972) 1-12

[2] M. Valin and P. Marmet, J. Phys. B 8(18) (1975) 2953–2967

[3] O. Zatsarinny and K. Bartschat, Phys. Rev. A 77 (2008) 062701

[4] O. Zatsarinny, https://github.com/zatsaroi

[5] O. Zatsarinny and C. Froese Fischer, Comp. Phys. Commun. 202 (2016) 287-303

Probing Radiative Lifetimes in Lithium Dimer Ion-Pair States of 61Σg+ symmetry using Time-Resolved Molecular Spectroscopy

We performed time-resolved molecular spectroscopy experiments to measure the radiative lifetimes of alkali dimer ion-pair states of 6Σg+ symmetry, with a specific focus on our current project involving lithium molecules. Using pulsed-lasers and a double-resonance spectroscopy method, we conducted lifetime measurements through a time-correlated photon-counting technique at various temperatures and pressures. Our presentation includes detailed methods used to determine the radiative lifetimes in the collision-free regime. The results demonstrate close agreements within the error limits with theoretical lifetime calculations.    

Experimental Study of Highly Excited 1Σg+ and 1Πg States of the Cesium Dimer

We report the results of an experimental study on the highly excited 11 ¹Σ_g⁺ and 6 ¹Π_g electronic states of the cesium dimer. The rovibrational structure of these states was probed using the optical-optical double resonance (OODR) technique in which Cs₂ molecules from thermally populated levels in the X ¹Σ_g⁺ ground state were excited through intermediate levels in either the B¹Π_u state or the mixed A¹Σ_u⁺ ∼ b³Π_u manifold. The probe laser resonance frequencies were determined by detecting laser induced fluorescence (LIF) from the target states to the a³Σ_u⁺ triplet ground state. The observed states were identified as ¹Σ_g⁺ and ¹Π_g electronic states based on the selection rules for dipole allowed transitions followed by the line patterns in the recorded excitation spectra. Bound-bound fluorescence spectra from rovibrational levels in the target states down to the A ∼ b manifold were also taken to further confirm electronic state multiplicity. Two sets of Dunham coefficients corresponding to the two target states were fitted from experimentally determined term values and are reported in the present work. Potential energy curves constructed from these Dunham coefficients are also presented and compared to ab initio curves from our collaborators.   

Stochastic simulations of collisional-radiative processes in Rydberg plasmas

Rydberg plasmas have been identified as a source of radio recombination lines coming from H II nebulae, and are also a key element in the understanding of the evolution of the Universe during the recombination era when the first neutral atoms were formed and when radiation decoupled from the matter sector. Several processes govern the dynamics of recombination of Rydberg atoms that eventually lead to the creation of atoms in the ground state. Results are presented contrasting energy transfer and angular momentum transfer in collisions of Rydberg atoms with protons and electrons. These results, as well as the interaction of Rydberg atoms with radiation background, determine the evolution of populations of various states simulated using a stochastic algorithm, inspired by the kinetic Monte-Carlo method invented by D. Gillespie for computing chemical reaction rates. The chemical reaction rate differential equations define the average dynamics of populations involved in a network of reactions. In contrast, stochastic simulation provides mode detailed information about the distribution of atomic level populations.   

Lifetimes of Excited States of the Lanthanum Negative Ion

The negative ion of lanthanum has one of the richest bound state spectra observed for an atomic negative ion and it has been proposed as a promising candidate for laser cooling, which has not yet been achieved for atomic negative ions. In the present experiments, the radiative lifetimes of low-lying bound excited states of La^- were measured at the DESIREE cryogenic electrostatic storage ring facility at Stockholm University. La^- ions were injected into the ring and the populations of ground-state and excited ions were monitored over storage times of up to 800 s using state-selective photodetachment. The results test theoretical predictions of the transition rates and provide insights into the potential of La^{​​​​​​​-} for laser cooling.   

Detection of collective resonances using optical two-dimensional coherent spectroscopy

Optical two-dimensional coherent spectroscopy (2DCS) is a powerful technique with high sensitivity and temporal resolution that has been established as a vital tool for measuring ultrafast processes and couplings in complex systems such as atomic ensembles, molecules, and 2D materials. In this presentation, we will demonstrate the ability of 2DCS to probe weak transition dipole-dipole interactions through detection of collective resonances in a rubidium (Rb) vapor. Our methodology involves focusing four sequential pulses onto a Rb vapor cell, with each pulse controlled with time delays. This pulse sequence generates a nonlinear fluorescence signal due to collective resonances of multiple atoms. By performing Fourier transform analysis on the resulting signal, a 2D spectrum is generated in the frequency domain. The spectra reveal insights into coupling information and ultrafast processes. We measure collective resonances of Dicke states with up to 8 correlated atoms. These resonances arise from the cooperative behavior of the atomic ensemble and can be harnessed for various multi-atom applications in quantum information processing and quantum technologies. We propose extending the application of 2DCS to measure collective resonances in cold Rb atoms, thereby gaining an understanding of how many-body interactions can vary in two distinct temperature environments.

    

Statistical and theoretical atomic data calculations for moderately-charged lanthanide ions in order to compute opacities in the context of early-phase kilonovae modeling

The LIGO-VIRGO collaboration observed a neutron star merger (GW170817) thanks to the first detection of gravitational waves. An electromagnetic emission called kilonova is also observed. In the latter, nuclear reactions take place and form heavy nuclei e.g. lanthanides which contribute strongly to the luminosity and spectra of the kilonova. Such elements produce millions of lines due to their complex configurations characterized by an unfilled 4f subshell.

To interpret the spectrum of a kilonova, it is therefore crucial to precisely know the radiative parameters characterizing these elements. In recent years, several studies have been carried out, for the first degrees of ionisation (up to 3+) but almost all these investigations were limited to the analysis of kilonovae in a temperature range below 20000 K. To extend the study to early phases of kilonovae, it is essential to know the radiative parameters of lanthanide ions in higher charge stages.

The present work focusses on atomic data and opacity calculations for lanthanides (La to Lu) from the fourth to the sixth degree of ionization, for typical ejecta conditions such as the density ρ = 10^-10 g cm^-3, the time after the merger t = 0.1 day and temperatures T > 20000 K. In order to do that, we used the pseudo-relativistic Hartree-Fock (HFR) method as implemented in Cowan’s codes to calculate the radiative parameters. The expansion formalism was then used to compute the opacity, at 25000 K, 35000 K and 40000 K.

Since lanthanides (Eu to Lu) from the seventh to the ninth are characterized by complex configurations (i.e. unfilled 4f and 5p subshells), their atomic data are difficult to obtain with theoretical method. Indeed, the huge size of the energy matrices makes the diagonalization of the Hamiltonian extremely challenging. In order to simulate atomic data, we used the Resolved Transition Arrays (RTA) statistical method. Such method was tested for Sm VIII and Eu VI, two ions whose atomic data were already calculated by computational methods, in order to validate the obtained opacities by comparing them with the results deduced from full atomic calculations. Using compact formulae from RTA approach, we simulated atomic data for Dy VIII (Z = 66) and present the corresponding expansion opacity   

New atomic data in heavy elements for the determination of kilonova ejecta opacity

The production of elements heavier than iron in the Universe still remains an unsolved mystery. About half of them are thought to be produced by the astrophysical r-process (rapid neutron-capture process), for which one of the most promising production sites are neutron star mergers (NSMs). In August 2017, gravitational waves generated by a NSM were detected for the first time by the LIGO detectors (event GW170817), and the observation of its electromagnetic counterpart, the kilonova (KN) AT2017gfo, suggested the presence of heavy elements in the KN ejecta. The luminosity and spectra of such KN emission depend significantly on the ejecta opacity, which is thought to be dominated by millions of lines from the heavy elements produced by the r-process, in particular f-shell elements, i.e. lanthanides and actinides. Atomic data and opacities for these elements are thus sorely needed to model and interpret KN light curves and spectra.

In this context, the present work focusses on large-scale atomic data and opacity computations for all heavy elements with Z ≥ 20, with a special effort on lanthanides and actinides, for a grid of typical KN ejecta conditions (temperature, density and time post-merger) between one day and one week after the merger (corresponding to the LTE photosphere phase of the KN ejecta). In order to do so, we used the pseudo-relativistic Hartree-Fock (HFR) method as implemented in the Cowan’s codes, in which the choice of the interaction configuration model is of crucial importance. In this contribution, HFR atomic data and opacities for all lanthanides and actinides will be presented. Besides, we will also discuss the contribution of every single element with Z ≥ 20 to the total KN ejecta opacity for several NSM models, depending on their Planck mean opacities and elemental abundances deduced from NSM simulations. The impact of considering such atomic-physics based opacity data instead of typical crude approximation formulae for the determination of the total KN ejecta opacity used in KN light curve modeling will also be evaluated.   

Revived Confinement Resonances Near Inner Subshells Thresholds in Photoionzation Time Delay of Confined Atoms

We predict the revival of confinement resonances in the Wigner time delay in outer atomic shell photoionzation near inner shell thresholds. The near-threshold revival of confinement resonances in the time delay is caused by inter-shell correlation and serves as a sensitive probe of this effect. The revival is present even when the inner and outer shell thresholds are hundreds of electron volts apart. We illustrate this observation with a theoretical study of the outer shells of the Noble Gases (Ne, Ar, Kr, and Xe) confined in a C60 cage has been performed using the relativistic random phase approximation (RRPA) methodology [1]. The effects of the C60 potential modeled by a static spherical well which is reasonable in the energy region well above the C60 plasmons [2].

[1] W. R. Johnson and C. D. Lin, Phys. Rev. A 20, 964 (1979)

[2] V. K. Dolmatov, Adv. Quantum. Chem. 58, 13 (2009)   

Structure and photon induced dynamics of a Na cluster inside a giant fullerene

Atomic clusters and their endohedral complexes have attracted significant research interest in the recent past[1, 2]. In this work, we study the ground state structure and the photoionization dynamics of a sodium cluster endohedrally confined in a giant fullerene (Na₂₀@C₂₄₀). The result shows that the ground state of this cluster-fullerene spherical dimer involves Na₂₀ levels somewhat hybridized with the unoccupied levels of C₂₄₀. The photo-induced plasmon and Auger excitations, including single-electron innershell excitations, in C₂₄₀ trigger a variety of processes such as   the inter-Coulombic decay (ICD), Auger-ICD coherent decay and electron transfer mediated decay (ETMD).  The impact of these processes on different ionization levels of the system, as computed by a DFT technique, will be presented.

 

 

 REFERENCES

 

[1]Vitali Averbukh and Lorenz S Cederbaum. Interatomic electronic decay in endohedral fullerenes. Phys. Rev. Lett., 96, 053401 (2006).

 

[2] Rasheed Shaik et al., Plasmonic Resonant Intercluster Coulombic Decay, Phys. Rev. Lett 130, 233201 (2023).   

Interference between Multiple Photoionization Pathways in Chiral Molecules: Converging Continuum Results in Gaussian Bases.

This study focuses on the photoionization dynamics of chiral molecules. Our group has recently shown that the RABBITT (Reconstruction of Attosecond Beating by Interference of Two-photon Transitions) technique can be useful in measuring and understanding photoelectron circular dichroism (PECD) in randomly oriented chiral molecules [1][2]. PECD is a photoelectron asymmetry unique to these molecules. In this study, we address the challenge of explaining the continuum dynamics using a standard quantum chemistry basis set. Quantum chemistry basis sets are based on Gaussian functions, which are designed and optimized to accurately describe electron behavior in bound systems where electrons are localized around atoms or molecules. However, they lack precision and accuracy when it comes to representing electron density in a continuous regime. We employ time-dependent perturbation theory to determine PECD and show the significance of addressing continuum interactions within molecules by augmenting correlation-consistent quantum chemistry basis sets with large diffuse functions. The results show the convergence (and in some cases non-convergence) of PECD with diffuse functions.

[1] R. Esteban Goetz, Christiane P. Koch, and Loren Greenman Phys. Rev. Lett. 122, 013204 (2019)

[2]  arXiv:2104.07522v2 [physics.atom-ph]   

Quantum-mechanical treatment of sequential three-body fragmentation

We study the sequential fragmentation process of a triatomic molecule $ABC$ into its constituent atoms $A$, $B$, and $C$ --- e.g., $ABC$$\rightarrow$$AB$+$C$$\rightarrow$$A$+$B$+$C$, where the $AB$ intermediate is a ro-vibrational resonance.  The initial $ABC$ may be charged or neutral, ground- or excited-state, and produced via collision or photon absorption.  Our quantum-mechanical treatment yields the full momentum distribution of the atomic fragments.  With this, we will identify the conditions under which the long-used experimental signature of sequential fragmentation --- namely, a uniform angular distribution of the relative motion of $A$ and $B$ relative to $C$ --- are valid. In particular, we analyze in general terms what properties of $ABC$ and $AB$ are needed to produce the isotropic angular distribution.   

Ionization rates for cold collisions of metastable antihydrogen atoms

A recent study [Zammit et al, Phys. Rev. A 100, 042709 (2019)] suggested that it may be feasible to produce antihydrogen molecular ions in the near future by laser exciting antihydrogen atoms held in a magnetic trap. The desired antihydrogen molecular ion would then form by associative ionization that may occur during cold collisions of metastable antihydrogen atoms. The proposed experimental scheme relied on low energy extrapolations of thermal ionization rates which suggested associative ionization would be the fastest exothermic process. Our rigorous calculations presented here, however, show that associative ionization is less efficient than Penning ionization at the low temperatures required by the experimental scheme. Any future effort to pursue this formation route will therefore need to account for this trap loss mechanism.   

On the role of interatomic Coulombic decay in slow collisions of singly and doubly charged helium ions with neon dimers

We revisit previous model calculation for He²⁺-Ne₂ collisions¹ and extend the analysis of electron removal processes which result in dimer fragmentation. Specifically, instead of a standard independent-electron multinomial evaluation of single- and many-electron transitions we use a Slater-determinant-based method to account for the Pauli principle, and we take into account that the projectile changes its charge state when capturing an electron from the first atom of the dimer it encounters (assuming parallel orientation of the dimer with respect to the projectile beam axis). We confirm the previous prediction that interatomic Coulombic decay (ICD) is a strong channel at low collision energies. For singly-charged projectiles (He⁺ ions) we find that the total ICD cross section is smaller than for He²⁺ impact, but that there is no substantial competing process in the Ne⁺ - Ne⁺ fragmentation channel. We conclude that if one were to measure the kinetic energy release spectrum one would find a clean signature of ICD in it.

¹ T. Kirchner, J. Phys. B 54, 205201 (2021)   

Dipolar focusing in laser-assisted positronium formation

We use the Classical Trajectory Monte Carlo method to calculate positronium (Ps) formation in the $e^+ + {\rm H}(n)$ collisions for $n\geq 3$ in the presence of an infrared laser field. This process is assisted by the dipolar focusing due to nonzero dipole moment of the hydrogen atom in excited states. The effect is similar to the Coulomb focusing effect in radiative recombination [1] and bremsstrahlung [2] in the presence of an infrared laser field. The dipolar focusing effect makes positron approach the target even for large impact parameter. This effect significantly enhances the Ps formation cross section which appears to be infinite for certain values of the laser field phase. A similar effect can occur in collisions of positrons with other atoms in excited states which can lead to improvements in efficiency of Ps formation.

[1] I. I. Fabrikant and H. B Ambalampitiya, Phys. Rev. A 101, 053401 (2020).

[2] H. B Ambalampitiya and I. I. Fabrikant, Phys. Rev. A 99, 063404 (2019).   

The Photodetachment Cross Section of Ps- and Elastic e--Ps Scattering

Recently, we resolved the discrepancy in the photodetachment cross section of the positronium negative ion (Ps^-) between the prior Kohn variational calculation [1-3] and calculations using close-coupling wave functions [4-5]. Like the earlier calculations we evaluated this cross section in both the length and velocity forms . We are also considering the acceleration form of the cross section.  For the e^-- Ps   ¹P continuum wave function we used the Kohn and complex Kohn variational methods and for the ¹S bound-state wave function of Ps^- we used the Rayleigh-Ritz variational method. For elastic e^--Ps scattering below the Ps(n=2)-formation threshold we have computed ^1,3S and ^1,3P phase shifts using the Kohn, inverse Kohn, and complex Kohn variational methods with elaborate trial wave functions. We are currently computing ^1,3D phase shifts for e^--Ps scattering using these methods.

 

[1] S. J. Ward and M. R. C. McDowell, Europhys. Lett. 1, 167 (1986).

[2] S. J. Ward, Thesis, University of London, Unpublished (1986).

[3] S. J. Ward, J. W. Humberston and M. R. C. McDowell, J. Phys. B 30, 127 (1987).

[4] A. Igarashi, S. Nakazaki, and A. Ohsaki, Phys. Rev. A 61, 032710 (2000).

[5] A. Igarashi, I. Shimamura and N. Toshima, New J. Phys. 2, 17 (2000).   

Rf-Control of an Ultracold Photochemical Reaction via Quantum Interference

Ultracold atomic systems are a rich platform for studying numerous quantum phenomena due to their amenability to being precisely controlled and widely tunable. One such phenomenon we would like to study is control over the rate of photoassociation (PA) of two Rb atoms into an Rb2 molecule by carefully preparing the reactants in superposition states. We will report experimental progress on our study of PA in a radio frequency (RF)-dressed BEC. We propose the RF-dressed scheme allows full coherent control of the interference between PA pathways by varying the relative phase between the RF couplings.   

Effects of intermediate state detuning, atom-atom interactions, and electron spin in the two-photon excitation of ultralong-range Rydberg molecules

Ultralong-range Rydberg molecules (ULRRMs) comprise one or more weakly-bound ground-state atoms embedded in a Rydberg atom’s electron cloud. The rotational excitations of ULRRMs are largely unexplored. We present the rotational-excitation-resolved two-photon excitation spectra of dimer ULRRMs in cold ⁸⁶Sr and ⁸⁴Sr gases. Studies using ⁸⁶Sr 5sns ³S₁ (m=+1) dimer ULRRMs created in a week magnetic field (0.5G) show unexpected strong variations of rotational-state distributions that depend sensitively on the intermediate state detuning. Photoexcitation spectra for dimer ULRRMs of ⁸⁴Sr 5sns ³S₁ (m=+1), ⁸⁶Sr 5sns ¹S₀, and ⁸⁴Sr 5sns ¹S₀ states, however, yield rotational-state distributions that agree with the predictions of a model that considers both atom-atom scattering in the parent cold gas and the photon momentum transfer that accompanies Rydberg excitation. The reasons for the unexpected behavior in ⁸⁶Sr 5sns ³S₁ are the subject of ongoing studies. The observations suggest that ground-state atom-atom interactions, spin angular momentum, and excitation pathway all play important roles in determining the final distribution of rotational states.   

