Session K01: Poster Session II

Relativistic Effects on Subshell Energies for Superheavy Elements

A study of the subshell energies of the superheavy elements Z$=$102, 112 and 118 has been performed at the Dirac-Fock (DF) level and compared with nonrelativistic results to assess the qualitative and quantitative effects of relativistic interactions on the energies of the various subshells. The strength of these relativistic effects is of order Z$\alpha $, which is not small compared to unity for these elements, especially for inner shells. As a result, the energies of the inner shells are altered substantially by relativity, by as much as about 50 keV for 1s of Z$=$118, as compared to nonrelativistic energies. In addition, the wave functions of the inner shells are contracted by relativity, and these contracted wave functions screen the nucleus more effectively so that the outer shells experience a smaller effective nuclear charge, which tends to expand them. Thus, the relativistic contraction of the outer shell wave functions are counterbalanced by this expansion, leading to interesting phenomenology for outer-shell energies; this has been studied earlier at much lower Z [1,2]. [1] J.-P. Desclaux and Y. K. Kim, J. Phys. B \textbf{6}, 1177 (1975); [2] B. R. Tambe and S. T. Manson, Phys. Rev. A \textbf{30}, 256 (1984).   

Studies of high-$n$, n$^{\mathrm{1}}$G$_{\mathrm{4}}$ and n$^{\mathrm{1}}$H$_{\mathrm{5}}$ strontium Rydberg states using microwave-optical multiphoton excitation

We demonstrate that combined microwave/optical four- and five-photon excitation can be used to generate sizable numbers of high-$n$, 120$\le n\le $160, strontium n$^{\mathrm{1}}$G$_{\mathrm{4}}$ and n$^{\mathrm{1}}$H$_{\mathrm{5}}$ Rydberg states, respectively, for use in studies of novel ultralong-range Rydberg molecules, of autoionization, and of planetary atoms. The quantum defects for both these states (and the n$^{\mathrm{1}}$I$_{\mathrm{6}})_{\mathrm{\thinspace }}$were measured using microwave spectroscopy and are in good agreement with theoretical predictions based on a two-active-electron model.   

Generating up to 10$^{17}$ photons per second with energies reaching 400-MeV

The Gamma Factory (GF) is a proposal aiming at generation of up to 10$^{17}$~photons/s of the energies reaching 400~MeV. This exceeds the available $\gamma$-sources by several orders of magnitude. The idea is based on resonant scattering of “light” on ultrarelativistic (the Lorentz factor $\gamma_L$ between 10 and 2900) highly-stripped (very few electrons) ions. Due to the relativistic Doppler effect, the energy of the incident photons is boosted in the ion frame 2$\gamma_L$ times. Since the energy can be tuned by changing $\gamma_L$, this enables conventionally unavailable spectroscopy of various physical systems. Due to the ultrarelativistic motion of the ions, in the lab frame, spontaneously emitted photons are directed along the ion-propagation direction, boosting the energy of the photons by another factor of 2$\gamma_L$. In turn, the energy of the photons is increased 4$\gamma_L^2$ (e.g., conversion of 100-nm ``light'' into 10$^{-15}$~m radiation). Intensity of the radiation is very high as the conversion is resonant. During the presentation, the principles of the GF will be discussed and challenges of optical pumping of such ultrarelativistic highly charged ions will be be discussed. Potential applications of the GF for ``exotic’’ atomic physics will be also presented.   

A velocity characterized atomic hydrogen beam

We present a cryogenic and velocity-characterized ground state (1S) and metastable (2S) atomic hydrogen source.  We also present possibilities to manipulate the atomic trajectories through the 1S-2S two-photon transition.  For example, the two-photon transition can be used for laser cooling, or the trajectories of metastable 2S atoms can be affected with near-resonant visible wavelength lasers.    

Sr+ isotope shift measurement

Precision isotope shift spectroscopy can improve our knowledge of atomic and nuclear structure. Combined with a King plot analysis, such measurements could also constrain sources of new physics beyond the standard model of particle physics. We present preliminary isotope shift measurements of the $5s\ ^2S_{1/2} \rightarrow 5p\ ^2P_{1/2}$ electric dipole transition with a precision at the 100 kHz level. With $^{88}$Sr$^+$, $^{86}$Sr$^+$ and $^{84}$Sr$^+$, we will measure the isotope shifts of the dipole-allowed $4d\ ^2D_{5/2} \rightarrow 5p\ ^2P_{3/2}$ transition, and the narrow $5s\ ^2S_{1/2} \rightarrow 4d\ ^2D_{5/2}$ electric quadrupole transition. We plan to work with the radioisotope $^{90}$Sr$^{+}$ to test for King plot nonlinearities.   

Multi-photon processes in a waveguide-confined ensemble of laser-cooled atoms

We report the results and analysis of spectroscopy measurements of a ladder-scheme implemented using laser-cooled atomic cesium confined to a hollow-core photonic-bandgap fiber with mode diameter of the guided light \textasciitilde 7um. This fiber allows us to both confine a large number of atoms (\textasciitilde 10,000) into a quasi-1D geometry and guide light along the atom confining region. The setup grants us access to an atomic system with a large optical depth in excess of 100, as well as to high intensities of light at low power levels. Our goal is to demonstrate optical nonlinearities, such as wavelength conversion of single photons through four-wave mixing. As a precursor, we studied two-photon absorption of a weak probe in the presence of a strong pump coupling the excited states, expecting to see a single transparency window. Instead, we observed two and eventually three transparency windows for certain combinations of experimental parameters. We successfully modelled these phenomena by using additional atomic levels that the pump couples into as its power increases, resulting in multi-photon absorption.   

Core polarizability of rubidium using Rydberg spectroscopy

The electric polarizability of heavy alkali atoms includes a small but significant contribution from the ionic core. This contribution is important for precision applications such as black-body radiation shifts in atomic clocks and interpreting parity violation measurements. The polarizability of the core can be determined through spectroscopy of high angular momentum Rydberg states. We present the results of a high-precision measurements of the intervals between the $\ell =$ 4 to 6 levels of rubidium Rydberg states of n$=$17 to 19. The measuurements have been done using radio frequency and microwave spectroscopy of atoms in a thermal beam. The measurement results are precise enough that it is necessary to consider non-adiabatic corrections to the core polarization. We find a dipole polarizability $\alpha_{\mathrm{d}} \quad =$ 9.127(7) a$_{\mathrm{0}}^{\mathrm{3}}$, about three times more precise than previous results and in good agreement with theoretical expectations. .   

Experimental Study of the 4$^{\mathrm{3}}\Sigma _{\mathrm{g}}^{\mathrm{+}}$ and 3$^{\mathrm{3}}\Pi_{\mathrm{g}}$ States of Rubidium Dimer

We reports a high-resolution experimental study and a numerical analysis of the 4$^{\mathrm{3}}\Sigma_{\mathrm{g}}^{\mathrm{+}}$ and 3$^{\mathrm{3}}\Pi_{\mathrm{g}}$ electronic states of rubidium dimer. In the experiment the Rb$_{\mathrm{2}}$ molecules were initially excited from the ground X$^{\mathrm{1}}\Sigma_{\mathrm{g}}^{\mathrm{+}}$ state to an intermediate level of the mixed A$^{\mathrm{1}}\Sigma _{\mathrm{u}}^{\mathrm{+}}$\textasciitilde b$^{\mathrm{3}}\Pi _{\mathrm{u}}$ manifold using a narrow band tunable TiSa laser. In the next step the probe laser, a narrow band dye laser tunable in the 13000-14000cm$^{\mathrm{-1\thinspace }}$range, excited the molecules further to the target states. The resonances of the probe laser were observed by detecting the total fluorescence from the excited states to the a$^{\mathrm{3}}\Sigma_{\mathrm{u}}^{\mathrm{+}}$ state in the 500nm range. Large number of ro-vibrational term values spanning a wide range of the rotational and vibrational quantum numbers were measured using the optical-optical double resonance technique. Besides the term values, we observed the resolved fluorescence intensities with Condon structures from many of the levels. The Rydberg--Klein--Rees (RKR) potential energy curves were constructed and optimized to reproduce the experimental data reliably.   

X-ray spectroscopy of highly charged Fe plasma with the transition-edge-sensor-based microcalorimeter at the NIST EBIT

The electron beam ion trap (EBIT) facility at the National Institute of Standards and Technology (NIST) was used to produce x-ray spectra from highly charged ions of Fe with the beam energy varying between 6.6 keV and 18 keV. The spectra were recorded with an array of 192 transition-edge sensor (TES) based x-ray microcalorimeters [1] which covered the broadband energy range roughly from 500 eV to 10000 eV with an energy resolution of about 5 eV over this range. Calibration was performed using Kalpha emission lines from metallic Mg (1.25 keV), Al, Fe, Co and Ni (7.48 keV) produced by an external calibration source. The measured spectra clearly revealed the features due to the stabilizing radiative decays of high n autoionizing states as well as direct excitation lines. The analysis of the measured spectra was performed through the detailed collisional-radiative modeling of the non-Maxwellian plasma using the NOMAD code [2] which reproduced the resonance and excitation features. The interpretation of measurements as well as the details of theoretical simulations will be presented. [1] P. Szypryt et al., Rev. Sci. Instrum. 90, 123107 (2019). [2] Yu. Ralchenko and Y. Maron, J. Quant. Spectr. Rad. Transf. 71, 609 (2001).   

Measurement of the lifetimes of the $7p \: ^2P_{3/2}$ and $7p \: ^2P_{1/2}$ states of atomic cesium

We report measurements of the lifetimes of the $7p \: ^2P_{3/2}$ and $7p \: ^2P_{1/2}$ states of cesium, $^{133}$Cs. We collect the fluorescence from the spontaneous decay of atoms in the excited $7p \: ^2P_{3/2}$ and $7p \: ^2P_{1/2}$ states and employ a time-correlated single-photon counting technique to obtain the lifetimes of these states. We use these measurements with previous determinations of other electric dipole matrix elements of cesium to determine the $\langle 5d\,^2D_{5/2}||r|| 7p\,^2P_{3/2} \rangle$, $\langle 5d\,^2D_{3/2}||r|| 7p\,^2P_{3/2} \rangle$, and $\langle 5d\,^2D_{3/2}||r|| 7p\,^2P_{1/2} \rangle$ electric dipole matrix elements for cesium. The lifetimes and determined matrix elements provide a test of theoretical methods for calculating precise models of the electronic structure of cesium.   

An Electron Microscope for Viewing a Deformed Nucleus

The metastable $^2F_{7/2}$ state is predicted to be sensitive to the structure of the deformed ytterbium-173 nucleus in two ways. First, the high multiplicity of the electronic state ($J=7/2$) allows the high spin ($I=5/2$) nucleus to leave fingerprints of its multipole moments on the hyperfine structure, up to and including (at least in principle) the nuclear magnetic 32-pole moment. Using the fact that the F state is both long-lived and easily read out using techniques developed for quantum information processing, we are performing the first spectroscopy of this hyperfine structure. Second, the electric quadrupole hyperfine interaction in $^{173}Yb^+$ has been predicted to quench 4 of the 6 hyperfine levels of the $^2F_{7/2}$ state from the 5-year lifetime of the other isotopes to the clock-friendly timescale of about 1 day. We will present prospects for achieving sub-Hz accuracy of the hyperfine splittings and lifetime measurements of the quenched hyperfine levels of $^{173}Yb^+$ and their implications for clockwork and electron microscopy of the shape of a nucleus.   

Spectroscopy of one photon 5s - 6s electric field induced magnetic dipole transition in Rb

We are conducting a measurement of the electric field induced M1 magnetic dipole one photon 5s - 6s transition in Rb in a cell at about 7 mTorr, using a 0.5 W cw single frequency doubled diode laser at 497 nm. We detect cascade fluorescence from the decay of the 6s state at 1367 and 780 nm, and measure the ratios of the strengths of the four hyperfine components. From this, we can obtain the ratio M$_{\mathrm{hf}}$/M of the M1 transition strength, as well as the ratio M/$\beta $ and \textbar $\alpha $/$\beta $\textbar of the scalar and tensor components of the Stark transition polarizabilities.   

Precision spectroscopy in neutral beryllium-9

Four-electron systems are the current testing ground for many advanced theoretical models and also tests of quantum electrodynamics. We present our current progress on updated experimental measurements for a variety of energy levels in neutral beryllium-9, compare them to current theoretical predictions, and motivate future theoretical calculations to compare to these experimental results.   

X-ray spectroscopy of highly ionized atoms using Transition Edge Sensor (TES) microcalorimeters at the NIST EBIT

NIST has built a new broadband X-ray spectrometer from an array of 192 individual TES (Transition Edge Sensor) microcalorimeters, designed specifically for high resolution spectroscopy of X-ray transitions in highly ionized atoms, spanning a spectral range from a few hundred eV to 20 keV. Commissioned recently at the NIST EBIT (electron beam ion trap) facility, this time-resolved, photon-counting TES Spectrometer is dubbed the acronym ``NETS''. We present the earliest NETS observations of X-ray emissions from various ion species created in the NIST EBIT [1], which serve to illustrate its capabilities. Ongoing studies enabled by NETS, including tests of atomic theory and other potential applications, are also presented at this conference.~ [1] P. Szypryt, \textit{et al}., Rev. Sci. Instrum. \textbf{90}, 123107 (2019)   

Analysis of Spectral Lines of Ni I and Ni II in the Ultraviolet and Visible Region

A better understanding of the atomic properties of Ni could contribute to our understanding of astrophysical observations especially in the context of solar physics. Laboratory measurements can provide information important for interpreting these spectra and benchmarking theoretical calculations. There is still more work to be done in understanding the electronic structure for low charge states of Nickel. To this end, we perform analysis of UV/VIS spectroscopic data obtained from the Compact Toroidal Hybrid plasma experiment at Auburn University. We also look at relative line intensities by comparing intensities of multiple lines from the same upper energy state. We present spectral lines observed in this experiment for Ni I and Ni II.   

Measuring the isotope shift with noisy lasers in pastic 3d-printed mounts

We demonstrate the design, implementation and utility of a plastic (PLA) 3d-printed diode mount and associated simplified digital control system for free running laser diodes our students use to perform saturated absorption spectroscopy in Rubidium vapor for the determination of the isotope shift. We show this inexpensive, simpler approach to vapor cell nonlinear optics yields measurements which are statistically identical to those using commercial ECLDs and we compare the resulting isotope shift measurements to the accepted value found in high precision experiments.   

Measurements of f-, g-, and h-state quantum defects in Rydberg states of potassium

We report measurements of the quantum defects for the f, g, and h Rydberg states in potassium for principal quantum numbers $n = 26 - 29$. We made millimeter-wave measurements of the transition frequencies between $nd_j$ and the $n\ell$ states. Using the previously measured d-state quantum defects we can readily determine the $n\ell$ state quantum defects. We also report ionic dipole and quadrupole polarizabilities based on our measurements. The experiments were done in a magneto-optical trap. The cold atoms are excited to Rydberg states in steps from $4s$ to $5p$ and from $5p$ to $nd_j$ states using crossed, focussed (waist size 100 $\mu$m), lasers at 405 nm and 980 nm. Stray electric fields are nulled to less than 25 mV/cm in three dimensions using potentials applied to a set of mutually perpendicular rods surrounding the MOT cloud. Limits to the resolution of the measurements are due to the inhomogeneity of the stray fields. Our measurements of the f-state quantum defects are 5\% smaller than prior measurements and are, to the best of our knowledge, the first measurements of the g- and h-state quantum defects.   