Towards Enhanced Loading and Quantum Simulation in a new NaCs Tweezer Array Apparatus

To harness the potential of ultracold polar molecules for both quantum computation and quantum simulation, we propose a hybrid system consisting of a programmable array of optical tweezers and an optical lattice for quantum simulation and computation. Prior efforts in our group achieved the assembly of single NaCs molecules in a 1D array of optical tweezers and the observation of coherent dipolar interactions between molecules. Building from this foundation, this new system will scale-up to two-dimensions with hundreds of individually-controllable molecules. In the pursuit of unity-filling, we investigate a new method combining broad tweezers with cold gases of atoms as a starting point to create small, dense ensembles of molecules. We then plan to leverage electric field shielding techniques and spilling to isolate single ground-state molecules in a tweezer. With the large system size and high loading, this apparatus can study new regimes in the extended Bose-Hubbard model and pursue quantum computation gates. In addition, we detail features of our ongoing construction including an in-vacuum electrode system to polarize our molecules, water-coolable Feshbach coils, and a dual-species 2D+ MOT.   

Challenges in Optical Cycling of Calcium Phenoxide

The laser cooling of large polyatomic molecules presents an exciting but formidable challenge due to their numerous vibrational and rotational degrees of freedom. Here, we build on previous high-resolution spectroscopy of the large polyatomic molecule calcium phenoxide (CaOPh) and report optical cycling of 2-5 photons on the molecule at a scattering rate of 13.7 kHz. This falls short of the estimated budget of 20 photons before decay to the first vibrational state, and at a scattering rate far below expectations. The cause of these observations has remained unexplained. We suggest several hypotheses which may explain the observed anomalies, and offer potential remedies for future studies.   

Technical Improvements Towards Realizing a Quantum Degenerate Gas of SrF Molecules

Tremendous progress has been made in direct laser cooling and trapping of molecules. We recently demonstrated trapping of SrF molecules at sufficient densities to observe loss from inelastic molecule-molecule collisions. Our next goal is to implement microwave shielding, which promises to suppress these losses while enhancing the elastic collision rate; this is ideal for evaporative cooling to quantum degeneracy. Microwave shielding has been achieved in bialkali assembled molecules (where quantum degeneracy was achieved) and in optical tweezers of single CaF molecules, but has yet to be successfully realized in a bulk sample of laser-cooled SrF molecules. The substantial spin-rotation splitting in SrF (75 MHz) requires comparably high microwave Rabi frequencies for effective shielding. We intend to accomplish this using a high-gain horn antenna and ellipsoidal focusing mirror to deliver a focused, free-space microwave beam at the molecules. Using this system, we aim to achieve Rabi frequencies up to 50 MHz, shielding state lifetime in excess of 1 second, and polarization purity of greater than 90% circular. In addition, we have constructed a second-generation apparatus for our experiment, which features a number of upgrades designed to help increase the particle number in and phase-space density of our bulk gas. This includes reduced source slowing length and a fully integrated rubidium MOT for sympathetic cooling.   

C60 Resonant Charge Transfer Through the Formation of Temporary Quasi-molecules

Charge transfer’s many applications have caused the topic to be very well studied and well understood in atom-ion collisions. In these systems, the dynamics of the electrons are of critical importance to charge transfer reactions. In collisions involving more complex targets, such as fullerenes, the dynamics of the collisions and possible chemical reactions become important as well. The model of charge transfer that we will present takes into consideration the temporary bonds that form between colliding fullerenes. These two colliding fullerenes temporarily create “dumbbell shaped” quasi-molecules which allow for a more efficient transfer of the charge. Our model is in good agreement with experimental data and is the first model that, to our knowledge, accurately explains the large scattering angle cross section for C₆₀ resonant charge transfer­.   

Revival, Supression and Maximization of Coherent Control through a Change of Basis

Coherent control relies on the interference between different pathways created by the preparation of initial superpositions. However, interference is a basis-dependent quantity, and so is coherent control. To address this, we introduce a novel formalism, the Coherent Control Scattering (CCS) matrix. This matrix allows us to analyze the modifications in interference structure and controllability resulting from a change of basis. We show that the change in controllability can be linked to the non-commutativity of the transformation matrix with the CCS matrix, and the non-orthogonality of the transformation. Furthermore, we find that minimal interference is associated with the CCS eigenbasis, while the Fourier basis of the eigenvectors yields maximal interference, leading to optimal coherent control. To illustrate the impact of a basis change on controllability, we provide an example involving ⁸⁵Rb+ ⁸⁵Rb scattering. Additionally, we apply this developed formalism to interpret recent experimental findings on He + D₂ inelastic scattering, highlighting the presence or absence of interference based on the chosen basis.   

Isotopologue-selective laser cooling of molecules

We will report on isotopologue-selective optical cycling, imaging and laser cooling of 136BaF molecules. The manipulation of 136BaF is achieved without being influenced by, or affecting, the order of magnitude more abundant 138BaF isotopologue in the same molecular beam. Our approach can yield intense beams and high-fidelity detection of 136BaF and other laser-coolable molecular isotopologues of choice. Such beams are a first step towards isotopologue-selective molecular trapping and will be useful for applications in cold chemistry and precision tests of fundamental symmetries.   

Ultracold coherent control of molecular collisions at a Förster resonance

We show that the precise preparation of a quantum superposition between three rotational states of an ultracold dipolar molecule generates controllable interferences in their two-body scattering dynamics and collisional rate coefficients, at an electric field that produces a Förster resonance [1]. This proposal represents a feasible protocol to achieve coherent control on ultracold molecular collisions in current experiments [2, 3, 4]. It sets the basis for future studies in which one can think to control the amount of each produced pairs, including trapped entangled pairs of reactants, individual pairs of products in a chemical reaction, and measuring each of their scattering phase-shifts that could envision “complete chemical experiments” at ultracold temperatures [5].

[1] T. Delarue, G. Quéméner, "Ultracold coherent control of molecular collisions at a Förster resonance", arXiv:2312.13726 (2023)

[2] K. Matsuda, L. De Marco, J.-R. Li, W. G. Tobias, G. Valtolina, G. Quéméner, J. Ye, Science 370, 1324 (2020)

[3] J.-R. Li, W. G. Tobias, K. Matsuda, C. Miller, G. Valtolina, L. D. Marco, R. R. W. Wang, L. Lassablière, G. Quéméner, J. L. Bohn, J. Ye, Nat. Phys. 17, 1144 (2021)

[4] Y. Liu, M.-G. Hu, M. A. Nichols, D. Yang, D. Xie, H. Guo, K.-K. Ni, Nature 593, 379 (2021)

[5] J. L. Bohn, A. M. Rey, J. Ye, Science 357, 1002 (2017)   

Photoelectron-Photoion Cumulant Mapping Spectroscopy Reveals Multiparticle Correlation in Strong Field Ionization of Water Experiment

Photoelectron-Photoion Spectroscopy has become a crucial tool for understanding ultrafast dynamics, providing invaluable insights into complex atomic and molecular processes. Momentum Resolved Above-Threshold Ionization (MRATI) [1] has shown that fragment ions with different momenta have strikingly different photoelectron spectrum, shedding light on the ionization dynamics originating from different molecular orbitals. The recently developed multiparticle cumulant mapping (or higher-order covariances) method [2] has demonstrated promising capabilities in unveiling photoion-photoion correlation, which has the potential to accelerate the data acquisition speed and provide more ionization channels. We extend the method to look for photoelectron-photoion correlation in strong field ionization experiments with water molecules.

[1] Cheng, C., Forbes, R., Howard, A.J., Spanner, M., Bucksbaum, P.H. and Weinacht, T., 2020. Momentum-resolved above-threshold ionization of deuterated water. Physical Review A, 102(5), p.052813.

[2] Cheng, C., Frasinski, L.J., Moğol, G., Allum, F., Howard, A.J., Rolles, D., Bucksbaum, P.H., Brouard, M., Forbes, R. and Weinacht, T., 2023. Multiparticle Cumulant Mapping for Coulomb Explosion Imaging. Physical Review Letters, 130(9), p.093001.   

Laser-induced Coulomb explosion imaging of C4H8O isomers

Coulomb explosion imaging (CEI) is a promising technique that can intuitively connect the experimentally measured fragment ion momenta to the original three-dimensional molecular geometry. [DR1] Recent studies demonstrate that CEI triggered by ultrashort, intense near-infrared or X-ray pulses can offer a direct visualization of individual atoms within a molecule with more than ten atoms [1,2]. In most cases, the molecular (or recoil) frame is defined by the momentum vectors of two atomic ions that are uniquely identified by their mass-to-charge ratio. In this work, we investigate laser-induced CEI of C₄H₈O isomers, where oxygen is the only unique atom. We find that the momentum images of each of these molecules are distinct, allowing the differentiation of the isomers. By leveraging multidimensional information from coincidence measurements to lift the degeneracy of the carbon ions, we show that the momentum images of each molecule still provide a clear correspondence to its original molecular structure in real space. Our findings expand the application of CEI to a broader class of chemically relevant molecules and facilitate the differentiation of various isomer structures that may arise in pump-probe experiments.

[1] R. Boll. et al., Nat. Phys. 18, 423–428 (2022).

[2] H.V.S. Lam et al., Differentiating three-dimensional molecular structures using laser-induced Coulomb explosion imaging (2023, submitted).   

Potentials for time-resolved laser-induced electron diffraction imaging within the XUV + IR scheme

We theoretically investigate the possibility of extending the laser-induced electron diffraction (LIED) imaging technique by adding a relatively intense XUV pulse to control and enhance the returning electron wave-packet. By analyzing the exact solutions of the time-dependent Schrodinger equation, we show that the LIED signals can be increased by two orders of magnitude within this scheme. More importantly, the quality of the retrieved laser-free differential elastic electron-target ion scattering cross section is not affected by the presence of the XUV pulse. Furthermore, with precise control of the electron emission time provided by the XUV pulse, the temporal resolution of the measurement can be improved as compared to the standard LIED technique. An additional advantage of this scheme is that a relatively weak IR pulse can be used, thereby overcoming the difficulties associated with the depletion of the target ground state.

This work was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award Number DE-SC0023192.   

Imaging of Optical Lattices via High Harmonic Generation

Noah Welikson and Andreas Becker

JILA and Department of Physics, University of Colorado, Boulder,

CO 80309-0440, USA

High harmonic generation (HHG) is a highly nonlinear process to upconvert laser light frequencies from the optical and near-infrared into the extreme ultraviolet and the soft x-ray regime [3]. HHG is understood through a process in which electrons are ionized from their parent nuclei by an intense laser pulse, picking up energy via the interaction with the laser field before recombining with the parent nuclei and releasing this energy in the form of radiation at multiples of the driver frequency [4, 1]. Recently, there has been much effort in applying such HHG sources for the use in high-definition imaging of materials [2]. We further explore the limits of these techniques by simulating the direct stimulation of HHG in an optical lattice. Thus far we have applied numerical solutions of the time-dependent Schr ̈odinger equation to calculate the microscopic harmonic spectrum emitted by atoms arranged in a lattice in a high intensity infrared laser field, and propagated this radiation into the far-field to generate a diffraction image. We show that certain phase reconstruction techniques used in coherent diffracting imaging can be applied to these diffraction data to generate high definition images of the lattice.

References

[1] P. B. Corkum. “Plasma perspective on strong field multiphoton ionization”. In: Phys. Rev. Lett. 71 (13 Sept. 1993), pp. 1994–1997. doi: 10 . 1103 /PhysRevLett.71.1994.

[2] Robert M. Karl et al. “Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams”. In: Science Advances 4.10 (2018), eaau4295. doi: 10.1126/sciadv.aau4295.

[3] Tenio Popmintchev et al. “Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers”. In: Science(New York, N.Y.) 336 (June 2012), pp. 1287–91. doi: 10.1126/science.1218497.

[4] K. J. Schafer et al. “Above threshold ionization beyond the high harmonic cutoff”. In: Phys. Rev. Lett. 70 (11 Mar. 1993), pp. 1599–1602. doi: 10.1103/PhysRevLett.70.1599.   

Multi-body fragmentation of polyatomic molecules following ionization by intense laser pulses

Intense laser pulses that multiply ionize polyatomic molecules often create unstable molecular ions that can fragment in complex ways.  Coincidence momentum imaging of the ionic products reveals the fragmentation dynamics, including whether the process is concerted or sequential.  These processes are distinguished using the native frames analysis method.  For example, in both formic acid (HCOOD³⁺ → D⁺ + O⁺ + HCO⁺) and ethanol (CH₃CH₂OH²⁺ → H₃⁺ + C₂H₂O⁺ + H), different sequential processes lead to the same final products.  We identified several examples of hydrogen elimination as the first fragmentation step, such as eliminating both hydrogen atoms from HCOOD²⁺, forming a long-lived CO₂²⁺ intermediate.  In other cases, however, we find that eliminating a neutral is the final step stabilizing the intermediate ion, e.g. CH₃CH₂OH²⁺ → H₃⁺ + CH₃⁺ + CO.   

Strong-field ionization of excited Lithium atoms with optical vortex beams

Optical vortex beams, characterized by the phase variation of their wavefront, carry orbital angular momentum (OAM), which can influence atomic and molecular systems by altering the conventional selection rules for electronic transitions. The manifestation of OAM transfer can in principle be observed in the resulting structure of the photoelectron momentum distribution. However, in gas-phase atoms, efficient OAM transfer occurs primarily near the beam's center, precisely where the field intensity is minimal. This inherent challenge complicates experimental observations, as efficient OAM transfer necessitates effective sampling of the field's phase variation by the electronic wavefunction of the atom. In this study, we investigate multi-photon ionization of Lithium atoms under the influence of an intense optical vortex beam, employing a numerical treatment to solve the time-dependent Schrödinger equation in an inhomogeneous field. We explore the ionization rate and OAM transfer dynamics for Lithium atoms in various excited states and positioned at different distances from the beam center. Our analysis reveals the conditions required for successful experimental implementation and sheds light on novel strong-field phenomena associated with electron dynamics in a vortex beam.   

Enabling elliptically polarized high harmonic generation with short cross polarized laser pulses

In this work we address the question of whether elliptically polarized harmonics can be generated using a two-color cross-polarized driving laser configuration and if so, how it can be controlled. Previous theoretical predictions disagreed with experimental observations which showed that even-order harmonics with large ellipticity could be generated. We present a theoretical analysis of this process using numerical simulations of high harmonic generation in atoms initially in a s- or p-state interacting with the two-color orthogonally polarized driving laser. The amount and sign of the ellipticity depends on the relative carrier-envelope phase of the pulses, their intensity ratio and the duration of the pulses.   

Compact optical grating compressor.

Optical grating compressors are routinely used in high-power chirped-pulse amplification laser systems to create ultrashort laser pulses with peak power up to the petawatt level. However, compressors with a large dispersion require a large distance between the compressor’s elements that limits the size of the laser system and makes their use impractical outside of the lab and particularly on moving platforms.

A novel design for a grating-based optical pulse compressor is presented. This compressor provides a large group delay dispersion while keeping the compressor's linear size small. The design is based on a traditional Treacy compressor [1] with a modification where two lenses are inserted between the compressor’s gratings. This novel configuration substantially increases the group delay dispersion of the compressor for a given size or, alternatively, decreases the compressor size while maintaining its group delay dispersion [2].

Optical Two-Dimensional Coherent Spectroscopy of Cold Atoms

Optical Two-Dimensional Coherent Spectroscopy (2DCS) provides sensitive and background-free detection of many-body interactions and correlations in atomic vapors. Since cold atoms are an ideal system with a well-controlled environment, applying optical 2DCS in cold atoms will be useful. In this presentation, we report an experimental demonstration of optical 2DCS in cold atoms. The experiment combines a collinear 2DCS setup with a magneto-optical trap (MOT), in which cold rubidium (Rb) atoms are prepared at a temperature of about 200 μK and a number density of 10¹⁰ cm^-3. We measured the second and fourth-order nonlinear signals in one dimension. Then we acquired one-quantum and zero-quantum 2D spectra. The experiment demonstrates that our 2DCS technique has sufficient sensitivity to obtain a 2D spectrum from cold atoms. The results of this experiment represent an important first step toward optical 2DCS applications in ultracold systems, opening the possibility of performing a 2DCS study in an atom array with a deterministic number of atoms and spatial distributions.   

Effect of the composition and wavelength on strong-field photoelectron emission from plasmonic nanoparticles

We explore the generation of photoelectrons (PEs) by exposure of plasmonic nanoparticles to intense infrared laser pulses. We assess the material and wavelength dependence of PE spectra and destinguish direct and rescattered photoemission pathways. To conduct this analysis, we experimentally measured [1] and numerically simulated [2,3] the momentum distributions of emitted PEs from spherical gold, silver, and platinum nanoparticles (NPs) ranging in size from 2.5  to 50 nm in radius for peak intensities between 0.1×10¹³ and 3.0 ×10¹³ W/cm² and wavelengths ranging from 500 nm to 1800 nm.

[1] J. A. Powell, Ph.D. thesis, Kansas State University (2017)

[2] E. Saydanzad, J. Li, and U. Thumm, Phys. Rev. A 106, 033103 (2022)

[3] E. Saydanzad, J. Powell, et al., Nanophotonics 12(10), 1931–1942 (2023)   

Radio Frequency Sensing based on Rydberg-Atom Electrometry

Rydberg atom-based sensors are used to detect radio frequency (RF) electric fields. These sensors have useful properties such as self-calibration, broad carrier bandwidth and high transparency to RF electromagnetic fields. In a room temperature vapor cell filled with cesium atoms, both 2-photon and 3-photon excitation and readout schemes have been demonstrated. In this poster, several different technical advances that move Rydberg atom-based sensors towards real applications are described. First, we show a co-linear 3-photon scheme that minimizes the wavevector mismatch and thereby reaches sub-200 kHz linewidths at room temperature. We demonstrate the benefits of a narrow linewidth 3-photon setup in extending the self-calibrated regime to weaker RF field amplitudes, while obtaining high sensitivity to RF pulses. Second, we describe a laser system which can switch between wavelengths, spanning around 8 nm, in a few hundred microseconds. This narrow-linewidth, frequency stabilized laser solves the problem of rapidly changing the RF frequency that is detected. Finally, we present results on engineered vapor cells that can act as amplifiers for the RF electromagnetic field, enhancing the interactions between the RF field and atom.   