Computing ionization rates from periodic orbits in chaotic Rydberg atoms

When placed in a magnetic field, the electron trajectories of a classical hydrogenic atom are chaotic. The classical ionization rate of such a system can be computed with brute force Monte Carlo techniques, but these computations require enormous numbers of trajectories, provide little understanding of the dynamical mechanisms involved, and must be completely rerun for any change of system parameter, no matter how small. We demonstrate an alternative technique to classical trajectory Monte Carlo computations, based on classical periodic orbit theory. In this technique, ionization rates are computed from a relatively modest number, perhaps a few thousand, of periodic orbits of the system. One only needs the orbits' periods and stability eigenvalues. A major advantage is that as system parameters are varied, one does not need to repeat the entire analysis from scratch; one can numerically continue the periodic orbits as the parameters are varied. We demonstrate the periodic orbit technique for the ionization of a hydrogen Rydberg atom in applied parallel electric and magnetic fields.   

Laser spectroscopy of metastable palladium at 340 and 363 nm

Palladium has 6 stable isotopes. (A = 102, 104,105,106,108, and 110). We performed isotope shift measurements of the $4d^9 5s \, ^3D_3 \to 4d^9 5p \, ^3F_4 $ transition at 340 nm, and the $4d^9 5s \, ^3D_3 \to 4d^9 5p \, ^3P_4 $ transition at 363 nm. The measurements were performed using saturation absorption spectroscopy at the $\sim 1$ MHz level. In addition we also determined the hyperfine structure constants of Palladium-105 (I=5/2), the only isotope with non-zero spin, for the states involved in the two transitions. These measurements will serve as a benchmark for upcoming laser spectroscopic investigations of neutron rich palladium isotopes as a probe of their nuclear structure.   

A calibration method based on atomic spin self-sustaining vector magnetometer

The self-sustaining atomic magnetometer has the advantage of high sensitivity and long spin coherence lifetime, based on which we demonstrate a novel method to calibrate the magnetic coil constants precisely. Via non-destructive phase measurement and coherent optical pumping, the spin polarization of rubidium atoms is regenerated coherently and the Larmor precession signal is oscillating continuously. In this stable state, the calibrating capability is achieved by applying current to coils and scan the magnetic components along x- and y-direction. The magnetic field magnitude is obtained from precession frequency and the coil constants can be derived from the fitting equation directly. The constants of coils in the experiment are 246.010±0.034 nT/mA and 197.452 ± 0.025 nT/mA in the x- and y-directions, respectively   

R-Matrix Calculations of Plasma Opacities

A renewed effort is in progress to implement the R-Matrix (RM) methodology developed for the Opacity Project to compute astrophysical opacities. The coupled channel (CC) calculations should be of higher accuracy than the distorted wave (DW) approximation heretofore employed for opacities calculations, and would precisely incorporate autoionization and coupling effects. The resulting energy distribution of the RM opacity spectrum at solar interior conditions is found to be significantly different than the DW, and mean opacities are higher than other opacity models [1]. Results are compared with available experimental data as well as other theoretical models. A new treatment of plasma broadening of autoionizing resonances is described, as well as an improved Equation-of-State. Specific features of bound-free photoionization cross sections relevant to plasma opacity are illustrated. Convergence of CC wavefunction expansion with respect to the large number of target ion levels included in the calculations, and completeness using "top-up" DW atomic data, is discussed. Future plans include extensive opacity calculations for iron and oxygen that are generally of higher abundance in stellar interiors than other metals. [1]. A.K. Pradhan and S.N. Nahar, PASP Conf. Ser., 515, 79, 2018.   

He-perturbed H$_{2}$ spectra: unprecedented agreement between ab initio theory and experimental data

Hydrogen molecule perturbed by the helium atom constitutes the simplest benchmark system for performing the tests of the ab initio quantum scattering theory on the ultra-accurate experimental spectra. Here, we report a full description of the collision-perturbed shapes of rovibrational lines for this particular system. We demonstrate, for the first time, agreement between measured and ab initio computed collision-perturbed shapes of molecular lines at the subpercent level: the root-mean-square difference between experimental and theoretical profiles is smaller than one-hundredth of the profile amplitude. In the analysis described here, we employed the state-of-the-art statistical model of the collision-perturbed shape of molecular lines, we obtained all the parameters of this model from quantum scattering calculations, and the dynamical calculations were performed on the most accurate potential energy surface to date.   

Influence of reagent rotation on exchange reaction rates in the $\mathrm{Li} + \mathrm{Li_2^*(A^1\Sigma_u^+)}$ system

We have measured collision-induced level-to-level inelastic and reactive rate constants for the system \begin{equation} \ ^7\mathrm{Li}_2^*(\mathrm{A}^1\mathrm{\Sigma}_u^+)(v_i,j_i)+\ ^7\mathrm{Li} \rightarrow \ ^7\mathrm{Li}+\ ^7\mathrm{Li}_2^*(\mathrm{A}^1\mathrm{\Sigma}_u^+)(v_f,j_f) \end{equation} under single-collision conditions at a temperature of 933K. The experiment was conducted for $j_i = $ 3 - 64 and $v_i =$ 2 - 5. We report over 1400 level-to-level inelastic and reactive rate constants with $-5\le \Delta v \le 2$ and $-40\le \Delta j \le 50$ . By varying initial rotational energy by more than two orders of magnitude, we are able to report the effect of initial molecular rotation on reactive energy transfer in $\mathrm{Li}_2-\mathrm{Li}$ collisions for the first time and compare the results with theory. Reactive $j_f$-distributions are well modeled by a modified statistical theory. We employ quasiclassical trajectory simulations in conjunction with Reverse Monte Carlo methods to fit a modified LEPS potential surface to our experimental data. Simulations using this fitted potential surface allow us to compare the $j_i$ dependence of total reactive cross sections with theory.   

Observation of Universal Efimov's Ratios across an Intermediate-Strength Feshbach Resonance in $^{39}\mathrm{K}$

Efimov's original scenario is featured by an infinite number of three-body bound states (trimers) accumulating at unitarity where $E=1/a=0$. The binding energies of these trimers have a self-similar structure with a fixed scaling factor between adjacent branches. This scheme is valid in the zero-range limit and in real systems only applies to highly-excited trimers with finite-range interactions. In this work, we unambiguously measured the benchmarks associated with the Efimov spectrum in $^{39}\mathrm{K}$, denoted as $a_{-}^{(n=0)}$, $a_{*}^{(n=1)}$ and $a_{+}^{(n=0)}$, with $n$ indexing the parentage of trimer. $a_{-}^{(n)}$ are tri-atomic resonances at $a<0$, $a_{*}^{(n)}$ are scattering resonances between atoms and Feshbach molecules at $a>0$, $a_{+}^{(n)}$ are interference minima in three-atom recombination at $a>0$. We report a universal ratio $a_{*}^{(1)}/a_{-}^{(0)}$ on the two lowest-lying trimers. The within-ten-percent consistency between this ratio and zero-range result implies that finite range perturbations are suppressed as expected for Feshbach resonances with intermediate strength. We introduce multi-channel van der Waals three-body model that can reproduce all three benchmarks.   

Building a Quantum Defect Theory model for Ultracold collisions of Lithium atoms.

For small separation distances, the atom-atom interaction is characterized by a deep potential well on the order of a few thousand Kelvin, while at larger separations distances, the interaction is modeled by a shallow attractive tail with energies on the order of $\mu K$ or $m K$. We are building a QDT model to describe the collisions of ultracold lithium atoms. We use the Morse/long-range potential model of Le Roy [J.Chem.Phys. 131,204309 (2009)], which accurately represents the short-range, deep potential well, and reduces to the Van der Waals $C_6/r^6$ (with higher order corrections) at long range. For these calculations, we have used a numerical variant of QDT based on Milne phase amplitude method that is capable of treating higher partial waves[PRA 87,032706 (2013)], which we have tested previously using square wells at short range against exact numerical solutions. We are now extending calculations of bound state energies, phase shifts and cross sections to incorporate multichannel effects within the lowest manifold of $X^1\Sigma^{+}_{g}$ potentials.   

Electron-Impact Ionization of He $1s 2s$ $^3S$

Electron-impact ionization cross sections are calculated for the $1s 2s$ $^3S$ excited state of the He atom. A time-dependent close-coupling method is used to calculate both single and double ionization cross sections. Theoretical double ionization cross sections are compared with crossed-beams experimental measurements at Louvain-la-Neuve, Belgium.   

Dielectronic Recombination in O$^{4+}$ Above and Below the Ionization Threshold

Relativistic perturbation theory calculations are carried out for O$^{4+}$ $1s^2 2s^2$ + e -> O$^{3+}$ $1s^2 2p^2 3l (l=0,1,2)$ dielectronic recombination. We find that 37 of the 57 levels in the $1s^2 2p^2 3l$ configurations lie above the O$^{4+}$ ionization limit. The largest cross sections are found at 1.7 eV for the $1s^2 2p^3 3d$ configuration.   

Partial time delays in elastic electron scattering by rectangular potential well with arising discrete levels.

We have investigated the partial Eisenbud-Wigner-Smith time delays for slow electrons scattered by rectangular attractive potentials as functions of the potential parameters, such as the potential well depth and the potential radius. We have focused our consideration on the vicinities of the parameters of the potential that are close to their critical values. The critical values are those, at which the bound states with zero binding energy appear in the potential well. The evaluations are performed mainly analytically. Specifically, we have considered potential depths U and potential radii R, in which the potential supports several discrete s-, p- and d-levels. Despite the potential simplicity, the presented analysis makes it possible to observe some specific features in the time delay behavior that have general character. It should be emphasized that although the investigated features of the considered-time delays were obtained for the simple rectangular potential well, it is not difficult to generalize the consideration for any short-range potential, obtaining qualitatively the same results.   

\textbf{Collisions of electrons with Fe atoms at E}$=$\textbf{ 1eV - 1 MeV:} \textbf{A Relativistic investigation}

A complex optical potential embodying the static, exchange, polarization and absorption effects is developed to solve Dirac relativistic equation in partial waves [1,2] for calculating elastic and inelastic cross sections due to $e^{-} - $Fe scattering at E $=$ 1 eV- 1 MeV. We present here the differential, integral, momentum transfer and viscosity cross sections along with their spin polarization. We also report the details of the critical minima in the elastic differential cross sections, the absorption, and total cross sections. For the critical minima due to electron impact there are neither any experimental nor any theoretical study presently available. Our predicted cross sections agree nicely with experimental and other theoretical findings. Details will be presented at the conference. [1] A. K. F. Haque, M. A. Uddin, D. H. Jakubassa -- Amundsen, and Bidhan. C. Saha, J. Phys. B \textbf{ 51}, 175202 (2018). [2] Haque \textit{et al}. Elastic scattering of e$^{\mathrm{\pm }}$ by Cd, Hg and Pb atoms at 1eV $\le $E $\le $1 GeV. AQC 83 [\textit{in press}], 2020.   

Impementation of a multipass laser system on a free-free apparatus

A free-free experiment investigates the emission or absorption of photons when an electron scatters from an atom in a laser field. For pulsed lasers of repetition rates of tens of hertz, and pulse durations of tens of nanoseconds, the experimental live-time is a few microseconds per year; typical experiments can take well over a week of continuous data taking. We have therefore developed and installed a multipass laser system on our free-free apparatus. The principal of the system is to use a Pockels cell to rotate the laser polarization $90^\circ$ as the beam enters a circuit which passes through the electron-scattering interaction region and then returns to a polarizing beamsplitter cube (PBS) placed just before the (now deactivated) Pockels cell. The orientation of the PBS is such that the beam is reflected through $90^\circ$ and therefore trapped in the circuit of path length 20~ns. Preliminary results are encouraging: the multipass system results in an increase of the free-free signal by a factor of 6.5, with a corresponding improvement in statistics from 3.6$\sigma$ to 8.1$\sigma$, over a single pass system. We will present a progress report on this system and plans to install a similar one on a second free-free apparatus.   

Low-energy electron elastic collisions with Th, Pu, Am, No and Lr actinide atoms

Recently, the experiment [1] measured the electron affinity (EA) of Th for the first time to be 0.608 eV. Following [2] we have used our robust Regge-pole methodology to probe negative-ion formation in the atoms Th, Pu, Am, No and Lr through the electron elastic total cross sections (TCSs) calculations. The TCSs are found to be characterized by ground, metastable and excited anionic formation, requiring careful identification. New manifestations in the TCSs for the Pu, Am, No and Lr atoms have been discovered; namely, atomic and fullerene molecular behavior near threshold [3]. Also, a polarization-induced metastable cross section with a deep Ramsauer-Townsend (R-T) minimum near threshold has been identified in the Am TCSs, which flips over to a shape resonance appearing very close to threshold in the TCSs for No. We have attributed these peculiar tunable behaviors in the TCSs to size effects impacting significantly the polarization interaction. This provides a novel mechanism of tuning a shape resonance and R-T minimum through the polarization interaction via the size effect. Our extracted anionic binding energies from the TCSs are compared with available EAs. 1. R. Tang \textit{et al}, Phys. Rev. Lett. \textbf{123}, 203002 (2019) 2. Z. Felfli and A.Z. Msezane, Appl. Phys. Research \textbf{11}, 52 (2019) 3. A.Z. Msezane and Z. Felfli, Chem. Phys. \textbf{503}, 50 (2018) .   

Time delay of slow electrons by a diatomic molecule described by non-overlapping atomic potentials model.

We study the elastic scattering of slow electrons by two-atomic molecule in the frame of non-overlapping atomic potentials model. The molecular continuum wave function is represented as a combination of a plane wave and two spherical $s$-waves, generated by the centers of atomic spheres. The asymptotic of this function determines in closed form the amplitude of elastic electron scattering. We show that this amplitude cannot be represented as a series of spherical functions. Therefore, it is impossible to use straightly the usual S-matrix methods to determine the scattering phases for non-spherical targets. We show that far from molecule the continuum wave function can be presented as an expansion in other than spherical orthonormal functions. The coefficients of this expansion determine the molecular scattering phases for non-spherical molecular systems. We calculated the scattering phases in the framework of an analytically solvable model and demonstrated the internal fundamental shortcoming of existing approaches. In the frame of the suggested approach, we calculate the Wigner times delay for slow electron scattered by two-atomic target. In principle, our approach can be easily generalized, thus permitting consideration of a multi-atomic molecule as a scattering target. .   