Chirp asymmetry in Zeeman electromagnetically induced transparency

The simplest three-level system exhibiting electromagnetically induced transparency (EIT) exhibits an effective conjugation symmetry as well as a permutation symmetry. Breaking conjugation symmetry leads to a distinct chirp asymmetry; the differential response to a frequency increase versus a frequency decrease. Hanle-Zeeman EIT resonance is an ideal platform for testing the theory of chirp asymmetry because so many parameters of the system can be changed experimentally. We describe the theory and our results from a recent experiment using 87Rb in a buffer gas cell that, in comparison with earlier multi-photon chirp asymmetry work, explores the asymmetry at nearly a billionth the earlier chirp rate. This universal picture of chirp asymmetry has potential metrological consequences for understanding the systematic dependence on modulation/demodulation parameters.   

Versatile 1D atomic array around an optical nanofiber created by an accordion lattice

We present our implementation of an optical accordion lattice surrounding an optical nanofiber to establish a 1D atomic array with adaptable inter-atomic distances. Utilizing a 4-f imaging system, we project a 1D phase grating onto the image plane, illuminating the nanofiber from its side. With an aspect ratio of 100, we achieve a 2-mm lattice extension to accommodate an array of approximately 1000 atoms along the nanofiber while maintaining laser power efficiency. The lattice constant is customizable by selecting one of the 250 phase gratings with varying grating constants, all compactly printed on a 2-inch diameter glass substrate. Each grating occupies an area of 100 um * 10 mm. This setup enables comprehensive coverage of lattice constants ranging from 1.0 * 780 nm to 2.5 * 780 nm with a resolution of 5 nm. Fine adjustments to the lattice constant are achieved by tilting the grating within a 5-degree range.

To build an atomic array, optically cooled rubidium atoms are first loaded onto two-color dipole-trap beams guided along the nanofiber, providing transverse and azimuthal confinement. Additionally, the free-space, blue-detuned accordion lattice introduces a longitudinal periodic confinement along the nanofiber. The successful establishment of the 1D array will be validated through Bragg reflection data. We plan to use this platform to study photon-mediated collective phenomena, including super-and-sub radiance transitions, cooperatively generated quantum beats, and long-range non-Markovian dynamics.   

Microwave spectroscopy assisted by electromagnetically induced transparency near natural Förster resonance on rubidium

Precise measurements of quantum defects are essential for refining theories and obtaining more precise values for various atomic properties, such as dipole moment. In this study, we have performed microwave spectroscopy by monitoring the EIT signal between the nD_5/2 and (n+2)P_3/2 and (n − 2)F_7/2 states, for n = 41 to 46, in a rubidium vapor cell. This interval is interesting because of the occurrence of a Förster resonance. We compare the obtained results with measurements made by other groups for the P_3/2 [1] and F_7/2 [2] series, allowing us to validate the best-measured quantum defect values. This validation is particularly crucial due to the emergence of discrepant values in recent years. We conclude that the measurements by Li and Han et al. are the most suitable for use, highlighting the reliability and consistency of these data.

[1] LI, W. et al. Millimeter-wave spectroscopy of cold rb Rydberg atoms in a magneto-optical trap: quantum defects of the ns, np, and nd series. Physical Review A, APS, v. 67, n. 5, p. 052502, 2003.

[2] HAN, J. et al. Rb n f quantum defects from millimeter-wave spectroscopy of cold rb 85 Rydberg atoms. Physical Review A, APS, v. 74, n. 5, p. 054502, 2006.   

Angular Momentum Orientation in Molecules Using the Autler-Townes Effect

We report an experimental demonstration of state selective molecular angular momentum orientation using dressed states created by a strong cw control laser. Our results show that the M-dependent Rabi frequency of the Autler-Townes effect for circular polarization allows for M-state selective molecular angular momentum orientation, where M is the projected angular momentum onto a lab fixed axis. Our results also show the square-root relationship between the splitting of adjacent M-levels and the power of the control laser, and thus the requirement for a strong control field to achieve M-state selectivity. The effect was observed using Li₂ molecules and a combination of left- and right-handed circularly polarized lasers.   

Separation of polarization singularities of optical fields generated by multiple point-like sources of light

In this presentation, we will present our study of morphology of polarization singularities of electromagnetic fields generated from interference of point-like optical sources. We identify C-lines, C-planes, L-lines and L-planes for circular (C) and linear (L) polarization of  electric and magnetic vector fields. In the far field, electromagnetic gauge invariance  requires inclusion of the longitudinal field components near the phase singularity, leading to formation of the singularity doublets.

We investigate spatial separation of electric- and magnetic-type singularities and demonstrate that splitting between them is at the wavelength scale, is propagation-invariant, {\it i.e.} it is protected against diffraction and depends on the topological charge of the singularity. Higher-order effects beyond the paraxial approximation are included in the theory analysis. Theory predictions are illustrated with a numerical analysis.   

High-dimensional interference through a multimode fiber using long coherence single photon from warm atomic ensemble

The light passing through the scattering medium makes speckle pattern. It is the result of interference in all paths of the light. it means that when we can control all paths, we can make specific mode we want and we can control the interference.

well-controlled scattered light can also make quantum properties robust and can be used to create multidimensional spatial entanglement.

It has to know transmission matrix(T-matrix) to control scattered lights. It uses iteration method to measure T-matrix. This method has the problem that it spends a lot of time to measure T-matrix and we have to measure properties of light, like interference fringe, in the optimization maintaining time.

However, phase conjugation can be measured at once and we can make spatial mode we want by controlling input beam shape and its phase. For example, we can make like a beam splitter. It means that the two output states are phase difference is pi. Furthermore, if we can make 4 output states that the phase difference is pi/2  each states.

These results demonstrate to be able to control multiple inputs and output states. Furthermore, these may have potential application in quantum information processing.

Long-wavelength Transitions in Yb Atom Arrays for Quantum Science

Neutral atoms trapped in arrays of optical tweezers are a leading platform for quantum information science. Optical tweezers provide precise control over atomic positions, which enables arbitrary system geometries and coherent transport of atoms. This tool facilitates programmable systems capable of exploring collective dynamics in ordered atomic systems and the integration of atoms with dispersion-engineered nanophotonic structures. A system of atoms in an ordered array will experience collective interactions that dramatically alter the optical response of the system. The radiation pattern of an atom in the array will be perturbed by the scattered field of nearby atoms at the same optical transition wavelength. Depending on the interatomic spacing, the scattered fields from the atoms will interfere in a cooperative response, which can be constructive (super-radiant) or destructive (sub-radiant). Controlling the collective response of the system leads to applications in quantum memories, quantum sensors, and the generation of non-classical states of light using atomic photonic elements. The photonic environment the atoms experience can also be engineered by coupling arrays of atoms to nanophotonic structures, enabling a modular quantum architecture for computing, sensing, and communication. In each case, we leverage long wavelength transitions in the telecom band (1.4 um to 1.9 um) connected to coherent metastable states in ytterbium (Yb). The telecom probe transitions realize a system capable of exploring collective effects when combined with shorter tweezer trapping wavelengths, and enable the use of established silicon nanofabrication techniques for these nanophotonic structures. We present progress toward probing collective effects in atom arrays and integrating these arrays with dispersion-engineered nanophotonics.   

Proposal for Spin-Synchronization in Cold Rubidium Vapor

Synchronization of coherently driven quantum mechanical spin systems is investigated theoretically. Starting from a microscopic framework that accounts for several auxiliary states in the rubidium-87 hyperfine state manifolds, an effective master equation for the spin-1 system is derived. Several level schemes and protocols for observing synchronization are benchmarked. Focusing on the so-called synchronization blockade [1], various synchronization measures are discussed and contrasted. To model an experimental protocol for the read-out of the coherences, which govern a subset of the synchronization measures, the propagation of read-out beams through a non-interacting atomic vapor is simulated by self-consistently solving the full atomic master equation and Maxwell's equations.

 

[1] R. Tan, C. Bruder, and M. Koppenhoefer, Quantum 6, 885 (2022).   

Chirped stimulated adiabatic passage with nonzero two-photon detuning

We develop a theory of stimulated Raman adiabatic passage (STIRAP), and fractional STIRAP (FSTIRAP) using frequency-chirped pulses. In both configurations, we find that pulse chirping faciliates higher contrast, a broader range of parameters for adiabaticity, and enhanced spectral selectivity. Additionally, we demonstrate that the pulse chirping allows for the relaxation of the condition of two-photon resonance necessary for adiabatic passage in STIRAP and FSTIRAP. Adiabatic passage to a predetermined state between two nearly degenerate final states, while unachievable in conventional STIRAP, is achived in chirped STIRAP by setting the condition |α|=|δ|/(t_p−t_s). This condition is accessible over a broad range of values for the two-photon detuning, δ, the chirp rate, α, and the pulse decay (tp-ts). In chirped FSTIRAP, chirping of the pump and Stokes pulses permits a complete compensation of the two-photon detuning that results in a selective maximum coherence of the initial and the target state with higher spectral resolution than in conventional F-STIRAP.

These proposed schemes will broaden the scope of quantum control methods and contribute to advancements in the fields of quantum imaging, sensing, and metrology.   

Realizing Optical Tweezer Arrays via Holographic Metasurfaces for Super- and Subradiance Studies with Strontium

We report our progress towards exploring super- and subradiance in optical tweezer arrays. Using holographic metasurfaces, we generate optical tweezer arrays that allow us to realize tightly packed atomic arrays with μm spacing. The metasurface-generated arrays are shown to produce highly uniform trap intensities and feature high power resilience. With such arrays, we have trapped single Sr atoms and achieved single-atom imaging fidelities >99%. In order to pursue super- and subradiance studies, we utilize the Sr ³P₂ -³D₃ transition in the mid-infrared at 2.9 μm. We discuss progress in realizing the necessary laser source and the techniques for state preparation into the ³P₂ state. Our work paves the way for a new platform to study quantum electrodynamics, with potential applications including atomic waveguides, novel atom-photon interfaces, and quantum memories.   

Hamiltonian estimation in trapped ion quantum simulators

Analog quantum simulators use native interactions between effective spins (qubits) to study complicated Hamiltonians. Characterizing a Hamiltonian's parameters is essential to have faith in the results of a quantum simulation. However, efficient full characterization of a general many-body Hamiltonian is challenging. Here, we explore new strategies for estimating Hamiltonian parameters by implementing the quantum-quench protocol [1] on our trapped Yb+ ion system with intrinsic long-range interactions. We also develop a new experimental tool for shelving a subset of our hyperfine qubits into an auxiliary Zeeman level within the detection manifold, preserving Hamiltonian terms on the remaining subsystem. We investigate the quench protocol and its interplay with our shelving tool to improve overall efficiency of a Hamiltonian estimation procedure. 

[1] Phys. Rev. Lett. 124, 160502 (2020)    

Rydberg quantum simulator with neutral cesium atoms

The complex behavior of quantum many-body physics unveils insights into information propagation and the susceptibility of these systems to external perturbations, defects and noise. To explore these questions, we are developing a Rydberg quantum simulator with neutral cesium atoms, demonstrating tunable interactions and flexible geometries. We present our latest experimental efforts on probing the trade-off between the complexity and the robustness of a quantum many body system.   

Progress on the design of a full stack quantum control framework for trapped ion quantum information processors

We present an initial design of a full stack quantum control framework for specifying atomic and quantum information experiments on trapped ion quantum information processors. The framework is intended to improve the usability of quantum information processors for users at varying levels of expertise by allowing experiments to be expressed at multiple levels of abstraction appropriate for the knowledge of the user and nature of the experiment. The modular design of the framework will enable better portability of the control stack between different trapped ion apparatuses. Here, we focus on prototype expressions for specifying quantum simulation and atomic physics experiments and calibrations and how they compile to an example trapped ion apparatus.   

Programmable quantum simulator based on Penning trapped ions

Two-dimensional ion crystals are a proven platform for generating many body spin-spin interactions. We describe recent work constructing a programmable quantum simulator using a few to hundreds of ⁴⁰Ca⁺ ions confined in a compact Penning trap. The motional modes of the ions are cooled near the motional ground state using dark resonance cooling, which is compared to a semi-classical model. We show progress towards simultaneous entanglement of all pairs of atoms through the application of a pair of global optical dipole force beams. Arbitrary Ising interaction graphs can be produced by alternately applying the global entangler with individually addressed one qubit rotations. Using a fast time-tagging camera, the state of each qubit is read out by imaging the planar ion crystal in its rotating frame. Combined, these tools are applied to MaxCut QAOA and could also be used for hybrid digital-analog quantum simulation.   

Combining Hamiltonian Learning Techniques with Variational Quantm Algorithms

The emergence of programmable quantum simulation platforms has opened up new avenues for tackling the quantum many-body problem. These platforms provide us with valuable tools to explore questions in fundamental physics and also carry practical implications, particularly in areas like quantum chemistry and material design. In this presentation, I will showcase advancements in Hamiltonian learning techniques used for investigating highly correlated quantum many-body states on programmable quantum hardware. This will encompass a range of applications, including the verification and characterization of analog and digital quantum simulation platforms, as well as the analysis of entanglement properties in many-body states prepared on programmable quantum simulators. Notably, I will report on experiments involving 51 trapped ions, where we have successfully extract entanglement features of subsystems within an ion chain comprising up to 20 lattice sites. The latter part of the presentation will delve into the exciting prospects of combining Hamiltonian learning techniques with variational quantum algorithms, showcasing their potential applications in quantum material design.   

Towards simulation of lattice gauge theories with ultracold ytterbium atoms in hybrid optical potentials

Gauge theories play a fundamental role for our understanding of nature, ranging from high-energy to condensed matter physics. Their formulation on a regularized periodic lattice geometry, so-called lattice gauge theories (LGTs), has proven invaluable for theoretical studies. Numerical studies on, e.g., their real-time dynamics are however computationally challenging. We report progress on developing a quantum simulator for LGTs using neutral ytterbium atoms. Ytterbium's internal level structure provides a ground and meta-stable clock state pair, and fermionic isotopes further host nuclear qubits. We combine optical lattice and optical tweezer technology that can enable robust and scalable implementation of LGTs. To realize state-selective control, we leverage magic and tune-out wavelengths. We present the first measurements of such wavelengths near the narrow cooling transition at 556 nm and discuss prospects in implementing local gauge invariance.   

Characterizing Topological Nodal Structures and Their Evolution With a Bose-Einstein Condensate

Characterizing topological nodal structures and how they evolve or even change their topology when parameters are continuously varied is important to the studies of topological states of matter but is challenging in experiments. Here, we observe the emergence of topological nodal rings and lines in the parameter space of the light (rf/microwave) fields that cyclically couple four atomic hyperfine spin states in a Bose-Einstein condensate. When the parameters are changed, the evolution of these nodal structures is probed by quench dynamics and Fourier spectroscopy. Our experimental results are consistent with the theory, which predicts that the nodal ring can change size and the two nodal lines can move and reconnect, but they can never be removed. Such evolution can be understood from the projection of a nodal hyperboloid into lower dimensions. This higher-dimensional perspective further reveals not only how the topology of the nodal rings and lines may be protected by the geometry of the nodal surface, but also how their topology may change, such as two nodal lines evolving into a ring. We also propose different light coupling schemes to create other nodal surfaces, whose projection reveals different evolution, such as creation and annihilation, of the lower-dimensional nodal structures. Our work provides experimental tools and further insights to study topological nodal structures and their evolution, including topological changes, in synthetic quantum matter.   

Quantum coarsening dynamics on a locally programmable atom array

Arrays of neutral atoms have emerged as a versatile platform for quantum simulation and computation, enabling coherent control of hundreds of atoms. In recent years, these systems have demonstrated the preparation of exotic phases of matter and have probed phase transitions via universal quantum critical dynamics [1]. While the dynamics across the phase transition are partially accounted for by the Kibble-Zurek mechanism, much is still unknown about the subsequent significant dynamics beyond it, known as coarsening [2]. Here, we experimentally study the nonequilibrium dynamics as the system is driven through the phase transition, observing power-law growth and scaling of the correlation length consistent with quantum coarsening dynamics. Microscopic snapshots of the system also show growth of the largest domains over time. Furthermore, we apply local detuning profiles to prepare deterministic domain shapes in the ordered state, enabling the study of curvature-driven dynamics of domain walls which are central to coarsening. This work opens further avenues for the exploration of many-body quantum dynamics in Rydberg atom arrays. Further applications to the dynamics of false vacuum decay will also be discussed.

[1] Ebadi, S., Wang, T.T., Levine, H. et al. Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 595, 227–232 (2021).

[2] Samajdar, R., Huse, D. Quantum and classical coarsening and their interplay with the Kibble-Zurek mechanism. arXiv:2401.15144  (2024)   

Rymax-One: A neutral atom quantum processor to solve optimization problems

From efficient distribution of workload in industrial manufacturing plants to short vehicle routes for parcel delivery - computationally hard optimization problems are a crucial part of our modern society. While finding solutions using classical solvers requires substantial computational ressources, quantum processors promise to yield better solutions in less time. 

To explore the potential of quantum computing for real-world applications, we are building Rymax-One, a quantum processor specifically designed to solve hard optimization problems. By using ultracold neutral Ytterbium atoms trapped in arbitrary arrays of optical tweezers, we aim for hardware-efficient encoding of optimization tasks. The level structure of Ytterbium provides qubit realizations with long coherence times, Rydberg-mediated interactions and high-fidelity gate operations, allowing us to realize a scalable platform for quantum processing to tackle real-world problems.   