Theoretical Studies of Dissociative Recombination of Electrons with SH$^+$ Ions

We are investigating the dissociative recombination (DR) of electrons with the molecular ion SH$^+$, i.e. $e^- + \mathrm{SH}^+ \rightarrow \mathrm{S + H}$. SH$^+$ is found in the interstellar medium, and understanding its loss through DR will lead to more accurate astrophysical models. Recently we addressed the $^2\Pi$ potential energy curves (PECs) of SH as a DR pathway\footnote{Kashinski \emph{et al.}, J.\,Chem.\,Phys. \textbf{146}, 204109\,(2017)}. We have extended this work to investigate alternate DR pathways. Early results suggest that direct-mechanism DR through a $^4\Pi$ pathway may resolve the low-energy ($< 10\,\mathrm{meV}$) discrepancy between experimentally determined rate coefficients and those determined through the indirect mechanism DR $^2\Pi$ pathway. PECs are obtained by performing large active space multi-reference configuration interaction (MRCI) electronic structure calculations for several values of SH separation. Rydberg-valence coupling has proven to be important. The block diagonalization method is used to disentangle interacting states forming a diabatic representation of the PECs. The status of this ongoing work will be presented at the conference.   

Negative ion formation in low-energy electron-fullerene collisions: Fullerene anionic catalysis

Negative-ion formation in the fullerene molecules C$_{\mathrm{44}}$, C$_{\mathrm{60}}$, C$_{\mathrm{100}}$, C$_{\mathrm{124}}$, C$_{\mathrm{128}}$ and C$_{\mathrm{136}}$ is explored through low-energy electron elastic scattering total cross sections (TCSs) calculations using our robust Regge-pole methodology. We find that the TCSs are characterized generally by ground, metastable and excited negative ion formation during the collisions, Ramsauer-Townsend minima and shape resonances. The novelty and generality of the Regge-pole approach is in the extraction of the negative ion binding energies (BEs) of complex heavy systems from the calculated TCSs. For ground states collisions these BEs correspond to the electron affinities (EAs), yielding excellent agreement with measured EAs for C$_{\mathrm{20}}$ through C$_{\mathrm{92}}$ [1, 2]. Utility of the formed fullerene negative ions is demonstrated in the catalysis of water oxidation to peroxide and water synthesis from H$_{\mathrm{2}}$ and O$_{\mathrm{2}}$ using the anionic fullerene catalysts C$_{\mathrm{20}}$\textbf{\textasciimacron } - C$_{\mathrm{136}}$\textbf{\textasciimacron }$_{\mathrm{.}}$ DFT transition state calculations found C$_{\mathrm{52}}$\textbf{\textasciimacron }and C$_{\mathrm{60}}$\textbf{\textasciimacron } numerically stable for both water and peroxide synthesis, C$_{\mathrm{100}}$\textbf{\textasciimacron } increases the energy barrier the most and C$_{\mathrm{136}}$\textbf{\textasciimacron } the most effective catalyst in both water synthesis and oxidation to H$_{\mathrm{2}}$O$_{\mathrm{2}}$. \begin{enumerate} \item A. Z. Msezane and Z. Felfli, Chem. Phys. \textbf{503}, 50 (2018) \item Z. Felfli and A.Z. Msezane, Euro. Phys. J. D \textbf{72}, 78 (2018) \end{enumerate}   

Pulse duration dependence of strong-field-induced fragmentation of ethylene and acetylene molecules

Understanding the fragmentation of small polyatomic molecules induced by a strong laser field is one of the key steps towards laser-controlled chemistry. For hydrocarbons, such fragmentation dynamics often involve hydrogen migration in different stages of the breakup process. Here we show how the breakup patterns of ethylene and acetylene molecules exposed to intense 800 nm laser fields change as a function of a laser pulse duration. Performing coincident momentum imaging of ionic fragments resulting from two- and three-body breakup of doubly and triply ionized molecules, we trace the signatures of hydrogen migration, analyze the role of different intermediate states, and discuss possible contributions of ``concerted'' and ``sequential'' fragmentation pathways.   

A classical model of channel-closing effects on strong-field ionization

Atoms in strong laser fields can ionize by absorbing energy from multiple photons so that an electron has sufficient energy to escape (multi-photon ionization), or by having the depth of its potential well lowered enough that an electron has a significant chance of tunneling out through the barrier (tunnel ionization). One might expect that as the intensity of the laser field increases, the probability that the atom will ionize increases until an intensity is reached that guarantees ionization. However, as the intensity increases the ground state of the atom is stark shifted so that a greater amount of energy is required for ionization to occur. In the multi-photon ionization model this shifting of the ground state energy results in a point being reached where the minimum number $n$ of photons that must be absorbed has increased to $n + 1$ (the ionization channel that corresponds to $n$ photon absorption has closed). The probability of absorbing $n + 1$ photons is much lower than for absorbing $n$ photons, so the probability of ionization decreases as the intensity increases past this point. Here we present a classical model of the effects of channel closing on ionization probabilities, and apply it to simulate strong-field experiments on argon.   

High Harmonic Generation (HHG) from ZnO crystals by two-color pulses

While HHG from gaseous atoms is relatively well understood, HHG in solids is still debated and has been scrutinized experimentally only recently [1,2]. Even though the typical setup for HHG uses single-color intense mid-IR laser pulses, there has been interest in analyzing the effects of coherently adding a second or higher harmonic pulse, to characterize the frequency response of the sample and obtain more efficient HH conversion [3,4] . We investigated intra- and interband contributions to HHG in ZnO model semiconductors driven by 1600 nm pump and 800 nm probe laser pulses with variable relative delay (pulse shape). We numerically calculated HH spectra by solving the time-dependent Schr\”odinger equation in single-active-electron approximation within an adiabatic basis-set expansion, including the entire first Brillouin Zone, and analyze HH yields and cutoff frequencies as a functions of the pulse shape and intensities. [1] F. Navarrete, et al., Phys. Rev. A 100, 033405 (2019). [2] S. Ghimire, et al., Nat. Phys, 7, 138 (2011). [3] Z. Wang, et al., Nat. Comm. 8, 1686 (2017). [4] T. T. Luu and H. J. W\"orner Phys. Rev. A 98, 041802(R) (2018).   

Light-field driven electron dynamics in graphene

Graphene is a unique material for lightfield-controlled electron dynamics inside of a (semi-) metal. Its Dirac cone dispersion relation represents a two-level system to study intricately coupled intraband motion and interband (Landau-Zener) transitions driven by the optical field of phase-controlled few-cycle laser pulses [1, 2, 3, 4]. Based on the coupled nature of the intraband and interband processes, we observe repeated coherent Landau-Zener transitions between valence and conduction band separated by around half an optical period of $\sim$1.3 fs, fully supported by numerical simulations. Because of the extremely fast dynamics, fully coherent Landau-Zener-Stückelberg (LZS) interferometry manifests itself in ultrafast current injection, with a record-fast turn-on timescale of 1 fs for a current in a metal. Moreover, we could show complex electron trajectory control by tailoring the polarization state of the driving laser pulses. This way, we can manipulate LZS interference [3].\\ $[1]$ T. Higuchi, C. Heide et al., Nature 550, 224–228 (2017)\\ $[2]$ C. Heide, T. Boolakee et al., NJP 21, 045003 (2019)\\ $[3]$ C. Heide, T. Higuchi et al., PRL 121, 207401 (2018)\\ $[4]$ C. Heide, M. Hauck et al., Nat. Photonics (2020) https://doi.org/10.1038 /s41566-019-0580-6   

High-harmonic generation (HHG) enhancement from Cr-doped MgO

HHG from crystals is a source of coherent extreme ultraviolet (XUV) attosecond radiation [1] and reveals band-structure information of the sample [2]. Increasing the HHG yield and HH cutoff frequency are fundamental goals in the development of efficient XUV sources, which we aim for by investigating the effects of doping on HHG spectra. The presence of dopants results in new electronic states in the band gap, as well as lattice defects, which modify the minimum band gap. Because the interband HHG yield depends exponentially on the minimum band-gap energy of the solid [3], we expect a substantial change of the HHG yield by doping [4]. We measured impurity-enhanced HHG yields [5] and analyze our experimental spectra in comparison with numerical solutions of the Semiconductor Bloch Equations. [1] G. Vampa, et al., IEEE J. Sel. Top. Quantum Electron. 21, 8700110 (2015). [2] N. Tancogne-Dejean, et al., Phys. Rev. Lett. 118, 087403 (2017). [3] F. Navarrete, et al., Phys. Rev. A 100, 033405 (2019). [4] T. Huang, et al., Phys.Rev. A 96, 043425 (2017). [5] V. Nefedova, et al., arXiv:2001.00839 (2020).   

Ultrafast laser-assisted photoprotection mechanism in the adenine cation

Attosecond pulses have become a mature tool for tracking in real time nuclear and electronic dynamics in systems with increasing complexity. Our particular interest is the ultrafast response of DNA building blocks upon irradiation, from which photostability and bond breaking emerge. Through time-resolved photo-fragmentation measurements, we demonstrate a laser-assisted photoprotection scheme in the adenine nucleobase. Surprisingly, a path to retain the molecule structurally intact arises when a near infrared (NIR) pulse is sent precisely 2.3 fs after ionization by an isolated attosecond XUV pulse. Without the properly timed NIR, the singly or doubly photoionized adenine dissociates, as confirmed by TDDFT simulations. Rate equations and ab-initio many-body time-dependent calculations based on Green's function associate this characteristic 2.3 fs delay to the population of a specific shake-up state after XUV ionization, driving the electronic density away from the molecular plane. Depletion of this shake-up state by the NIR pulse accounts for internal energy removal from the molecule and leads to a stable dication.   

Correlation effects on plasmonic photoelectrons in C\textunderscore 60 and C\textunderscore 240.

We investigate the effect of electron correlations in the C60 and C240 molecules stimulated by light. The Kohn-Sham equations of the valence electron clouds of the molecules are solved to obtain the ground state structures in the density functional theory [1]. Considering the dipole response of the systems to the incoming photon, the energy dependent induced electron-densities are then computed from the many body susceptibility in a linear response frame. This yielded the complex radial induced potentials which, at plasmon energies, probed the collective response of the molecules. This response suppresses the photon's dipole field, while inducing a strong attractive force, over the giant resonance region [2]. The effect of this force is revealed in the binding-well shapes of the imaginary parts of the induced potentials. Because of this transient attraction, the temporal delay of the photoelectron emission can be observably affected [3]. [1] J. Choi et al ., Phys. Rev. A, 95, 023404 (2017) [2] I. V. Hertel et al., Phys. Rev. Lett, 68, 784 (1992) [3] T. J. Barillot et al., Phys Rev. A, 91, 033413 (2015).   

Investigation of coupled nuclear and electronic motion in H2 photoionization

We investigate coupled nuclear and electronic dynamics in the photoionization time delays of H$_2$. We use a RABBITT technique to measure the photoionization time delays for several vibrational states of H$_2^+$ across a wide range of photoelectron kinetic energies. We observe discrepancies between our measured photoionization delays and a theoretical model which incorporates the vibrational state dependent ionization potential, but neglects motion of the nuclei. This difference between measurement and theory might indicate time variation of the scattering potential caused by nuclear dynamics. We explore the relative importance of these dynamics near the ionization threshold.   

Dichroism in ionization of oriented Li(2p) atoms by circularly polarized laser radiation.

In this joint theoretical and experimental project, we investigate the response of laser-excited Li atoms prepared in the (2p,$m\!=\!+1$) state to circularly polarized infrared (IR) radiation with the same or opposite helicity of the initial state. Our calculations are based on the single-active electron (SAE) approximation, in which the valence electron is moving in the field of the He-like Li$^+$($\rm 1s^2$) core and subjected to few-cycle intense laser pulses. The peak intensity, pulse length, and wavelength of the probe laser are varied to simulate the experimental conditions. We study the dichroism $D = (S_{\rm co} - S_{\rm counter})/(S_{\rm co} + S_{\rm counter})$, where $S_{\rm co}$ and $S_{\rm counter}$ are the signals obtained for co-rotating and counter-rotating pump and probe laser fields, respectively. Results will be presented for both the energy spectrum and the momentum distribution of the ejected electrons. Good agreement between theory and experiment is obtained, thereby allowing us to study detailed effects such as resonant excitation via Rydberg states and the helicity-dependent appearance of the Autler-Townes effect.   

Non-collinear XUV-IR four-wave-mixing to study the dynamics of dark states.

Ultrafast electron dynamics associated with dark states, i.e., excited states that are not accessible through single-photon transitions, cannot be probed using traditional photo-absorption techniques. Characterization of the dynamical evolution of these states is possible through the use two-photon excitations; however, greater insights can be gained through noncollinear four-wave mixing (NFWM). By using tunable near-infrared (NIR) femtosecond pulses and extreme ultraviolet (XUV) attosecond pulse trains we invoke nonlinear parametric processes for investigations of dark state dynamics. The noncollinear configuration for wave-mixing provides versatility and has the advantage of yielding background-free signals. We use these studies investigate the lifetimes of autoionizing states in argon and oxygen.   

A combined B-spline R-matrix approach for the study of time-dependent multielectron dynamics in complex atoms.

Experiments with ultrafast lasers are becoming increasingly focused on the role of multi\-electron effects~[1] and the capabilities of mid-IR lasers~[2], both of which present considerable challenges to current computational methods. A successful time-dependent multi\-electron approach, therefore, requires two things: a compact, accurate atomic-structure description, and an efficient time-propagation scheme. Given their individual desirable characteristics and common $B$-spline basis, the time-independent $B$-spline atomic \hbox{$R$-matrix} code (BSR)~[3] and the $R$-matrix with time-dependence method (RMT)~[4] are natural choices to provide, respectively, the atomic-structure description and propagation scheme for probing time-dependent behaviors in general atomic systems. We present our efforts in combining the two approaches, which we hope will enable the investigation of phenomena such as auto-ionization and spin-orbit dynamics~[5] in multi\-electron systems. [1] T.~Mazza et al., Nat.\ Commun.~{\bf 6} (2015) 6799. [2] T.~Gaumnitz et al., Opt.\ Express~{\bf 25} (2017) 27506. [3] O.~Zatsarinny, Comput.\ Phys.\ Comm.~{\bf 174} (2006) 143. [4] A.~C. Brown et al., Comput.\ Phys.\ Comm.~(2019) 107062. [5] J.~Wragg et al., Phys.\ Rev.\ Lett.~{\bf 123} (2019) 163001.   

Exchange effects on time-resolved photoemission

The $1s2s$ singlet and triplet metastable states of the helium atom, which have remarkably long lifetimes, can be conveniently generated in a helium gas sample by discharge currents. In this work, we study theoretically the effect of exchange parity on the time-resolved photoionization of the atom from these two metastable states. In particular, we compare the non-resonant photoemission delays to the $1s\varepsilon_\ell$ and $2\ell\varepsilon_{\ell'}$ channels, as well as the resonant pump-probe ionization to the $2\ell\varepsilon_{\ell'}$ channels, mediated by the autoionizing doubly-excited states that converge to the $2s/2p$ He$^+$ threshold.   

Propensity rules and interference effects in laser-assisted photoionization of noble gases and closed-shell negative ions

We investigate the angle-resolved photoelectron spectra from laser-assisted photoionization, where an atom is photoionized by a field in the XUV range with an additional laser field in the IR range which \textit{dresses} the atom, $ A + \gamma_{\mathrm{XUV}} \pm q \gamma_{\mathrm{IR}} \to A^+ + e^-, $ for helium and neon atoms using an \textit{ab initio} method based on time-dependent surface flux and configuration interaction singles. We have found an interplay between a radial propensity rule and an angular interference effect to interpret the angular probability distribution (PAD) of the photoelectron, in which we find a different number of minima comparing absorption and emission processes with the magnetic quantum number resolved. In the low-energy limit the propensity rule explains why there is a difference between the PADs for absorption and emission processes in the continuum. In the high-energy limit, however, the PAD is mostly explained by the interference effects of partial waves, as expected from the soft-photon approximation. We further compare the results obtained in atoms to those in closed-shell negative fluorine ion where the remaining neutralized target exerts only a short-range potential, as opposed to the long-range Coulomb potential from ionized atoms.   