Probing string-breaking dynamics in a trapped-ion quantum simulator

In quantum chromodynamics, the theory of strong force in nature, color-charged particles do not exist in isolation. They are instead confined together to form color-neutral particles. A simple picture of confinement involves quark-antiquark pairs that are bound by a gluonic flux tube, or string. As the string energy increases (e.g. by separating out the color charges), it becomes energetically favorable to produce a new quark-antiquark pair, hence breaking the string. In this work, we experimentally study string breaking in a long-range Ising Hamiltonian with a trapped-ion quantum simulator. We model the color-charged particles with domain walls in the spin chain, and control the string energy with a longitudinal magnetic field. We characterize the complex dynamics of string breaking as we linearly ramp the string energy through the breaking threshold. With a short spin chain, the string breaks with all the spins flipping, and the probability of string breaking can be modeled via a Landau-Zener process. With a long spin chain, the string breaks by forming domains of flipped spins whose size varies with the ramping speed.   

Floquet transverse-field Ising dynamics in a Rydberg-dressed optical tweezer array

The transverse-field Ising model (TFIM) is a paradigmatic model of quantum magnetism with broader applications in quantum control and computation. With time-dependent control of its two noncommuting terms — the interactions and the transverse field — it becomes a powerful tool for optimal control of entanglement, quantum optimization algorithms, emulating more complex spin models, or exploring driven quantum systems with no equilibrium analog. The transverse-field Ising model may be naturally implemented for cold atoms by periodically alternating between pulses of Rydberg dressing to induce interactions and microwave rotations to emulate the transverse field. In previous experimental work in a bulk gas of cesium atoms, we demonstrated such a Floquet implementation of the transverse-field Ising model, observing dynamical signatures of a mean-field paramagnet-ferromagnet phase transition. By optimizing the Rydberg dressing pulse sequence, we extended the coherence time of the interactions to generate squeezed spin states for quantum-enhanced sensing. In this poster, we present experimental upgrades to an array of single atoms in optical tweezers and discuss three directions enabled by the optical control of Ising interactions afforded by Rydberg dressing: (a) Realization of Floquet symmetry-protected topological phases, (b) simulation of emergent black hole dynamics based on a Floquet conformal field theory, and (c) optimal control of entanglement for quantum metrology.   

Entangled states of motion in a two-dimensional ion microtrap array

Two-dimensional arrays of ions trapped in individual, dynamically tunable microtraps are a promising technology for quantum computation and simulation. By controlling the motional excitations of the ions (phonons), one may be able to generate multipartite motional and internal entanglement between ions trapped in such an array and also simulate complex Hamiltonians such as bosons in synthetic gauge fields. We trap three ⁹Be⁺ ions in a microfabricated surface electrode ion trap that has three confining potential wells spaced 30 mm apart on the vertices of an equilateral triangle. By applying static potentials to the trap electrodes, we can individually tune the potential curvatures at each trapping site. When site curvatures are nearly equal, the individual ion motional modes hybridize into collective normal modes that we can excite using resolved motional sideband transitions. Here, we report on our progress toward using these collective excitations to entangle the motion of all three ions. With equal curvatures in all three sites, two normal modes of motion have the same frequency and the third mode is separated by an energy gap.  When this mode is occupied by a single phonon, the three ions share this excitation, and their local motion is entangled in a W-type state. We will study the structure of such an entangled state, whether the energy gap protects the entangled state, and, if so, which external perturbations are suppressed by that protection.   

Accelerating the assembly of defect-free atomic arrays with maximum parallelisms

Defect-free atomic arrays have been demonstrated as a scalable and fully controllable platform for quantum simulations and quantum computations. To push the qubit size limit of this platform further, we design an integrated measurement and feedback system, based on field programmable gate array (FPGA), to quickly assemble a two-dimensional defect-free atomic array using maximum parallelisms. The total time cost of the rearrangement is first reduced by processing atom detection, atomic occupation analysis, rearrangement strategy formulation, and acousto-optic deflectors (AOD)driving signal generation in parallel in time. Then, by simultaneously moving multiple atoms in the same row (column), we save rearrangement time by parallelism in space. To best utilize these parallelisms, we propose a new algorithm named Tetris algorithm to reassemble atoms to arbitrary target array geometry from two-dimensional stochastically loaded atomic arrays. For an L×L target array geometry, the number of moves scales as L, and the total rearrangement time scales at most as L^2. We simulate the performance of our FPGA system experimentally with all components integrated except for the atoms. We present the overall performance for different target geometries and demonstrate a dramatic boost in rearrangement time cost and the potential to scale up defect-free atomic array to 1000 atoms in room-temperature platform and 10000 atoms in a cryogenic environment. We have also conducted performance tests of the FPGA system on atoms without the Tetris algorithm and successfully achieved a defect-free array of several hundred atoms.   

Progress towards reconfigurable atom array assembly with projected optical tweezers

Reconfigurable atom array has been a versatile platform for many applications, including quantum simulation and scalable quantum computation. Here we discuss our innovative approach to creating fully-populated atom arrays with projected optical tweezers, an integral component of the Quantum Matter Synthesizer (QMS) quantum simulation apparatus. In contrast to the conventional method of generating tweezer arrays with multiple RF tones using Acoustic-Optical Deflectors (AODs), our scheme employs dynamical projection of laser light on a digital micromirror device (DMD) through a high-resolution optical microscope. This technique is highly scalable to many optical tweezers and permits merging and splitting of the tweezer potential. Furthermore, it can be integrated into optical lattices with sub-wavelength spacing to perform Hubbard-type quantum simulation. We will detail the current progress on the DMD-based tweezer generation and characterization, atom loading and rearrangment.   

Observation of Discrete Time Quasi-Crystalline Order in a Strongly Interacting Spin Ensemble in Diamond

Floquet driven systems offer a versatile toolkit for exploring non-equilibrium phases of matter. Introducing a single-frequency drive allows the realization of a novel phase of matter dubbed a 'discrete time crystal' (DTC), characterized by a persistent oscillatory response with a subharmonic frequency. More intriguing phenomena emerges as one replaces the single frequency drive with a multi-frequency one with incommensurate frequencies. In this study, we delve into the realm of discrete time quasicrystals (DTQC) utilizing a strongly interacting spin ensemble in diamond. When subjected to a quasi-periodic drive, the DTQC exhibits multiple subharmonic responses at various frequencies. Notably, we demonstrate the robustness of these responses against perturbation, protected by the many-body interactions within the spin ensemble. To quantify this rigidity, we map out the phase diagram of the DTQC by manipulating the interaction strength and the perturbation magnitude. Our findings significantly expand the scope of simulating and characterizing many-body phenomena in quasi-periodically driven systems.   

Development of Yb tweezer arrays for quantum simulation and communication

Neutral atoms trapped in optical tweezer arrays are a rapidly advancing platform for quantum science. Pairing this versatile platform with the unique atomic structure of ytterbium atoms enables myriad opportunities for novel implementations of quantum computation, simulation, and communication. We aim to perform simulations of quark-level effective field theories (EFTs) for quantum chromodynamics (QCD). EFTs are commonly used to explore low-energy, emergent phenomena in QCD where ab-initio calculations are impossible. Furthermore, the short-range interactions commonly employed in EFTs map favorably onto the natural interactions between tweezer-trapped Rydberg atoms. We report progress toward implementing experimental capabilities necessary to perform these simulations including site-selective state manipulation using the ¹S₀ to ³P₀ “clock” transition and excitation to Rydberg states using 302 nm laser light. Additionally, we report progress toward leveraging telecom wavelength transitions from the ³P₀ state to herald entanglement between atoms via bell state measurements of emitted photons sent across an optical fiber network.   

Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation

Computing finite temperature properties of a quantum many-body system is key to describing a broad range of correlated quantum many-body physics from quantum chemistry and condensed matter to thermal quantum field theories. Quantum computing with rapid developments in recent years has a huge potential to impact the computation of quantum thermodynamics. To fulfill the potential impacts, it is crucial to design quantum algorithms that utilize the computation power of the quantum computing devices. Here we present a quantum kernel function expansion (QKFE) algorithm for solving thermodynamic properties of quantum many-body systems. In this quantum algorithm, the many-body density of states is approximated by a kernel-Fourier expansion, whose expansion moments are obtained by random state sampling and quantum interferometric measurements. As compared to its classical counterpart, namely the kernel polynomial method (KPM), QKFE has an exponential advantage in the cost of both time and memory. In computing low temperature properties, QKFE becomes inefficient, as similar to classical KPM. To resolve this difficulty, we further construct a thermal ensemble iteration (THEI) protocol, which starts from the trivial limit of infinite temperature ensemble and approaches the low temperature regime stepby-step. For quantum Hamiltonians, whose ground states are preparable with polynomial quantum circuits, THEI has an overall polynomial complexity. We demonstrate its efficiency with applications to one and two-dimensional quantum spin models, and a fermionic lattice. With our analysis on the realization with digital and analogue quantum devices, we expect the quantum algorithm is accessible to current quantum technology.   

Accelerating the Assembly of Defect-Free Atomic Arrays with Maximum Parallelisms

Defect-free atomic arrays have been demonstrated as a scalable and fully controllable platform for quantum simulations and quantum computations. To push the qubit size limit of this platform further, we design an integrated measurement and feedback system, based on field-programmable gate array (FPGA), to quickly assemble two-dimensional defect-free atomic array using maximum parallelisms. The total time cost of the rearrangement is first reduced by processing atom detection, atomic occupation analysis, rearrangement strategy formulation, and acousto-optic deflectors driving signal generation in parallel in time. Then, by simultaneously moving multiple atoms in the same row (column), we save rearrangement time by parallelism in space. To best utilize these parallelisms, we propose an alternative algorithm named the Tetris algorithm to reassemble atoms to arbitrary target array geometry from two-dimensional stochastically loaded atomic arrays. For an L-by-L target array geometry, the number of moves scales as L, and the total rearrangement time scales at most as L². We present the overall performance for different target geometries, and demonstrate a dramatic boost in rearrangement time cost and the potential to scale up defect-free atomic array to 1000 atoms in room-temperature platform and 10000 atoms in cryogenic environment.   

Simulations of Classical Three-Body Thermalization in One Dimension

One-dimensional systems, such as nanowires, or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of point-like particles, typically the dominant process for reaching thermal equilibrium in higher dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_ij ∝ 1/|x_i − x_j|ⁿ, or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ²T^{1/2 − 1/n} where ρ is the number density, and the corresponding proportionality constant decreases with increasing n.   

Temperature characterization of a 2D to 3D magneto-optical trap

Magneto-optical traps (MOTs) play a pivotal role in achieving rapid and effective loading of atoms while reducing the energy and temperature of the system. In ultracold atomic physics platforms, the MOT is the initial stage of cooling. This study from our lab at University of San Diego provides a concise overview of MOT physics and discusses the continued progress toward creating and characterizing the temperature of our 2-dimensional and 3-dimensional MOT. We elaborate on the design of the laser system, optics platform, and initial calibration procedures for the system.   

Hyperfine structure and superfluidity of molecular Bose-Einstein condensates

In our first work, we investigate the phase transformation from atomic to molecular Bose-Einstein condensates (BEC). Coupling between atoms and diatomic molecules can be expressed as a process of annihilating a molecule to create two atoms and vice versa.  If we include the phase of the atomic and molecular wavefunctions into this exchange, the system will remain invariant as long as the phase of the molecular wavefunction is twice as that of the atomic wavefunction. To probe this phase doubling, we implement an interferometric technique utilizing vortices. Quantum vortices are characterized by the phase winding of the macroscopic wavefunction around the annulus.  The phase of the vortex is doubled when we convert an atomic BEC containing a single vortex into a molecular one. To detect this phase transformation, we perform interferometry using an optical lattice to create interference fringes. The vorticity will affect the formation of the interference fringes.

In our second work, we explore the near-threshold hyperfine structure of Cs2 molecules. While molecular states near the lowest energy manifold are well understood, an experimental and theoretical picture of the molecular states near the f₁ = 3, f₂ = 4 manifold is still lacking. We discuss the results of spectroscopy experiments mapping g-wave states in this new regime and compare our results to coupled-channel scattering calculations to extract quantum numbers. The states identified in this work introduce new possibilities in the study of coherent, many-body chemistry by enabling precise state control of BEC of Feshbach molecules in various quasibound rotational and hyperfine states.   

Upgrades and Advanced Capabilities for NASA’s Cold Atom Lab

The long-term production and control of exotic quantum states, such as Bose-Einstein Condensates, has been recently extended from terrestrial to space laboratories. The microgravity environment allows researchers to observe and interact with these macroscopic quantum phenomena in the essentially limitless free-fall of space to facilitate unprecedented fundamental physics investigations. Such space studies of interacting ultracold quantum gases have been pursued with NASA's multi-user Cold Atom Lab (CAL) facility, which has operated onboard the International Space Station since its launch in 2018. In addition to the toolbox of capabilities originally built into CAL, near-term instrument upgrades are planned to enable novel science and precision measurements. This poster discusses the addition of a mesoscopic atom-chip-based trap and presents the compatibility tests for an optical dipole trap as potential upgrades to the CAL instrument. We will also discuss how these implementations can further enhance the association of weakly-bound diatomic molecules from rubidium and/or potassium atomic mixtures for space-enabled studies of ultracold molecules.   

Controlling the expansion of a dipolar BEC of NaCs molecules

Starting from a dipolar BEC of NaCs molecules [1], we observe the BEC expansion in time-of-flight.  We find that it substantially deviates from the expansion of a non-dipolar condensate. By changing the microwave fields that shield the molecules, we tune the orientation and magnitude of the effective dipole moment induced in the molecules. We compare the observed expansion to an ab-initio calculation using a variational Gaussian ansatz and to numerical solutions of the extended Gross-Pitaevskii equation. Our models take into account the induced dipole moment and the s-wave scattering length as obtained from coupled channel calculations. We find good agreement between the theory and the experimental results.

[1] “Observation of Bose-Einstein condensation in a gas of dipolar molecules,” Bigagli, N., Yuan, W., Zhang, S., Bulatovic, B., Karman, T., Stevenson, I., Will, S., arXiv:2312.10965 (2023).   

Potassium condensates in optical tweezers

We present progress on a compact optical tweezer apparatus featuring multiple Bose-Einstein condensates (BECs) of potassium 39. The experiment aims to study systems whose evolution is governed by an interplay between measurement, feedback, and unitary evolution: a regime sometimes called quantum interactive dynamics. Additional scientific goals include the study of quantum thermodynamic engines. Relevant experimental capabilities include non-destructive phase-contrast imaging, Feshbach-tuned contact interactions, and Rydberg interactions.   

Implementation of a cloud-based system to study localized turbulence

Tabletop ultracold atom systems offer a versatile platform for investigating complex dynamics, including quantum turbulence. Traditionally, such studies have relied on custom cold-atom apparatuses housed in universities worldwide. However, the advent of cloud-based quantum technologies now enables remote experimentation, circumventing the need for costly and intricate local systems. This study presents and compares experimental data obtained from both a custom-built cold atom apparatus and a cloud-based counterpart, reflecting on the advantages and challenges of conducting research remotely. Furthermore, we discuss the potential for smaller institutions to participate in quantum research without significant initial funding requirements.   

Experiments with two dimensional arrays of atomic Bose-Einstein condensates: interference and collapse dynamics

We create a two-dimensional BEC array where each sites capture one Bose-Einstein

condensate. This provides us new abilities to integrate many-body features into the defect-free

BEC array. Based on this new platform, we study the matter-wave interference and the

stochastic collapse of Bose-Einstein condensates. By repeating measuring many sample simultaneously,

we extract out the physical laws of stochastic collapse utilizing the machine learning and

statistical inference.   

A new apparatus for a degenerate alkali-lanthanide mixture

We present a new platform for the creation of a degenerate mixture of erbium and lithium atoms. A dual-species oven generates co-propagating atomic beams. The species are magneto-optically trapped in an all-titanium chamber and optically transported to a nano-textured glass cell. The gas is imaged via a microscope objective (NA = 0.6). This alkali-lanthanide mixture offers exciting new possibilities, including long-range interactions via phonon exchange, mixed dimensional systems, collective spin physics, and few-body phenomena.   

Dynamic similarity of vortex shedding in atomic Bose-Einstein condensate

We numerically investigate the dynamic similarity of vortex shedding in atomic Bose-Einstein Condensates (BECs) using the two-dimensional Gross-Pitaevskii equation with a moving Gaussian potential. By comparing the local sound velocity with the flow speed around the potential barrier, we estimate the dynamic effective diameter of the Gaussian potential for both penetrable and impenetrable potentials. As the velocity of the flow around the potential barrier increases, the dynamic effective diameter correspondingly increases further, which aligns with the vortex formation region observed in real space. Furthermore, we investigate the drag and lift forces exerted by the Gaussian potential, relating them to the superfluid Reynolds number derived from the estimated dynamic effective diameter. The drag force is proportional to the velocity minus the critical velocity at which vortex shedding initiates, and the modified drag coefficient demonstrates a universal behavior with respect to the superfluid Reynolds number, paralleling its counterpart in classical fluid dynamics. The frequency of the oscillation in the lift force also exhibits a universal trend, even in the penetrable potential. Our study enhances the understanding of quantum fluid in relation to classical fluid dynamics.   

Dual-Species Bose-Einstein Condensates of Lithium And Cesium

We present the creation of dual-species Bose-Einstein condensates (BECs) of lithium (Li) and cesium (Cs), unveiling a novel mixture with potential for advancing the exploration of quantum gas mixtures. In this work, we demonstrate precise tuning of both intra- and interspecies interactions, as well as the capability to manipulate each species to achieve ultra-low temperatures. Leveraging the large mass disparity between Li and Cs, these dual-species condensates provide unique research opportunities, particularly in the investigation of polarons, Efimov trimers, and ground-state bi-alkali molecules.   

Supersolidity in a driven quantum gas

Driven systems are of fundamental scientific interest, as they can display properties that are radically different from similar systems at equilibrium. However, systems out of equilibrium are difficult to describe theoretically, as they are inherently time-dependent and deeply nonlinear. This makes the study of such systems an ideal task for quantum field simulators, in which complex dynamics emerge naturally and can be probed experimentally. Here, we demonstrate the emergence of supersolidity in a driven, two-dimensional superfluid that only has contact interactions. The self-stabilized system emerges as a result of large occupations of phononic modes due to driving [1] and can be described theoretically using an out-of-equilibrium fixed point of amplitude equations [2]. To demonstrate the hallmarks of supersolidity, we induce collective modes of the lattice, and show that the system supports lattice phonon propagation. We also show that the state maintains phase rigidity, a key property of superfluidity. This work introduces a novel type of supersolid that is readily experimentally accessible, and establishes a conceptual framework for describing elementary excitations of driven systems.

[1] N. Liebster, et al., arXiv:cond-mat/2309.03792 (2023)

[2] K. Fujii, et al., arXiv:cond-mat/2309.03829 (2023)   

Light Pulse Atom Interferometry with Sodium Spinor Bose-Einstein Condensates

We present recent improvements to our spinor Bose-Einstein condensate (BEC) apparatus to enable light-pulse atom interferometry for quantum-enhanced inertial sensing and gravimetry. In our F=1 antiferromagnetic sodium spinor BEC, entangled pairs of atoms with magnetic quantum numbers m=+1 and m=-1 are created via spin-exchange collisions. Previous experiments by our group focused on spin-mixing interferometry where all spin states were overlapping in the trap. New modifications will allow us to perform Raman or Bragg light-pulse atom interferometry, splitting and recombining the BEC vertically. After relocation into a new lab space that offers better environmental control, we added the Raman and Bragg beam optics for light pulse atom interferometry, performed a redesign of our dipole-trap and optical system to improve shot-to-shot number stability in the BEC, designed a new magnetic field control system for more stable initial state preparation, and improved our laser locking by switching from saturated absorption spectroscopy to modulation transfer spectroscopy. The resulting improved experimental sensitivity will aid in demonstrating quantum-enhanced light pulse atom interferometry in antiferromagnetic spinor BECs.   

How Long Does A Tunnelling Particle Take To Escape Before It Is Detected?

A strong measurement of a particle's position localizes it within the region of the measuring probe. If the particle is tunnelling through a barrier, such a measurement may disturb the tunnelling and gives the particle enough energy to exist in the previously "forbidden" region. Instead, one can imagine weakly probing such a particle's position; this may be realized with a weak Larmor measurement combined with post-selection. If this probe is present for a long time, throughout the particle-barrier interaction, the system appears time-independent and must conserve energy, so a tunnelling will not appear to be "found" inside the barrier. However, if the probe is only on for a short time, the transmission and reflection probabilities may be modified, indicating real propagation above the barrier. We discover a new time scale which corresponds to the duration over which particles are significantly disturbed in this way. This time scale exhibits a characteristic position dependence within the barrier region, which persists over a range of scattering parameters. This time scale suggests a new perspective on the decades-old tunnelling time question, as it may be interpreted as the amount of time a particle takes to "escape" the probe region undetected.   

Exploring driven quantum matter with bosonic lithium

We report progress in experiments using bosonic lithium, useful for its low mass and tunable interactions, to explore disparate regimes of periodically driven quantum matter: adiabatic thermodynamic engine cycles with a Bose-condensed working fluid; Floquet engineering of a novel platform for continuously-trapped atom interferometry; the quantum Kapitza pendulum in a strongly-driven prethermal regime; and boundary-modulated quantum gases.   

Chaos assisted many-body tunneling

We study the interplay of chaos and tunneling between two weakly coupled Bose-Josephson junctions. The classical phase space of the composite system has a mixed structure including quasi-integrable self-trapping islands for particles and excitations, separated by a chaotic sea. We show that the many-body dynamical tunneling gap between macroscopic Schrödinger cat states supported by these islands is chaos-enhanced. The many-body tunneling rate fluctuates over several orders of magnitude with small variations of the system parameters or the particle number.   

Collective excitation of a shell-shaped Bose-Einstein condensate

We investigate the hollowing transition of a shell-shaped Bose-Einstein condensate (BEC) with collective excitation. The shell is created using a double species BEC in the immiscible regime, with the hollowness of the shell BEC controlled by tuning the repulsive interspecies interaction by a Feshbach resonance. Our study reveals two distinct monopole modes in which the two condensates oscillate in-phase and out-of-phase relative to each other, respectively. While the frequency of the in-phase mode remains largely constant, the frequency of the out-of-phase mode changes significantly, providing a clear signature of the topology change from a filled to a hollow condensate. Furthermore, we observe a strong dependence of the critical point of the hollowing transition on the number ratio of the two species. Our findings offer a comprehensive understanding of the topology change in this curved quantum gas system and pave the way for future research into quantum many-body phenomena in curved spaces.   

Exact results for heavy unitary Bose polarons

We consider the problem of unitary Bose polarons, i.e., impurities interacting via a potential with infinite scattering length with a bath of weakly interacting bosons. We show that this problem can be solved analytically in two regimes, where the impurity-boson interaction potential has a range both much smaller and larger than the healing length of the bath. We provide various expressions for the energy and other quasiparticle properties of the polaron in those regimes. Furthermore, we perform numerically exact Diffusion Monte Carlo calculations and we demonstrate that the simple Gross-Pitaevskii theory provides a remarkably accurate description of heavy unitary Bose polarons throughout the whole experimentally relevant range of gas densities.   

Microwave-shielded polar molecules: from evaporation to tetratomic molecules

Thanks to their strong electric dipole moments and rich internal structure, ultracold

polar molecules are a promising platform for realizing exotic quantum matter, for

implementing quantum information schemes and for performing precision

measurements.

In many of these applications, samples of interacting molecular need to be prepared

in the quantum-degenerate regime. For a long time, employing direct evaporative

cooling via elastic collisions has been prevented by intrinsically unstable two-body

collisions of molecules at short range. Protecting molecules against such detrimental processes can be

achieved by engineering a repulsive barrier using a blue-detuned, circularly polarized

microwave field which couples the two lowest rotational states.

Here, I demonstrate how microwave shielding can be employed to evaporatively cool

a fermionic, three-dimensional gas of ²³Na⁴⁰K well below the Fermi temperature.

Furthermore, I will show how the microwave field can be tuned to shape the

intermolecular potential, independently tuning dipolar and contact interaction,

allowing us to observe of a novel kind of scattering resonance. These universal fieldlinked

resonances arise due to the existence of stable, tetratomic bound states. I will

also present our results regarding the creation and observation of these bound

states, whose properties agree very well with parameter-free theory calculations.

Lastly, I will lay out our pathway towards achieving ever colder samples, that

will allow us to explore quantum many-body phenomena like p-wave superfluidity or

the extended Fermi-Hubbard-models. Besides the physical aspect of microwave

shielding, I will also discuss the technical challenges associated with

building and controlling the requisite high-power microwave setups.   

Exact Thermodynamics of High Partial-Wave Normal-Phase Quantum Gas: Equations of State, Contacts and Chemical Reaction Rate

While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial-waves has not yet been reported. We provide closed-form expressions for the equations of state for weakly interacting systems with arbitrary partial-waves in the normal phase. All thermodynamics, including contact, loss rate, compressibility, and heat capacity, can be derived over the entire temperature regime. To showcase its power, we calculated the contact as a function of the temperature, which agrees with literature both in the low and high temperatures. Using the virial expansion, we find that, while the contact of weakly-interacting $s$-wave Bose gases in the normal phase is a pure two-body quantity, that of weakly-interacting $p$-wave Fermi gases displays pronounced three-body effects even at temperatures as high as the degeneracy temperature. This effect is shown to arise from many-body dressing, i.e., the emergence of quasi-particles at leading order in the interaction strength. Our results offer an improved thermometer for ultracold atoms and molecules with weak high-partial wave interactions.   

Observation and quantification of the pseudogap in unitary Fermi gases

The microscopic origin of high-temperature superconductivity in cuprates remains unknown. It is widely believed that substantial progress could be achieved by better understanding of the pseudogap phase, a normal non-superconducting state of cuprates. In particular, a central issue is whether the pseudogap could originate from strong pairing fluctuations. Unitary Fermi gases, in which the pseudogap—if it exists—necessarily arises from many-body pairing, offer ideal quantum simulators to address this question. Here we report the observation of a pair-fluctuation-driven pseudogap in homogeneous unitary Fermi gases of lithium-6 atoms, by precisely measuring the fermion spectral function through momentum-resolved microwave spectroscopy and without spurious effects from final-state interactions. The temperature dependence of the pairing gap, inverse pair lifetime and single-particle scattering rate are quantitatively determined by analysing the spectra. We find a large pseudogap above the superfluid transition temperature. The inverse pair lifetime exhibits a thermally activated exponential behaviour, uncovering the microscopic virtual pair breaking and recombination mechanism. The obtained large, temperature-independent single-particle scattering rate is comparable with that set by the Planckian limit. Our findings quantitatively characterize the pseudogap in strongly interacting Fermi gases and they lend support for the role of preformed pairing as a precursor to superfluidity.   

Fermi liquid properties of ultra-cold Rydberg-dressed gases

We investigate the Landau-Fermi liquid properties such as the quasiparticle self-energy, the many-body effective mass, and the renormalization constant of a three-dimensional

system of Rydberg-dressed ultra-cold fermions within the G0W approximation. We use the static structure factor data from the Fermi-hypernetted-chain approximation to calculate

the screened interaction (i.e., the many-body local field factors), and then the Kukkonene-Overhauser effective interaction. At strong interaction strengths and intermediate

soft-core radius, we observe deeps and jumps in the real and imaginary parts of the self-energy, respectively. This behavior is related to the inelastic scattering of quasiparticles from the collective density modes. The quasiparticle lifetime diverges at the Fermi surface, and its wave-vector dependence deviates from the standard Landau Fermi liquid’s prediction,

i.e., |k−k_F |^{−2} for large soft-core radius and strong interactions, where the homogeneous system is close to the density-wave instability, i.e., droplet crystallization.

In the homogeneous liquid phase, the renormalization constant is suppressed by increasing either the interaction strength or soft-core radius. The many-body effective

mass is also reduced compared to its non-interacting values but its dependence on the coupling strength and soft-core radius is not monotonic. Signatures of approaching

the droplet crystal phase are observed in both the renormalization constant and effective mass. In the single-particle spectral function, two additional heavy modes emerge

at strong couplings. These composite excitations are undamped at small wave vectors. Due to the repulsion between the quasiparticle and composite excitations, we observe a

gap-like feature between the quasiparticle and composite excitation bands. The dispersions of composite modes merge at large wave vectors but remain well separated from the

single-particle excitation.   

Simulating evaporative cooling of ultracold polar molecules.

Major progress has been made over the past few years in cooling polar molecules to ultracold temperatures. Common to these advances is evaporative cooling, where the gas distribution has its hot tail systematically truncated while elastic collisions work to maintain thermal equilibrium. However, the large 2 and 3-body loss mechanisms in kinetic molecular samples still pose a major hurdle for many groups in achieving stable quantum degenerate samples at their desired regimes. In light of this, we present a numerical tool for simulating evaporation in polar molecules. Our technique employs a Monte Carlo algorithm that allows for the inclusion of many-body quantum statistics. We also develop an efficient technique to include the accurate anisotropic energy dependent scattering cross sections for various regimes of operation, employing the use of Gaussian process interpolation. Our tools showcase good agreement with experimental data from the Max-Planck-Institute for Quantum Optics, paving the way for explorations of optimal evaporation schemes.   

First Sound Damping in the Imbalanced Fermi Spin Mixture

Strongly interacting spin-imbalanced Fermi gases are ubiquitious in nature - for example magnetized electrons, nuclear matter with unequal proton-neutron components, and quark mixtures - but are difficult to understand due to the notorious sign problem. Ultracold atomic gases near a Feshbach resonance, in addition to providing a highly clean system with well-understood microscopic interactions and accessible probes, also allow the spin imbalance to be freely tuned; they are thus an optimal tool for studying these physics. In this work, we prepare homogeneous, highly degenerate two-species mixtures of 6Li near unitarity with controllable levels of spin imbalance. Using our box trap, we excite and probe collective modes of density oscillations - first sound - in order to understand damping properties in the hydrodynamic regime. We observe a dramatic increase in the first sound damping with increasing imbalance, consistent with an increase in the mean free path.   

Density-controlled Crossing of a Quantum Phase Transition in a Spin-1 BEC

We explore the crossing of a quantum phase transition in a spin-1, ferromagnetic BEC. By changing the ratio of the quadratic Zeeman energy and the collisional energy of the BEC, we can control the spin dynamics across the critical point between the polar and broken-axis phases. Typical experimental procedures traverse the two quantum phases through sudden reduction of the magnetic field strength, which has potential experimental drawbacks originating from field instabilities. Our technique instead replaces this magnetic field “quench” with a change in the BEC’s density, inducing the necessary change in the atomic interactions. When allowed to evolve, the resultant dynamics produce spin-nematic squeezing. Correcting for the detection noise, we observed a squeezing of -8dB using this procedure. This demonstrates a new method by which to cross a quantum phase transition and points the way toward further work employing density-induced quenches to traverse a quantum critical point and engineer other exotic quantum phenomena, such as parametric squeezing and Dicke states.   

Spectroscopy of Quasiparticle Excitations in Fermi-Hubbard Systems

Itinerant spin polarons, bound states of a dopant and a spin-flip, even in the absence of superexchange interactions, have been theoretically predicted in geometrically frustrated lattices. We directly image itinerant spin polarons in a triangular lattice Fermi-Hubbard system realised with ultracold Lithium-6 atoms [1]. Using full spin-charge resolution, we are able to measure arbitrary n-point correlation functions for a range of dopings and interaction strengths. We also present preliminary work towards characterization of systems of strongly interacting lattice fermions with Raman spectroscopy. This powerful approach can characterize excitations with energy and momentum resolution, allowing for measurement of the full many-body spectral function. As a first step, we benchmark this technique in the square lattice, where we directly inject magnon excitations and measure their binding energy. This scheme is applicable to general lattice geometries, and the application to frustrated lattices (such as the triangular) should allow spectroscopic characterization of the itinerant spin polarons present in this setting [2].

[1] arXiv:2308.12951

[2] arXiv:2312.00768   

Quantum simulation with ultracold bosons in frustrated optical lattices

We present results from our experiments using bosonic ³⁹K atoms in optical lattices as an analogue quantum simulator for the Bose-Hubbard model on the triangular and kagome lattices. Because these lattices are nonbipartite, they exhibit geometric frustration. This gives rise to two inequivalent band maxima in the triangular lattice and a flat band in the kagome lattice band structure. Since the effects of frustration are only seen at the top of the lowest set of touching bands, we prepare atoms at a negative absolute temperature such that these highest energy states are preferentially occupied. 

In the triangular lattice we have studied the bosonic superfluid to Mott insulator phase transition at negative temperature. We observed a marked difference in the critical interaction strength when compared to the positive temperature (unfrustrated) system and found dynamical signatures pointing towards an intervening chiral Mott insulator between the (chiral) superfluid and the Mott insulator. In the kagome lattice we have observed the melting of the Mott insulator into the flat band.    

Realizing exotic dynamical phenomena with ultracold strontium

Ultracold atoms in 1D bichromatic optical lattices realize the Aubry-André-Harper model, enabling the study of localization in quasiperiodic systems as well as topological properties inherited from higher dimensions. Dipolar modulation, which mimics an oscillating force, can induce dynamic localization, while modulation of the phasonic degree of freedom tunes the effective strength of the quasi-periodic disorder. We present the results of experiments exploring the effects of dipolar and phasonic modulation and their interplay, and discuss a mapping to 2D quantum Hall matter in which the relative phase between the two modulations emerges as the polarization of an optical driving field. By tuning this polarization we can change the topological properties of the undriven system and Floquet engineer an extended critical phase. Separately, we discuss ongoing developments in the use of structured light fields to generate an oscillating linear gradient force, and resultant experimental possibilities such as quantum simulation of high harmonic generation and ultrafast phenomena.   

The Quantum Gas Magnifier as a Coherence Microscope

Imaging is crucial for gaining insight into physical systems. In the case of ultracold atoms in optical lattices, the novel technique of quantum gas magnification opens the way to explore 3D systems with large occupation numbers with sub-lattice site resolution. 

We report on the realization of an all-optical quantum gas magnifier for ultracold Lithium-7 atoms. The all-optical approach allows us to address the broad Feshbach resonance of Lithium to control the interaction strength. With this technique, we directly image the Talbot carpet that forms when releasing the atoms from an optical lattice. After certain ballistic expansion times, the wave packets originating from each lattice site overlap and constructively interfere with each other, such that an image of the original density distribution is obtained. We map out the spatial coherence by analyzing the contrast of consecutive Talbot copies. The technique should also allow to reconstruct the fluctuating phase profile of individual samples imaged at a single Talbot copy. This will realize a coherence microscope with spatially resolved access to phase information allowing to study domain walls, thermally activated vortex pairs, or to locally evaluate coherence in inhomogeneous quantum many-body systems.   

Interaction-induced splitting of Dirac monopoles in the topological Thouless pumping of strongly interacting Bosons and SU($N$) Fermions

Motivated by the observation of the breakdown of quantization for the Thouless pump in the presence of strong interaction [Walter et. al. Nat. Phys. (2023), Viebahn et. al. arXiv:2308.03756], we study the interplay of strong interaction and topology in the (1+1)-dimensional interacting Rice-Mele model. We point out that the quantization of the interacting Thouless pump is dictated by the Chern number, i.e., the Dirac monopoles enclosed by the generalized Brillouin zone of the many-body wave function. We analytically derive how interaction displaces the monopoles. Our model is applicable for arbitrary interaction strength and agrees with the mean-field approximation in the weak-interaction limit. Our predictions could be observed in strongly interacting SU($N$) Fermi gases or Bose gases in optical lattices and explain the ETH experiment on the pumping of strongly interacting SU(2) Fermi gases in 2023. In addition, we find interesting even-odd effects and unification of SU($N$) Fermi gases to $N$ bosons.   