A multicolor interferometric method for extracting phase information on continuum-continuum couplings.

The reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) [1] method is a widely employed technique to measure attosecond time delays of photoionization processes. One consequence of this technique is the introduction of an additional component to the time delay, the continuum-continuum (CC) time delay~[2], caused by the interaction of the probe field with the photo\-electron. While well studied theoretically, this CC time delay is difficult to observe experimentally~[3]. Following up on the method outlined in~[4] for atomic hydrogen, we describe an approach capable of isolating this CC delay for Ar, which is experimentally easier to access. We show theoretical predictions obtained by the multi\-electron $R$-matrix with time dependence method (RMT)~[5] for two RABBITT measurements of the $3p$ photoionization delay in argon with different orders of CC transitions. The results will be compared with data from experiments currently in progress. [1] P.~Paul et al., Science {\bf 292} (2001) 1689. [2] J.~Dahlstr{\"o}m et al., Chem. Phys. {\bf 414} (2013) 53. [3] J. Fuchs et al., Optica {\bf 7} (2020) 154-161. [4] A.~Harth et al., Phys.\ Rev.\ A~{\bf 99} (2019) 023410. [5] A.~C. Brown et al., Comput.\ Phys.\ Comm.~(2019) 107062.   

Sideband oscillations in four-photon RABBIFT scans.

Extracting sideband phase information from standard \hbox{RABBITT} (reconstruction of attosecond beating by interference of {\bf two}-photon transitions) scans is a common technique to measure atto\-second time delays in photoionization [1]. Here we further investigate the {\bf four}-photon setup (RABBIFT), suggested in~[2], where the intensity of the sidebands generated by a probe frequency $\omega_p$ oscillates according to $I(\tau) \propto$ cos$(-4\,\omega_p\tau+\Delta \phi_{\epsilon})$, where $\tau$ is the delay between the XUV and IR pulses and $\Delta \phi_{\epsilon}$ is an energy-dependent phase. Here we examine the intensity and pulse-length dependence of $\Delta\phi_{\epsilon}$ for realistic experimental setups ($I_{\rm XUV} = 10^9\,$W/cm$^2$, $I_{\rm IR} = 10^{11}-10^{12}$\,W/cm$^2$, pulse lengths $20-100\,$fs) by comparing RABBIFT scans from {\it ab initio} TDSE calculations~[3] for atomic hydrogen produced by different probe pulse durations and intensities. Preliminary results suggest a non-negligible dependence of $\Delta\phi_{\epsilon}$ on the latter parameters. [1]~P.~Paul et al., Science {\bf 292} (2001) 1689. [2]~A.~Harth et al., Phys. Rev. A~{\bf 99} (2019) 023410. [3]~N.~Douguet et al., Phys. Rev. A~{\bf 93} (2016) 033402.   

Shake-up photoemission delay in Neon

In the ionization of an atom, electrons emerge from different shells with different delays. A longstanding controversy surrounding the measured ($21\pm5$~as at 105~eV) and computed ($\leq 10$~as) time delay difference between the $2s$- and $2p$-shell photoemission from neon [1] has been explained in a recent experimental work [2]. Shake-up channels, which were not resolved in [1], were responsible for the discrepancy between theoretical calculations and the experimental data. This new finding, however, still awaits quantitative theoretical confirmation. In particular, it is still to be determined whether other channels beyond the one identified as being responsible for the measurement bias, might also contribute. In this work, we report advances of a theoretical study conducted with the \footnotesize\textsc{NEWSTOCK} {\it ab initio} method to analyze and quantify the effect of shake-up channels above 70~eV photon energy in neon. [1] M. Sch\"{u}ltze {\it et al.} Science {\bf 328} 1658 (2010), [2] M. Isinger {\it et al.} Science {\bf 358} 893 (2017).   

Argon dark autoionizing states decay probed with four-wave mixing

Ultrafast pump-probe spectroscopies employing trains of attosecond pulses have emerged as a useful tool for studying electron dynamics in atoms and molecules. In the first implementations of these schemes, pump and probe pulses are collinear and have commensurable frequencies. As a consequence, multiple distinct processes give rise to overlapping signals that are difficult to disentangle. Recent experimental advances have led to the extension of the original schemes to more general non-collinear four-wave mixing spectroscopies with independently tunable probe pulses. These spectroscopies spatially separate signals arising from different excitation pathways. Here, we present an \emph{ab initio} calculation of the four-wave-mixing signal from the argon atom, excited to the $3s^{-1}n\ell$ autoionizing states by an extreme ultraviolet attosecond pulse train, and probed by two independent angled IR pulses. The calculation accounts for the collective emission from the interaction region and are in good agreement with measurements from the group of Arvinder Sandhu. Furthermore, using an essential-states model, we investigate how the resonant four-wave mixing signal depends on the lifetimes of the bright and dark autoionizing states, whose radiative coupling dominate the spectrum.   

Vibrational coherence induced by intramolecular photoelectron scattering

We study theoretically in real time, with the help of a 1D model, the photoionization of a neutral hetero-nuclear diatomic molecule from a localized core orbital. The nuclear motion is modeled with a simple harmonic oscillator, with identical parameters in both the neutral and ionized state of the molecule, within the Born-Oppenheimer approximation. Even within this elementary framework, the system exhibits strong deviations from the Frank Condon approximation, due to the recoil associated to the photoelectron emission, and to the intramolecular scattering of the photoelectron. As a consequence, the ionization of the molecule leaves behind a vibrationally excited ion. The vibrationally resolved signals in the photoelectron spectrum map holographically the intramolecular photoelectron scattering dynamics as well as the coherence of the vibrational state of the residual ion. We compute the time-dependent density matrix and Wigner distribution of the parent-ion, and show that the ion residual coherence manifests itself in an effective delay in the periodic oscillation of the excited vibrational wave packet created by the ionization event.   

Towards Observing Site Selective Chemistry in Real Time

The possibility of site-selective photochemistry, where element and site selective excitation or ionization using x-ray photons guides the outcome of the dissociation has been an intriguing problem since the advent of high average flux sources at synchrotrons. So far, only limited selectivity has been observed, hinting at efficient charge redistribution before decay processes happen. The ability to probe this process as it happens is now becoming a reality at x-ray free electron lasers, with the ability to produce two pulses commensurate with the core-hole lifetimes, with very different photon energies, and soon high repetition rates. By initiating an inner shell process at one molecular site and probing at another place in the molecule, one will be able to observe the evolution of the electronic properties, starting from the ionization energies of the core excited states. Making sense of the data will require comparison with high accuracy computational predictions, such as using our newly developed scalar-relativistic delta-coupled-cluster method. We will present calculations for a class of fluoro-alkane molecules that will be the focus of a demonstration experiment at LCLS this year.   

Femtosecond-resolved multiphoton ionization of C60 using X-ray pump X-ray probe with the LCLS FEL

We studied the time-resolved ionization of C$_{\mathrm{60}}$ using X-ray pump X-ray probe with 640 eV photons to examine the role of chemical effects, such as chemical bonds and charge transfer, on the fragmentation following multiple ionization of the molecule. The advanced simulations revealed that despite substantial ionization induced by the ultrashort (20 fs) X-ray pump pulse, the fragmentation of C$_{\mathrm{60}}$ is considerably delayed. This work uncovered the persistence of the molecular structure of C$_{\mathrm{60}}$, which hinders fragmentation over a timescale of hundreds of femtoseconds. Furthermore, we demonstrate that a substantial fraction of the ejected fragments are neutral carbon atoms.   