Quantum gas microscopy of triangular-lattice Mott insulators

This poster highlights our recent advances in the quantum simulation of electronic systems employing ultracold atoms in geometrically frustrated lattices. Frustrated quantum systems, known for hosting exotic phases like spin liquids, present a formidable challenge to condensed matter theory due to their extensive ground state degeneracy. Our focus centers on a triangular lattice, a paradigmatic example of geometric frustration where the degree of frustration is tunable. The triangular Hubbard model is a paradigm system for the study of kinetic frustration, which shows up in destructive interference between paths of holes, leading to antiferromagnetic polarons in hole-doped regime even at elevated high-temperatures. In our work, we showcase the realization of a Mott insulator of lithium-6 on a symmetric triangular lattice with a lattice spacing of 1003 nm [1]. Spin removal techniques allow us to resolve individual spins and measure nearest neighbor spin-spin correlations across different interaction strengths. We find good agreement with numerical linked cluster expansion calculations and Quantum Monte Carlo simulations [2]. In the future, we will explore bound states in strongly repulsive interacting systems. Expanding our scope, we plan to delve into the transport properties of two-dimensional Fermi-Hubbard systems. We will leverage additional optical potentials generated by a Digital Micro-mirror Device (DMD). Projecting repulsive light using a DMD will enable the realization of a kagome Hubbard system, offering a unique platform for studying geometric frustration and predicted topological phases.

[1] Mongkolkiattichai et al., Phys. Rev. A 108, L061301 (2023)

[2] Garwood et al., Phys. Rev. A 106, 013310 (2022)   

Delocalization in a partially disordered interacting many-body system

We study a partially disordered one-dimensional system with interacting particles. Concretely, we only impose a disorder potential to every other site, followed by a clean site. The numerical analysis of finite systems reveals that the ergodic regime with a large entanglement extends to higher disorder strengths compared to a fully disordered system. More importantly, at large disorder, there exist eigenstates with large entanglement entropies and significant correlations between the clean sites. These states have almost volume-law scaling, embedded into a sea of area-law states, reminiscent of inverted scar states. These eigenstate features leave fingerprints in the nonequilibrium dynamics even at large disorder regime, with a significant initial state dependence. We demonstrate that certain types of initial charge density wave states decay significantly, while others preserve their initial inhomogeneity as is typical for many-body localized systems. This initial condition-dependent dynamics may give us extra control over the system to study delocalization dynamics at large disorder strength and should be experimentally feasible with ultracold atoms in optical lattices.   

Topological Floquet Engineering in One-Dimensional Optical Lattices through Simultaneous Amplitude and Phase Modulations

We present a numerical study on the topological properties of a three-band system in one-dimensional optical lattices subjected to periodic driving. We explore scenarios involving simultaneous modulations of the amplitude and phase of the optical lattice potential, and observe the emergence of topologically nontrivial bands when the modulation frequency resonates with the s-d band transition, contingent on the relative phase of the amplitude and phase modulations. Calculations of the Zak phase and the entanglement spectrum of the Floquet bands illustrate the topologically nontrivial characteristics. We show that parity-time reversal symmetry is the protective symmetry governing the system's topology. Finally, we discuss an experimental scheme to realize this three-band model.   

Towards Quantum Simulations with Strontium Atoms

Cold atom platforms with single particle/spin detection and control offer fascinating opportunities for emerging quantum technologies. Among quantum simulators trapped atoms in programmable optical tweezer arrays and excited to Rydberg states are well-suited systems to study quantum spin models and open interesting perspectives for quantum computation. Yet, simulating fermions on such systems remains a long-standing goal and the study of three-dimensional problems on arbitrary lattice structures is still to be explored. A complementary platform for quantum simulation is a quantum gas microscope where large atomic clouds are trapped in optical lattices. Whereas quantum statistics and itinerant models are natively implemented in these experiments, the current lack of programmability and long cycle time limit their capabilities. Our vision to overcome these challenges in quantum simulation is to combine atom manipulation using optical tweezers with quantum gas microscopy on a unique quantum simulation platform. We report on the development of a new  quantum simulation apparatus operating with strontium with which we aim to study topological phases in three-dimensional frustrated spin systems and the SU(N) Fermi-Hubbard model.   

A clock-magic quantum-gas microscope for ultracold strontium

Atomic strontium has many favorable properties for its application in quantum science and technology. A major feature is its ultranarrow optical-clock transition at 698 nm, which is often exploited in optical lattices and tweezers at a “magic” trapping condition. In this poster I present a quantum-gas microscope for strontium [1], working on a clock-magic optical lattice at 813 nm. I will describe the main features of our experimental setup and of the site-resolved imaging procedure. I will also describe a technique, based on resonant excitation, that enhances atom numbers in strontium magneto-optical traps [2].

[1] S. Buob et al., “A strontium quantum-gas microscope” arXiv: 2312.14818 (2023)

[2] J. Höschele et al., “Atom-Number Enhancement by Shielding Atoms From Losses in Strontium Magneto-Optical Traps”, Phys. Rev. Applied 19, 064011 (2023)   

New Apparatus for Quantum Simulation with 6Li

We present a new apparatus for creating and studying novel quantum phases of matter in optical lattices. Our scheme employs narrow linewidth cooling on the 2S-3P UV transition of ⁶Li in an optical trap [1]. Based on experience we expect a cycling time of 12 s to cool 10⁶ atoms to T = 0.05 T_F. We discuss our motivation for a Ti science chamber, which features large optical access with a numerical aperture of 0.7 along the vertical direction. Hence, we expect that this chamber facilitates precise shaping of the optical potential using spatial light modulators to remove the inhomogeneity. Such capabilities enable us to further explore the spin-imbalanced Fermi gas in the quasi-1D regime [2] and other phases of matter that are targets for quantum simulation with optical lattice potentials.   

Simulating Exact New Mobility Edges using Rydberg Raman superarray

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This work may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.   

Microscopic parton construction of Rydberg quantum spin liquid

Quantum Spin Liquids (QSL) represent an exotic phase of matter elusive to experiments. One hallmark property is the absence of magnetic spin order even at zero temperature. Despite numerous attempts, the unambiguous experimental confirmation of QSL states remains difficult. In this context, the possibility of realizing QSL physics on Rydberg atom-based quantum simulators has been a promising avenue for investigation [1].

 

Recently, the existence of a QSL state has been investigated numerically in a system of Rydberg atoms on a honeycomb lattice featuring density-dependent Peierls phases [2]. Later investigations using projective symmetry group arguments [3] confirmed the state to be a chiral spin liquid by comparing ground-states of ansatz Hamiltonians with exact diagonalization results. In this work, we take a different approach, deriving explicitly the mean-field parton Hamiltonian starting from the microscopic Rydberg model. A subsequent variational ansatz yields a more accurate representation of the true Rydberg many-body state.

 

[1] Semeghini et al., Science 374 (2021)

[2] Ohler et al., Phys. Rev. Res. 5, 013157 (2023)

[3] Tarabunga et al. Phys. Rev. B 108, 075118 (2023)   

GPU-assisted numerical simulation of spin-orbit coupling in spinor Bose-Einstein condensates

Ultracold atomic gases serve as an excellent platform for exploring many-body physics. By utilizing Raman processes, we can engineer a spin-orbit coupled Hamiltonian with adjustable interactions, allowing for the investigation of neutral atom dynamics under artificial gauge fields within specific parameter regimes. This study employs the time-splitting spectral method (TSSM), a numerical technique, to efficiently solve the multi-component Gross-Pitaevskii equation and simulate the effects of spin-orbit coupling fields in Bose-Einstein condensates. To tackle the computational challenges associated with increasing degrees of freedom, we leverage GPU hardware, achieving significantly faster run times. By tuning spin-orbit coupling and interparticle interactions, our goal is to emulate magnetic Hamiltonian models, and study the resulting phase diagrams resulting from the competition between interparticle interactions and spin-orbit coupling, including the emergence of superfluid vortices and phase separation. Throughout this work, we focus on realistic implementations in Feshbach-tuned ³⁹K.   

Non-Hermitian spin-orbit coupling and beyond

Spin-orbit coupling, as an effective tool for exploring topological insulators, has been extensively studied in well-isolated Hermitian systems and recently been brought to the open quantum system with gain and loss described by a non-Hermitian Hamiltonian [1]. Here, we demonstrate new tools for non-Hermitian spin-orbit coupled systems. First, we introduce Floquet engineering to the non-Hermitian topological lattice by applying a periodic driving signal to the spin-orbit coupling. This approach allows us to investigate the interplay between Floquet engineering and non-Hermitian physics, including the non-Hermitian skin effect [2]. We also explore higher-order exceptional points (EPs) in a dissipative three-level spin-orbit-coupled fermions system. The tunable dissipation in this system enables us to observe abrupt phase transitions and adjust the energy gap.   

Observation of the dynamics of stripe patterns of a spin-orbit-coupled supersolid

With their characteristic simultaneous breaking of the phase and translational symmetry, supersolids are an exotic phase of matter that have sparked much debate over their features and the validity of different platforms. Here, we report on the first in-situ observation of the density modulation of supersolid stripes in a spin-orbit-coupled Bose-Einstein condensate. We use a mixture of two spin states of 41K, coupled with a two-photon Raman transition, and prepare the system in the so-called supersolid stripe phase. By magnifying the density pattern using a matter-wave lensing technique, we can resolve the stripe spacing and observe its dependence on the Raman coupling strength. This observation disproves the common misconception that the density modulation is determined exclusively by the wavelength of the Raman coupling laser. Further evidence of the flexibility of the stripe pattern is obtained when exciting its compression mode and observing the spacing of the stripes oscillate. Finally, we have exploited the softening of this mode to reveal the supersolid-to-plane-wave phase transition. Moreover, thanks to the Feshbach resonances of 41K, we can tune the different interaction parameters of the system and modify the transition point. Experimentally, we find an excellent agreement with theoretical predictions in all configurations, demonstrating that spin-orbit-coupled condensates offer a competitive platform to study novel properties of supersolidity.   

Rapidly rotating quantum gas in a box potential

We use a rapidly-rotating Bose-Einstein condensate confined by a cylindrical optical potential to realize a uniform quantum fluid subject to a synthetic magnetic field. We use this setup to explore the propagation of chiral edge modes at the boundary, and the physics of homogenous vortex liquids. For edge states, we study their transport properties as a function of the wall steepness, revealing the crossover from ExB drift to sharp wall limit. We demonstrate that the edge modes are topologically protected against static disorders. For vortex liquids we show that the bulk vortex density equals to Feynman's number, and the vortex-vortex correlation function directly reflects their pair-wise interaction. Intriguingly, even in the limit of non-interacting bosons in the lowest Landau level, the vortices, as zeroes of random polynomials, are still predicted to repel.   

Strongly interacting impurity in the Bose-hubbard model

The detection of quantum phase transitions in many-body systems can be a challenging task. Here, we study the effect of Mott insulator to superfluid phase transition (MI-SF) in a Bose Hubbard lattice on an impurity immersed within it. By exploiting the quantum Gutzwiller approach and generalizing it to the strongly interacting limit, using a novel theoretical approach, we show that the energy of the quasiparticle jumps at the critical point and the nature of the jump depends on the crossing point of the transition, proving that the impurity can certainly be used as a probe for the transition. We discuss the characteristics of the low-lying excitations of the Bose gas including the Goldstone and Higgs modes across the transition and how that plays a significant role in explaining the behavior of the polaron energy. We also show that the polaron energy can be used to detect the transition with high accuracy and to gain insights into the underlying physics of these phenomena.   

From mixD to 2D: quantum simulations of doped Fermi-Hubbard model

Quantum simulation using ultracold atoms has emerged as a powerful tool for studying strongly correlated matter which is essential to the investigation of many classes of unconventional superconductors. We use ultracold fermionic ⁶Li atoms loaded into optical superlattices and conduct site-resolved measurements of their spin and density. Using optical superlattices, we can engineer mixed-dimensional system in which the pairing energy of dopants is boosted. This enables us to observe hole pairing in 2D and extended density structures which could be viewed as precursors of stripe phases. Furthermore, quantum gas microscopy allows us to probe local multi-point correlators of spin and charge around mobile dopants, as a function of doping and temperature. We find dominant 4^th and 5^th order correlations which help us explore the onset of the much-debated pseudogap phase.   

Ferro- and Ferrimagnetic States of Ultracold Fermions in a Hubbard System

Ferromagnetism is one of most visible manifestations of quantum physics at the macroscopic scale. Understanding its emergence from first principles can however be challenging in strongly correlated systems. A prime example is the Fermi-Hubbard model, a simplified model that is central to describing a wide array of quantum materials but for which the existence of ferromagnetic phases has only been rigorously established in a handful of limiting cases. Ultracold fermions in optical lattices can shed light on itinerant electron magnetism by offering a pristine realization of the Hubbard model with access to single-particle resolved spin and charge observables.

Here, we report on two cold-atom realizations of intriguing magnetic states arising in Hubbard systems where interactions are large compared to kinetic energy scales. First, we demonstrate the existence of Nagaoka polarons in a particle-doped Mott insulator, imaged as extended ferromagnetic bubbles around single particle dopants that are stabilized by quantum path interference. Key to our observations is a triangular lattice, where kinetic magnetism is strongly enhanced due to frustration and the existence of short-length loops. Second, we report on the existence of a ferrimagnetic state realized in a Lieb lattice at half-filling, a paradigmatic example of a flat-band system whose large state degeneracy is lifted by weak interactions. This ferrimagnetic state is characterized by antialigned magnetic moments concomitant with a finite spin polarization. We demonstrate its robustness when increasing repulsive interactions to the Heisenberg regime, and study its emergence when continuously tuning the lattice unit cell from a square to a Lieb geometry. Future progress augurs the exploration of exotic low-temperature phases such as quantum spin liquids in kagome lattices and striped phases in cuprate compounds.   

Nagaoka polarons and ferromagnetism in Hubbard models

The search for elusive Nagaoka-type ferromagnetism in the Hubbard model has recently enjoyed renewed attention with the advent of a variety of experimental platforms, including ultracold atoms in optical lattices. Here, we demonstrate a universal mechanism for Nagaoka ferromagnetism (that applies to both bipartite and nonbipartite lattices) based on the formation of ferromagnetic polarons consisting of a dopant dressed with polarized spins. We present a comprehensive study of the ferromagnetic polaron in an electron-doped Hubbard model, establishing various polaronic properties such as its size and energetics. Moreover, we systematically probe the internal structure of the magnetic state—through the use of pinning fields and three-point spin-charge-spin correlation functions—for both the single-polaron limit and the high-density regime of interacting polarons. Our results highlight the crucial role of mobile polarons in the birth of global ferromagnetic order from local ferromagnetism and provide a unified framework to understand the development and demise of the Nagaoka-type ferromagnetic state across dopings.   

Experimental exploration of the 1D anyon-Hubbard model in an optical lattice

Using ultracold rubidium-87 atoms in an optical lattice, we use Floquet techniques to engineer one-dimensional (1D) abelian anyons with arbitrary exchange statistics. By modulating a tilted lattice, we engineer a density dependent Peierls phase, effectively realizing the anyon-Hubbard model (AHM). This technique is analogous to flux attachment in 2D systems, where the density dependent phase plays the role of the Aharonov-Bohm phase. In our previous work, we used Hanburry Brown-Twiss interference of two particles to probe the effect of exchange phase on the system dynamics. Now, we make use of the independent control over Hamiltonian parameters our technique offers to engineer the AHM ground state and explore equilibrium physics.

By tuning AHM parameters in a finite 1D chain, we adiabatically ramp into the AHM ground state with a given statistical phase. We then use two probes to explore the ground state behavior. The first is the in situ density profile, where the fermionization of the particles manifests via the buildup of Friedel oscillations as the statistical phase increases from 0 to 𝜋. The second is the asymmetric expansion of particles in the lattice after quenching the confining potential, which occurs at anyonic phases due to the presence of chiral bound states. We further probe this chirality by colliding the expanding ground state with a potential barrier, showing that these bound states are only able to propagate in one direction and will disperse after a collision.

These probes demonstrate that the AHM ground state can be used as a platform to realize continuous fermionization and chiral bounds states. In larger systems, these simple properties likely underlie the development of additional many-body phases, and so our ability to realize and control these small systems opens new opportunities for exploring more complex phenomena.   

Fermi-Hubbard Interaction Quench for Revealing Pair Ordering and Pairing Onset Temperature

The attractive Fermi-Hubbard model is an archetypal model of pairing in quantum many-body systems of fermions. Previously, we experimentally explored the "pseudo-gap" regime, in which the system has full spin pairing at temperatures above the superfluid transition temperature. Depending on the interaction strength, the pair size in this regime varies from tightly bound pairs on a single site to long range pairs with a size approaching the interatomic spacing. By quenching the interaction strength at an appropriate rate, we convert non-local pairs into local pairs without introducing additional pairing or disrupting the long range structure. The observation of local pairs after the interaction quench provides additional evidence for non-local pairing in the attractive Fermi-Hubbard system. Furthermore, using the single-site measurement capabilities of our quantum gas microscope, we detect previously obfuscated charge density wave ordering of the non-local pairs. Finally, conversion of non-local pairs into local pairs allows for lower noise detection of the temperature at which the system becomes fully paired, T*. We exploit this measurement procedure to measure T* over a range of interaction strengths.   

Towards a cryogenic quantum gas microscope for low-temperature Fermi-Hubbard physics

The Fermi-Hubbard model is conjectured to capture some of the most exotic and important features of strongly correlated electrons in condensed matter systems. This 

includes the intriguing case of cuprate materials, known for high-temperature superconductivity. However, despite its relative simplicity, exploring the Fermi-Hubbard system with analytical or numerical methods is notoriously difficult. As an alternative,, ultracold atoms trapped in optical lattices have been used as an analog simulator to study the Fermi-Hubbard Hamiltonian, allowing precise tuning of the system parameters and single-site-resolved measurements of charge and spin. Despite tremendous progress, there is still approximately a factor of five discrepancy between the state-of-the-art and the estimated temperature to observe the d-wave superconducting phase as well as potentially other intriguing phases. One key hypothesis of preventing experiments to reach colder systems is the heating due to holes stochastically generated deep in the Fermi sea, among other reasons, background gas collision due to imperfect vacuum could have a major contribution. Here we present the design of a cryogenic quantum gas microscope to reduce the hole generation rate, by cryopumping of the background gas; we further report on other design choices for improved Hubbard model temperatures.   

Homogeneous fermionic Hubbard gases in flat-top optical lattices

The repulsive fermionic Hubbard model (FHM) is central to our understanding of electron behaviors in strongly correlated materials. At half filling, its ground state is characterized by an antiferromagnetic phase, which is reminiscent of the parent state in high-temperature cuprate superconductors. Introducing dopants into the antiferromagnet, the fermionic Hubbard (FH) system is believed to give rise to various exotic quantum phases, including stripe order, pseudogap, and d-wave superconductivity. We realize a three-dimensional homogeneous fermionic Hubbard gas confined in a hybrid potential, combining a flat-top optical lattice with an optical box trap. In contrast to harmonic or compensating optical lattices, our homogeneous setup provides nearly uniform Hubbard parameters, thereby supporting the emergence of the antiferromagnetic phase. Using spin-sensitive Bragg diffraction of light, we measure the spin structure factor (SSF) of the system. We observe divergences in the SSF by finely tuning the interaction strength, temperature, and doping concentration to approach their respective critical values for the antiferromagnetic phase transition, which are consistent with a power-law scaling in the Heisenberg universality class. Our results pave the way for exploring the low-temperature phase diagram of the FHM.   

Towards Quantum-Logic Spectroscopy of Highly Charged Ions for Tests of Fundamental Physics

Optical clocks based on highly charged ions (HCIs) offer a number of promising avenues for the study of physics beyond the standard model. Among these are searches for time variation of the fine structure constant, 𝛼̇/𝛼, and tests of quantum electrodynamics (QED). Due to level crossings occurring at high charge states, narrow linewidth, optically accessible transitions with a high sensitivity to 𝛼̇/𝛼 are predicted in both Pr¹⁰⁺ and Nd¹⁰⁺. We introduce a system capable of measuring these transitions consisting of table-top, permanent magnet Electron Beam Ion Trap (EBIT) connected via a beamline to a cryogenic Paul trap where HCI spectroscopy will be done. The EBIT, capable of both gas injection and laser ablation loading, has demonstrated pulsed production of several ions of interest including Pr¹⁰⁺,  Nd¹⁰⁺, Ar¹³⁺, and Fe¹³⁺. We present our efforts towards cotrapping these HCIs with Be⁺  for cooling and quantum-logic spectroscopy (QLS).    

Entanglement generation and excitation transport in dissipative trapped ion chains.

Trapped ion platforms offer a high degree of coherent control making them an ideal platform for generating entangled states that can be further utilized for quantum simulation or quantum metrology purposes. It is well known, however, that coherent entanglement generation is fragile with respect to noise and dissipation making it challenging to keep the entangled states protected from decoherence. Recently [1,2], it has been proposed that one could take advantage of those dissipative channels to prepare a more robust steady-state entanglement. Here, we explore the dynamics of an ion chain composed of logical and auxiliary qubits, the latter used to cool the motional modes of the chain. Depending on the location of the qubits in the chain, this platform can be used to study the generation of highly entangled spin states or to study long-range transport of spin excitations along the chain, extending the results on [3] and [4], respectively. We show that different regimes of these phenomena can be achieved by tuning the relative strengths of the three relevant energy scales of the model: the spin-spin interactions, the spin-phonon coupling, and the cooling rate of the motional modes.

 

References

Addressed two-qubit gate interactions in microwave-driven trapped ions

Trapped ions are a promising platform for quantum computing as they can form fundamentally identical qubits with long coherence times. Quantum logic gates are often performed using lasers but can also be driven by microwave fields, for which the technology is cheaper, more reliable, and hence easier to scale up. However, due to the centimeter wavelength of microwaves, the radiation cannot be focused to a small spot size as with a laser. This complicates the addressing of qubits within a cluster of ions confined in the same potential well. Here, we demonstrate a novel electronic microwave control method to implement addressed two-qubit gates in such a register. More specifically, we demonstrate the ability to suppress a spin-dependent force using a single ion, and find the required interaction introduces 3.7(4)×10⁻⁴ error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of ∼10⁻⁵.   

Toward a large-scale trapped ion quantum simulator with in-situ mid-circuit measurement

With long coherence times and relatively short gate times, the trapped ion platform has become a promising platform for quantum information processing (QIP). Here we show the progress of our segmented blade trapped-ion system with control of coherent and incoherent operations on individual Yb+ ions. We are developing a dual Acousto-Optic Deflector based Raman addressing system that is optimized for over thirty qubits, with low intensity crosstalk. We incorporate optical Fourier holography to create ~1E-4 intensity crosstalk of optical pumping and detection beams, and fast state detection for high-fidelity, in-situ mid-circuit measurement and resets. The vacuum chamber and its internals have been carefully prepared to achieve <1E-12 mbar pressure at room temperature, to maximize the lifetime of a long ion chain. This simulator will allow us to perform a wide range of QIP experiments, like measurement-based quantum simulations of spin Hamiltonian's and hybrid digital-analog quantum algorithms.   

Trapped Electrons in a linear Paul trap

Recent advancements in quantum computing have introduced trapped electrons as a potential qubit system. They have the potential of exhibiting long coherence times, akin to ions, but with the added advantage of faster gate operations. Furthermore, using electron spins as qubit states, state leakages are inherently eliminated due to the simplicity of the spins' two-level system. Being a novel system, challenges persist in trapping, controlling, and readout at both room and cryogenic temperatures. Here we report on our progress including successfully trapping electrons at room temperature in a linear Paul trap and we will give an update on our cryogenic system designed to read out the quantum state of a single electron.   

Operating the metastable qubit in Yb+

The metastable ("m-type") qubit defined on zero-field hyperfine clock states in the long-lived ²F_7/2⁰ manifold in Yb⁺ gives a promising pathway to low cross-talk, high fidelity multi-qubit operations using the same ion species via the recently proposed "omg blueprint'' for atomic quantum processing [1]. We demonstrate heralded state preparation, single-qubit operations, and state measurement in the m-type qubit of ¹⁷¹Yb⁺, achieving a SPAM infidelity of 4⁺³_-2 X 10^-4. We report progress on a new ion trap apparatus, as well as our progress on utilizing an iodine-referenced Doppler cooling laser [2]. We also report our progress towards extending the toolbox of the m-type qubit by coupling to additional metastable states which can be used to implement two-qubit gates. 

[1] Allock et al., Appl. Phys. Lett., 119, 214002 (2021)

[2] Chen et al., Chinese Journal of Physics, https://doi.org/10.1016/j.cjph.2023.12.007 (2023)   

Identification of Dark Ions in Mixed Species Coulomb Crystals

The parameters of radiofrequency (Paul) traps can be configured such that particles with different charge to mass ratios can be co-trapped. Often, one of the species of trapped ions is used for all dissipative tasks, such as cooling and detection. Since the secular frequencies for each species are unique, the ions’ resonant response to an additional oscillating electric field can be used for the identification of the other, non-fluorescent ions. Using the SIMION, LAMMPS, and (py)LIon simulation software, we investigate the number of counted photons versus frequency over a range of crystal compositions. We have simulated the motion of co-trapped Be⁺, O⁺, and O₂⁺ ions in an rf trap. The Be⁺ ions’ cycling transition allows for laser cooling and fluorescence detection, both of which are included in our simulations. This will be of use in experiments whose results involve molecular dissociation or chemical reactions that form new compounds.   

Cryogenic ion trap of 88Sr+ with a superconductive helical RF resonator

Cryogenic ion trap is a crucial technique for implementing high-fidelity quantum logic gates with planer circuit traps. When a trap apparatus is cooled to a few kelvins, a motional decoherence caused by electric noise from the electrodes, known as the anomalous heating [1], can be suppressed. It is necessary to apply RF voltages higher than 100 V on the trap to levitate ions, while managing heat production inside the cryostat to maintain the cryogenic environment. To minimize the trapping RF power, we have developed a superconductive helical RF resonator, which is made from copper plated with lead. The skin of the resonator became superconducting below 7.2 K, and its quality factor reached 10⁴. Combined with a non-superconductive electrode trap, trapping of ⁸⁸Sr⁺ ions has been achieved with an RF power below +5 dBm.

[1] M. Brownnutt et al., Rev. Mod. Phys. 87, 1419 (2015).   

Supression of differential light shifts in hyperfine 171Yb+ qubits

Laser-based gates in trapped ion quantum computers can induce differential light shifts that dephase qubits, limiting coherence lifetimes. Magnetic-field-induced vector light shifts are polarization dependent however, such that with appropriate choice of polarization for a given magnetic field, this differential light shift may be eliminated. Used commonly in optical dipole traps, this "magic" polarization technique is relatively simple to implement, and has been applied to other trapped ion species [1]. We demonstrate in the ground-state hyperfine qubit of ¹⁷¹Yb⁺ that it is possible to supress the differential light shift at typical values of the static bias magnetic field by adjusting the gate laser polarization.

[1] Samuel R. Vizvary, et al. Eliminating qubit type cross-talk in the omg protocol, 2023. arXiv.   

Progress Towards Trapping and Cooling of Barium-133

Barium-133 has often been called the "Goldilocks Qubit" because of all the advantages it has over other trapped-ion qubit species. The nuclear spin of 1/2 provides a hyperfine splitting without the magnetic sensitivity of a nuclear spin of 3/2, the vast majority of the lasers used for quantum operations on it are in the visible spectrum, which are safer and have much more readily available optical components, and it has an extremely high State Preparation and Measurement (SPAM) fidelity (Christensen, 2018). Here we demonstrate our progress towards making a barium-133 chamber and all the accompanying optics and imaging systems, as well as laser cooling it. We look forward to the new opportunities for experimentation with the new qubit species we have access to. We will take full advantage of the efforts of our colleagues at AFRL with photonics chips to replace bulk optics. We also will observe background free state detection. Additionally, using two chambers allows us to network the barium qubits across the two chambers. Approved for Public Release; Distribution Unlimited: AFRL-2023-6141   

Phase and Amplitude Control of light patterns for Trapped-Ion Quantum Simulation

Trapped ions provide a natural platform for the quantum simulation of spin and spin-boson models with a high degree of control and long coherence times achieved via tailored laser fields. Here we describe an optical setup wherein a phase-only spatial light modulator is used to shape a single incident Gaussian beam into an array of Hermite-Gaussian beams with arbitrary phase and intensity control [1]. The transverse electric field gradient of the Hermite-Gaussian beams will allow for coupling to axial modes of motion using a beam array that is orthogonal to the trap axis [2]. This will be achieved with geometric phase gates that have been shown to have high fidelities [3] and can be used to simulate spin-spin interactions between ions [4]. The beam array will address the quadrupole transition ²S_1/2-²D_3/2 to implement zz spin-spin interactions on the hyperfine qubit of 171Yb⁺ ions [5]. We present computational and experimental results of the optical scheme and optimization algorithm, including the characterization of the resulting beams' phase and intensity transverse profiles using an interferometer.

[1] L. Wu, et al., 2015 Sci Rep 5 15426

[2] A. D. West, et al., Quantum Sci. Technol. 6 024003 (2021)

[3] V. Schäfer, et al., Nature 555, 75–78 (2018)

[4] J. Britton, et al., Nature 484, 489–492 (2012)

[5] C. H. Baldwin, et al., Phys. Rev. A, 103, 012603 (2021)   

Point charge versus charge distributions in ion-atom reactions

Hybrid ion-atom traps are the cornerstone of cold chemistry involving charged-neutral interactions. In these systems, a single ion is held in a time-dependent trap and exposed to a neutral gas. This leads to exciting chemical reactions such as charge exchange, radiative association, or three-body recombination. In all these reactions, it is assumed the ion is a point charge. However, the colliding partner could feel the interaction as a charge distribution since the ion is trapped. In this work, we present a theoretical study on ion-neutral collisions, considering the extension of the ground state of the ion in the trapping potential. As a result, we analyze the role of the trapping potential on the reaction dynamics. On the other hand, this system presents an interpretive dichotomy: does the neutral see a point charge in any collision, or does it feel a charge distribution? Hence, this system presents an exciting scenario for interpreting quantum mechanics.   

Quantum information protocols in mixed qubit type registers of 137Ba+ ions

Trapped barium ions are very well-suited to omg-style architectures [1] due to the long (∼ 30 s) lifetime of the metastable D_5/2 level. We present a system capable of controlling registers of ¹³⁷Ba⁺ ions utilising qubits encoded in both the ground and the metastable level. We achieve individual optical addressing with very low cross-talk within the ion chain via a fibre network coupled to a laser-written waveguide device [2].

We demonstrate full control over the different qubit types within ¹³⁷Ba⁺, facilitating the implementation of in-sequence dissipative operations on the ground level qubits, while maintaining the coherence of the metastable ones. These capabilities have allowed us to achieve extremely low SPAM errors for all three qubit types.

[1] D. T. C. Allcock et al. omg blueprint for trapped ion quantum computing with metastable states. Applied Physics Letters, 119(21):214002, 2021.

[2] A. S. Sotirova et al. Low Cross-Talk Optical Addressing of Trapped-Ion Qubits Using a Novel Integrated Photonic Chip, October 2023. arXiv:2310.13419.   

A Three-Dimensional Monolithic Ion Trap for Quantum Simulation and Computation

Trapped ions are a promising platform for quantum simulation and computation thanks to technological developments over the past few decades. Our work focuses on improving their core technology, the ion trap, by combining the features of scalability, repeatability and geometrical accuracy of precision microfabrication with the features of macroscopic three-dimensional traps which offer deep and symmetric trapping potentials, robustness to stray fields, and higher and multidirectional optical access compared to 2D planar traps. We report on the latest developments in the design and characterization of a novel monolithic, segmented 3D ion trap, manufactured by Translume Inc., tested in a collaborative effort by our groups at Rice and Duke University to ensure its repeatability. Improving on the thermal and electrical design of our first-generation monolithic trap assembly, we have trapped Yb ions in our second-generation monolithic trap. We will discuss our characterization measurements on the axial and radial collective motional modes, residual micromotion in the trap, and the ion heating rate. We will also discuss our progress in building an individual addressing scheme for Raman beams to coherently manipulate long ion-chains, and optical schemes for coherent and incoherent electron shelving for partial measurements.

 

This work is a collaborative effort between the groups of Prof. Pagano (Rice University), Prof. Linke (Duke University) and Translume Inc. (MI).   

Towards microwave-driven trapped ions with superconducting circuits

Hyperfine qubits realized in trapped ions allow for high-fidelity single- and two-qubit gate operations. Universal control of those qubits has traditionally been achieved through the utilization of optical Raman transitions with carefully controlled multiple laser beams. Recently, microwave-based entangling methods without lasers have been demonstrated using on-chip circuitry with surface-trapped ions. The direct access to the hyperfine transitions enabled by microwave fields provides high-fidelity operations that are not limited by spontaneous optical Raman emission. Moreover, utilizing mature microwave off-the-shelf components enhances scalability due to their compact sizes and superior controllability of frequencies, phases, and amplitudes. A challenge encountered in microwave-based entangling operations is the generation of joule heat resulting from sub-ampere AC current flowing through relatively narrow microwave waveguides. This substantial amount of joule heat from normal conductors would impose limitations on entanglement fidelity and scalability. To address this issue, we demonstrate an all-superconducting surface trap chip incorporating high-Q superconducting microwave resonators. A sub-ampere current flowing through narrow superconducting electrodes generates a high magnetic field gradient at the ion position, potentially enabling fast microwave Mølmer–Sørensen gates with low joule heat generation and reduced input microwave power.   

Frequency Comb Referenced Scanning and Experiment Control in Saturated Absorption Spectroscopy

We report on the systems we use to control our frequency comb-referenced laser and collect precision spectroscopy data in our lab at Smith College. The newest method involves producing two beams offset by slightly less than the frequency comb mode spacing, so one beam will always be outside of the border area next to the comb mode which is traditionally a forbidden zone. By switching which beam is being used for frequency stabilization, we can step-scan in a controlled manner over ranges on the order 6 GHz. Combined with simple automation techniques, the result is a system which can self correct and automatically switch between runs at different pressures, laser powers, and discharge powers.   

Precision Measurement of the Differential dc Stark Shift of the 5S1/2 to 6S1/2 Transition in Rb

Using Doppler-free two-photon spectroscopy in a temperature-controlled vapor cell, we measure the static Stark shift for the of the Rb 5S_1/2 to 6S_1/2 transition in both isotopes of rubidium. We lock a tunable microwave-driven EOM sideband of the 993 nm laser to an ultra-stable very high finesse cavity, achieving microwave frequency accuracy for the relative laser tuning. We discuss our progress towards measuring the Stark shift as a function of the applied electric field and determining the differential scalar polarizability  of the 5S_1/2 to 6S_1/2 transition.   

Cryogenic supersonic beams of hydrogen and deuterium atoms

Slowly moving, high density beams of atomic hydrogen isotopes are of interest for precision tests of fundamental physics, including measurements of the absolute neutrino mass [1,2]. With these applications in mind, we have developed a cryogenically-cooled supersonic beam source of hydrogen and deuterium atoms. This source is based upon the dissociation of H₂ or D₂ molecules in an electron-seeded discharge at the exit of a pulsed valve operated at 34 K. The phase space characteristics of the beams have been measured by resonance enhanced multi-photon ionization spectroscopy. The ground-state hydrogen atoms in these beams, with longitudinal speeds of ~900 m/s, are well suited for confinement in magnetic storage rings. The way in which the beams are operated is compatible with the production of tritium atoms by dissociation of T₂ molecules for absolute neutrino mass measurements.

[1] S. Scheidegger, D. Schlander, J. A Agner, H. Schmutz, P. Jansen and F. Merkt, J. Phys. B: At. Mol. Opt. Phys. 55 155002 (2022)

[2] S. Scheidegger, J. A. Agner, H. Schmutz and F. Merkt, Phys. Rev. A 108, 042803 (2023)

[2] A. A. Esfahani et al., J. Phys. G: Nucl. Part. Phys. 44 054004 (2017)   

Precise atomic structure measurements in Pb using vapor-cell and atomic-beam spectroscopy

Recently, we employed a Faraday rotation spectroscopy technique with microradian precision to complete the first ever direct measurement of the forbidden electric quadrupole (E2) transition in Pb at 939 nm [1]. Since then, we have adapted our apparatus to perform Faraday spectroscopy in the blue and near-UV, allowing us to measure transition amplitude ratios of transitions starting from the ground state to those originating from low-lying thermally-excited states. Currently we are completing precision measurements of the 368 nm (6p²) ³P₁ → (6p7s) ³P₀ and the 406 nm (6p²) ³P₂ → (6p7s)³P₁ E1 transition amplitudes using samples in quartz vapor cells at precisely controlled temperatures.  The UV Faraday spectroscopy has been facilitated by the use of a new CeF₃ single-crystal Faraday modulator which we have extensively characterized. In related spectroscopy work, and following up on previous work with thallium and indium, we are also pursuing a new measurement of lead (scalar and tensor) polarizability in these same excited-state E1 transitions using our high-flux atomic beam apparatus, high-voltage field plates, and a transverse spectroscopy arrangement.  In our current experiment, a stabilized in-beam laser cavity enables ‘pre-pumping’ of ground-state Pb atoms to enhance the metastable ³P₁ state population prior to excitation by the UV laser. Current results will be presented.

[1] - D. L. Maser et al., Phys. Rev. A 100, 052506 (2019)   

Modeling a Helium Metastable Beam Source used in a Precision Helium Fine Stucture Experiment.*

A helium metatstable beam source used in precision laser spectroscopy of helium fine stucture is studied. The source, which uses electron excitation of a thermal helium beam, is described using a simplified analysis along with more detailed numerical modeling (with COMSOL Multiphysics®). These results are compared to experimental measurements and source performance. The expected effects of various parameters are examined, such as source pressure, background pressure, excitation/deexcitation cross sections, recoil, and electron space charge.   

A Novel Method of Spectrometer Calibration using Multiple Spectral Orders of Unknown Lines

Calibration in diffraction spectroscopy typically depends on identifying strong, well-known lines in the recorded spectra and fitting a calibration function to them. The uncertainty in the calibration process can be a significant component of the uncertainty in measurements related to atomic structure [1], nuclear physics [2], and astrophysics [3]. We propose a novel method (order penalization) for improving spectroscopic calibrations by extending non-linear least squares fitting of the calibration curve. The method introduces an extra term into the minimized quantity that penalizes disagreement in the positions of spectral lines observed in multiple diffraction orders. The primary advantage of this method is that the lines used do not have to be identified, except for establishing the fact that they are different orders of the same line. This increases the number of constraints on the calibration curve, potentially in spectral regions without regular calibration lines. The mathematical basis of this method is described, and the performance of this method is evaluated on simulated data and experimental data from the National Institute of Standards and Technology (NIST) Electron Beam Ion Trap. We demonstrate the method's effectiveness on the spectra of highly charged Ag-like Re²⁸⁺ and nearby charge state ions.

[1] J. D. Gillaspy, Testing QED in sodium-like gold and xenon: using atomic spectroscopy and an EBIT to probe the quantum vacuum, Journal of Instrumentation 5 (10) (2010) C10005–C10005.

[2] R. Silwal, A. Lapierre, J. D. Gillaspy, J. M. Dreiling, S. A. Blundell, Dipti, A. Borovik, G. Gwinner, A. C. C. Villari,

Yu. Ralchenko, E. Takacs, Measuring the difference in nuclear charge radius of Xe isotopes by EUV spectroscopy

of highly charged Na-like ions, Physical Review A 98 (5) (2018) 052502,

[3] J. D. Gillaspy, T. Lin, L. Tedesco, J. N. Tan, J. M. Pomeroy, J. M. Laming, N. Brickhouse, G.-X. Chen, E. Silver, Fe

xvii X-ray Line Ratios For Accurate Astrophysical Plasma Diagnostics, The Astrophysical Journal 728 (2) (2011)

132   

Space-Enabled Quantum Science with NASA's Cold Atom Lab (CAL) Operating on the International Space Station

The CAL facility launched to the International Space Station (ISS) in May 2018, and has been operating since that time as the world’s first multi-user facility for the study of ultra-cold quantum gases in space. The unique microgravity environment of the ISS is utilized with CAL by a national group of principal investigators to achieve sub-nanokelvin temperature gases, to study and utilize their quantum properties in an environment free from the perturbing force of gravity, and to observe and interact with these gases in the essentially limitless freefall of Earth’s orbit. In addition to the toolbox of capabilities originally built into CAL, an upgrade in 2020 enabled the study of atom interferometry in orbit, and a 2021 upgrade and repair facilitated investigations of the interactions between mixtures of 87Rb, 39K, and 41K and dual-species (87Rb - 41K or 87Rb - 39K) atom interferometry. This poster will review the up-to-date quantum gas research explored with CAL and the technical accomplishments to operate, maintain, and upgrade CAL during its tenure in the microgravity environment of the ISS. This research has broad applications in fundamental physics and precision sensing to open the door for future quantum-enabled mission opportunities.   

Precision measurement of the n=2 triplet P J=1-to-J=0 fine structure of atomic helium using frequency-offset separated oscillatory fields

Increasing accuracy of the theory and experiment of the n=2 ³P fine structure of helium has allowed for increasingly-precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond-the-Standard-Model physics. Here we present a 2-part-per-billion (ppb) measurement of the J=1-to-J=0 interval. A helium beam is produced using a liquid-nitrogen-cooled dc-discharge source, and is intensified  using a two-dimentional magnetooptical trap. The microwave measurement is performed using frequency-offset separated oscillatory fields (FOSOF) [1]. Laser excitation to a Rydberg state, followed by Stark ionization allows for efficient detection. Our result of 29,616,955,018(60)~Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

[1] A. C. Vutha and E. A. Hessels, Phys. Rev. A 92, 052504 (2015).   

Helium-4 mass for electron mass

There is currently a 1.3(0.2) x 10^-10 (6.5-sigma) discrepancy between a recent precision measurement [1] of the mass of ⁴He and the value in CODATA-2018 [2].  Motivated by this discrepancy we are using precision single-ion Penning trap techniques to measure the atomic mass of ⁴He with a precision goal of 1 x 10^-11. A precision atomic mass of ⁴He is needed so that future measurements of the electron-spin flip frequency, f_sf, and cyclotron frequency, f_c, of a single ⁴He⁺ in a strong magnetic field can be used to determine the atomic mass of the electron, m_e, through the relation f_sf/f_c = g_ion(m_ion/2m_e), where m_ion is the mass of ⁴He⁺, and g_ion is the ⁴He⁺ g-factor, which can be calculated to a few parts in 10^-13. Compared to determining m_e from f_sf and f_c in C⁵⁺ [3], which produces the current CODATA value of m_e, ⁴He⁺ has the advantage of smaller nuclear size and QED uncertainties in the g-factor theory. A new “g-factor” m_e is especially pressing due to developments in precision rovibrational spectroscopy and theory for HD⁺. Combined with the atomic mass of the deuteron m_d [4] and the mass ratio m_p/m_d [5], HD⁺ spectroscopy has produced a value for m_e which is competitive, and in 2-sigma tension, with the value obtained from C⁵⁺.

[1] S. Sasidharan, et al, PRL 131, 093201 (2023), [2] E. Tiesinga, et al. RMP 93, 025010 (2021), [3] J. Zatorski, et al. PRA 96, 012502 (2017), [4] S. Rau, et al, Nature, 585, 43 (2020), [5] D. J. Fink and E. G. Myers, PRL 124, 013001(2020); PRL 127, 243001(2021).   

Developing a testbed for optically pumped magnetometers

Highly precise and accurate magnetic field sensing finds real-world applications in non-destructive testing [1], bio-medical imaging [2], positioning and navigation [3], and transient electromagnetic measurements [4]. Here we present our work towards an experimental test platform for such sensors based on optically pumped magnetometry. An atomic vapor cell containing Cs-133 is heated to 80°C and spin-polarized via a VCSEL-laser, which is frequency stabilized on the D1-line at 895 nm. The cell is surrounded by three pairs of Helmholtz coils and a mu-metal (permalloy) shield. After optically polarizing the atomic sample, we measure its Larmor precession under the i1nfluence of a known magnetic field. We aim to test the feasibility of uncoated, paraffin-coated, and buffer-gas cells, enabling a direct comparison of their operational usability. Future work will be application-driven and include simplification, ruggedization, and miniaturization of the setup and finding a decent trade-off between sensitivity and dynamic range.

[1] S. Youssef, Journal of Nondestructive Testing 21, 19390 (2016)

[2] P. K. Mandal, Front. Comput. Neurosci. 12 (2018)

[3] A. J. Canciani, AFIT, Dissertation, https://scholar.afit.edu/etd/251, (2016)

[4] A. Chwala, SEG Technical Program, 779-783 (2010)   

Transition Metal-Containing Molecules for Quantum Science and Precision Measurement

The broad scientific opportunities promised by ultracold molecules have spurred recent efforts to apply direct laser cooling to diverse sets of molecules. In recent years, increasing attention has been attracted by molecules that offer new resources to the areas of quantum science and precision measurements. This includes molecules with complex structure, where long-lived states arising from internal angular momenta provide qubit platforms and/or internal co-magnetometers for robust systematic error rejection. Here, we focus on a new class of diatomic molecules that we have identified as hosting optical cycling centers: coinage metals bonded to carbon-group atoms. We will describe theoretical and experimental efforts focused on molecules such as CuX, AgX, and AuX (X=C and Pb). We will also present theoretical investigations into other molecules with desirable ground-state properties that may be of interest to next-generation precision measurements, where ²Π_1/2 ground states can be assembled from laser-cooled atoms.   

Nuclear Spin Coherence of Molecules Trapped in Solid Parahydrogen

We use NMR techniques to measure the T2* and T2 coherence times of HD molecules trapped in parahydrogen matrices. We can control the level of orthohydrogen impurities in our matrix, and we find that T2* scales inversely with the orthohydrogen fraction. We are able to resolve the ~50 Hz splitting of the proton resonance due to nuclear spin-spin interactions in the HD molecule. We are exploring the limits on T2* in this system. If similarly long coherence times can be obtained for certain heavy polar molecules, this system would be of interest for experimental searches for T violation.   

An Optical Molecular Clock for New Physics Searches

Some vibrational transitions in molecules have the potential to serve as optical clocks or as probes for new physics.[1] The vibrational overtones in homonuclear molecules such as O₂⁺ are electric-dipole forbidden and thus intrinsically narrow and immune from some systematic shifts.[2] Here, we present our progress towards investigations of these transitions in an ion trap. Photoionization from a pulsed molecular beam allows loading of vibrationally selected molecular ions. Co-trapping with atomic ions provides sympathetic cooling. Molecular state detection is from dissociation followed by identification of the resulting atomic ions. We will describe production of O⁺ ions with multi-photon dissociation at 266 nm. Current experiments focus on two-photon spectroscopy at optical wavelengths. 

[1] D. Hanneke, B. Kuzhan, A. Lunstad, Optical clocks based on molecular vibrations as probes of variation of the proton-to-electron mass ratio, Quantum Science and Technology 6, 014005 (2021)

[2] R. Carollo, A. Frenett, D. Hanneke, Two-Photon Vibrational Transitions in ¹⁶O₂⁺ as Probes of Variation of the Proton-to-Electron Mass Ratio, Atoms 7, 1 (2018)   

Short-range force sensing with an optically levitated nanosphere

Optically levitating dielectric particles are a promising tool for precision measurement experiments. Our system consists of a 300 nm silica nanosphere that is capable of measuring Zeptonewtonian (10^-21 N) force sensitivities. We plan to use this nanosphere to advance the search for short distance gravitational forces that go beyond our fundamental understanding of Newtonian gravity and the standard model. To probe such new exotic forces, we can position the levitating nanosphere at micron length scales away from a surface. In this poster presentation, I will explain the importance of refining our techniques of capturing, cooling, and precisely controlling the position of the nanosphere in order to tighten the bounds on short distance gravity. I will also describe various measurements that we plan to do in the future.   

Matter-wave Interference and Precision Tests of Gravity with Levitated Nano-spheres

Optical levitation in ultra-high vacuum (UHV) and cryogenic environments provides a platform potentially capable of providing quantum coherences of tens to hundreds of milliseconds for objects such as silica nano-spheres which are much more massive than atoms and molecules.  Demonstration of matter-wave interference with optically levitated nanospheres has the potential to extend the current limit on matter-wave interference by three to four orders of magnitude, pushing the experimental limits on matter-wave duality. This would provide pathways towards the realization of gravity-induced entanglement experiments, tests of decoherence and wave function collapse models. To preserve a coherence time of approximately 200ms, experimental challenges such as near motional ground state cooling pressures below 10⁻¹³mbar, internal temperatures below 100K, and relative position stability on the order of tens of nanometers must be overcome. This apparatus additionally allows for precision measurements of short-range forces to test Newtonian gravity at sub-micron scales, the Casimir Polder force, matter neutrality, and other fundamental forces.   

Constraining CP violating nucleon-nucleon long-range interactions in diatomic eEDM searches and chiral molecules

The searches for CP violating effects in diatomic molecules are typically interpreted as a probe of the electron's electric dipole moment, a new electron-nucleon interaction, and a new electron-electron interaction. However, in the case of non-vanishing nuclear spin, a new CP violating nucleon-nucleon long-range force will also affect the measurement. I will discuss our use of the HfF+ eEDM result to set a new bound on this hypothetical interaction, which is the most stringent from terrestrial experiments. These multiple new physics sources motivate independent searches in different molecular species for CP violation at low energy that result in model-independent bounds, insensitive to cancellation among them. I will discuss using precision spectroscopy of chiral molecules to constrain such a new CP violating nucleon-nucleon long-range force.   

Quantum-Limited Detection and Special Relativity: Promising New Tools for Greatly Improved Electron Magnetic Moment Measurements

The most precise test of the Standard Model (SM) is the comparison of its prediction of the electron’s magnetic moment with its measured value [1-4]. This comparison, at the sub-parts per trillion level, is a powerful tool in our search for physics beyond the SM as any deviations between measurement and prediction would point to new physics. Additionally, it provides a strong constraint on new physics as any new theoretical models must agree with it.

In this poster, I will highlight two promising approaches that together promise a factor of 10 improvement in future measurements. The first is employing a quantum-limited detector (SQUID amplifier) to perform state readout of our single-electron qubit system. The second is to use the relativistic mass shift due to spin-flips and cyclotron jumps as for “quantum non-demolition” (QND) detection. This will allow us to reduce the electron’s temperature by a factor of 20 leading to reductions in resonance linewidths by this factor and a large reduction in current systematic errors.

This elegant new approach along with expected improvements in the SM prediction, arising from improved measurements in the fine structure constant, would improve the most precise test of the SM by a factor of 100.

1.    X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Phys. Rev. Lett. 130, 071801 (2023)

2.    R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, Science 360 (2018) 191

3.    Léo Morel, Zhibin Yao, Pierre Cladé & Saïda Guellati-Khélifa, Nature Vol. 588, pg 61–65 (2020)

4.    T. Aoyama, T. Kinoshita,  M. Nio, Atoms 2019, 7, 28.   

Strontium molecular clock for physics searches beyond the Standard Model

We present a Sr₂ molecular lattice clock and describe its unique opportunities as a precision measurement platform. This includes supplying the most precise frequency reference in the THz frequency range and providing the ability to constrain non-Newtonian gravity at ultrashort range. We are working toward a vibrational isotope shift measurement in order to place constraints on Yukawa-type mass-dependent forces at the nanometer scale. Here we discuss progress toward producing the ⁸⁶Sr₂ isotopologue at ultracold temperatures, including addressing isotope shifts for cooling and trapping atoms, and photoassociating the molecules. We also discuss implementation of a new lattice configuration to reduce lattice light scattering and reactive collisions to improve the clock precision.   

Floquet engineering with multilevel dipole-interacting Rydberg atoms for quantum simulation

Qubit-based quantum simulators have demonstrated success in investigating quantum magnetism and non-equilibrium many-body phenomena. The emerging control of atomic systems featuring rich multi-level internal structure, presents new prospects for quantum simulation with higher- dimensional spin systems. Here, we explore new opportunities for quantum simulation and non- equilibrium many body dynamics using three-level Rydberg atoms in a programmable tweezer array. Alongside naturally occurring spin exchange dipolar interactions, we demonstrate that periodically driving transitions between the Rydberg levels with microwave fields can additionally lead to the emergence of the density-density interactions and even new spin-exchange interactions that were previously dipole forbidden. The relative strength of all these interactions is finely tunable, con- tingent upon selection of participating Rydberg states and the specifics of the applied microwave driving. By strategically manipulating a precise sequence of drives between the different Rydberg levels, we show how the above interactions can be combined to realize a diverse variety of Floquet Hamiltonians. Within this setting we explore non-equilibrium spin relaxation as a function of initial spin configuration, interaction strengths in system. Our results can be relevant for studies of non- equilibrium dynamics and many-body state preparation in a broad range of AMO systems featuring multilevel exchange interactions.   

Computations of forbidden transition probabilities in lanthanide ions of interest for kilonova nebular phase analysis

In 2017, a gravitational waves signal (GW170819) associated with a neutron star merger was detected by the LIGO/Virgo collaboration. The coalescence of these two compact objects released a large quantity of matter in the space which was the site of nuclear reactions producing chemical elements heavier than iron such as lanthanides. This ejecta produced a transient electromagnetic phenomenon, most known as a kilonova. In the early phase, the spectrum of the kilonova is dominated by the millions of allowed transitions arising from these heavy elements. In the late times, when the kilonova is said to be in his nebular phase, the temperature and the density of the ejecta decrease so much that the ionization stage does not exceed the doubly charged species. Only low-lying levels, such as metastable levels, are populated giving rise to so-called emission forbidden lines, such as the magnetic dipole (M1) and electric quadrupole (E2) transitions. More recently, in March 2023, the James Webb Space Telescope reported spectroscopic observations of a transient afterglow similar to the AT2017gfo kilonova. Studies of the late recorded spectra showed some spectral features that could be explained by different candidate forbidden transitions like neodymium, erbium, or also other heavy elements. Element identification in nebular phase spectra is quite challenging since atomic data and especially forbidden line lists for heavy elements are scarce in the literature.

In order to extend the study of kilonovae in their nebular phase, we carried out new calculations of transition probabilities for M1 and E2 lines between low-lying levels in singly and doubly ionized lanthanide atoms. Given the lack of data in the literature, two theoretical methods were used in this work to model the atomic structure of these ions and to compute the radiative parameters. The first one is the fully-relativistic Multi-Configurational-Dirac-Hartree-Fock (MCDHF) method with the GRASP2018 code. The computed values were then compared to the results deduced from pseudo-relativistic Hartree-Fock (HFR) calculations in order to check their reliability. This allowed us to obtain a new consistent set of atomic data and to highlight the most intense lanthanides forbidden lines which are likely to be observed in the infrared spectrum of kilonovae in their nebular phase.