State-selective Pump-probe Studies on CO$_{\mathrm{2}}$ with Extreme Ultraviolet (XUV) and Near-infrared (NIR) Pulses

State-selective excitation to a single (or a small subset of) excited neutral or ionic state(s), versus excitation to many possible states, with a broadband pulse is a powerful tool for the study and control of ultrafast molecular dynamics. We use a single-harmonic extreme ultraviolet (XUV) pulse, produced as the 11$^{\mathrm{th}}$ harmonic of an 800-nm near-infrared (NIR) laser, to ionize carbon dioxide (CO$_{\mathrm{2}})$ to the vibrationally excited ground (X $^{\mathrm{2}}\prod_{\mathrm{g}})$ state or to the first excited (A $^{\mathrm{2}}\prod_{\mathrm{u}})$ state of the mono-cation (CO$_{\mathrm{2}}^{\mathrm{+}})$. Using a delay-controlled NIR probe pulse, the mono-cation is fragmented via different pathways to yield CO$^{\mathrm{+}}$ or O$^{\mathrm{+}}$ fragments. By comparing the results to a second measurement performed with the 13$^{\mathrm{th}}$ harmonic and to a similar pump-probe experiment with a comb of harmonics, where the excited ionic state is determined by photoelectron and photo-ion coincidence, we can clearly separate the role played by each ionic state and confirm the role of molecular rotation in the time-dependent ion yields.   

RIXS Reveals Hidden Electronic Transitions of the Aqueous OH Radical

We present RIXS spectra of the short-lived hydroxyl radical formed via proton transfer after ionization of pure liquid water [1]. Photoexcitation at the OH-resonance at 526 eV gives rise to an energy loss feature at 4 eV, corresponding to the localized A$\leftarrow$X transition of the OH$(aq)$ radical -- which is hidden by charge transfer transitions in the direct UV absorption spectrum. Theoretical calculations predict relative intensities of localized and deloclized RIXS transitions for OH$(aq)$ and the OH$^-(aq)$ anion. Time-resolved RIXS highlights the localized transitions in the transient OH$(aq)$ radical and may be used to track the electronic state evolution of this chemically aggressive species. [1] Z-H Loh {\it et al.} Science {\bf367}, 179-182 (2020)   

Vibrational relaxation of photoexcited electrons in fullerenes

Electron-phonon coupling in stimulated molecular systems underpins the mobility and collection of carriers in organic devices [1], finds applications in radiation damage or astrochemistry, besides fundamental interests [2]. We study the vibrational relaxation dynamics of photoexcited electrons to the fullerene band-edge driven by electron-phonon coupling. Time dependent density functional approach in the frame of non-adiabatic molecular dynamics (MD) [3] is used for simulations. MD with fewest switches surface hopping technique versus solving Schrodinger equation will be compared. Transition dipole moments, non-adiabatic electron-phonon couplings, and ultrafast time-dependent population decays from initially populated excited states will be presented. The work may motivate and complement recent interests [2] in ultrafast relaxation measurements in molecules by attosecond XUV pulses. [1] A. V. Akimov and O.V Prezhdo, \textit{J. Chem. Theory Comput.} \textbf{9}, 11 (2013); [2] Marciniak \textit{et al., Nature Comm.} \textbf{10}, 337 (2019); [3] Madjet \textit{et al., Phys. Chem. Chem. Phys.} \textbf{18}, 5219 (2016).   

Study of Optically Excited Nitrobenzene through Nonlinear Ultrafast Polarization Spectroscopy

A Kerr gating pulse induces a third order non-linear polarization response in a media of interest. This response can then sampled by a probing pulse resulting in a change in polarization of the probe that can be measured using the technique of optical Kerr effect spectroscopy. Such techniques have been used in the past to study dynamics in solid, liquid and gas phase systems on picosecond and femtosecond time scales. With the addition of a third excitation pulse, the non-linear response of the system due to the gating pulse is modified. Here, we present measurements and electronic structure calculations of optically excited liquid nitrobenzene and discuss potential origins of the ultrafast polarization response of the system. We then discuss the extension of this method to study ultrafast dynamics in polyatomic gas phase systems.   

Neutral dissociation and strong-field ionization of iodine-containing halomethanes studied by time-resolved coincident ion momentum imaging

We study the UV-induced dissociation and NIR-strong-field ionization of CH3I and iodine-containing dihalomethanes using a time-resolved coincident ion momentum imaging technique. Upon absorption of a single 263 nm photon, the molecules dissociate primarily via C-I bond cleavage, and the dissociating neutral molecule is then ionized after a variable time delay by an intense 23-fs 790 nm pulse. We compare the observed delay-dependent ion kinetic energy release to a numerical model that relates the experimental data to the shape of the dissociative neutral and di-/tri-cationic potential energy curves. Our time-resolved coincidence data also allows identifying competing two- and three-photon excitation channels in the pump step.   

Quantum wave-mechanics of the simple pendulum via non-diffracting pendulum optical beams

We simulate quantum-mechanical probabilities for the simple pendulum using non-diffracting optical beams bearing Mathieu spatial modes. These are solutions to the Helmholtz equation in elliptical coordinates, whose angular form is identical to the Schrodinger equation for the simple pendulum. As a consequence the intensity of the modes in the Fourier plane are a direct mapping of the quantum mechanical probability. We investigate stationary states and wavepackets dynamics of the pendulum via modal superpopositions.   

Interfacing single photons from a quantum dot with fiber-confined cold atomic ensemble

We report our progress on development of a proof-of-principle hybrid quantum repeater. We generate entangled photon pairs from InAsP quantum dots (QD) embedded in semiconductor nanowire and store them in a quantum memory based on an ensemble of laser-cooled caesium atoms confined inside a hollow-core optical fiber. We also investigate the wavelength conversion of single photons generated by the QD (894.6 nm) to telecom wavelength through four-wave mixing in the fiber-confined cloud. Our approach combines the advantages available from a deterministic and tunable solid-state source of bright entangled photon pairs with the potential for long-lived quantum memory and high-efficiency wavelength conversion that are achievable in laser cooled atomic cloud with large optical depths and tight confinement.   

Towards Near IR and Telecom Photons Entangled With Ba+

Towards Near IR and Telecom Photons Entangled With Ba$^{+}$ J. D. Siverns, J. Hannegan, J. Cassell, and Q. Quraishi Quantum memories with matter-flying qubit entanglement may be used to establish a quantum network, however photons from trapped ions have limited range. We present our progress in generating matter-entangled photons either at telecom wavelengths or at wavelengths compatible with neutral Rb[1,2]. This platform provides both long distance compatible, and user-defined, wavelengths for entanglement-based networking. A high-NA lens is used to collect single 493-nm photons, polarization-entangled with a single Ba$^+$ ion, and a nonlinear waveguide converts these photons to 780-nm in a single stage or to telecom wavelengths using two-stages. We discuss single-photon production rates, conversion efficiencies, noise properties and factors affecting the entanglement fidelity. Finally, we examine potential rates and fidelities for homogenous Ba$^+$-Ba$^+$ entanglement as well as for hybrid Ba$^+$-Rb entanglement. [1] J. D. Siverns, J. Hannegan, Q. Quraishi, Sci. Adv. 5 (10), eaav4651 (2019) [2] A. N. Craddock, J. Hannegan, D. Ornelas, et al., PRL, 123, 213601 (2019)   

Praseodymium ions for solid state quantum memory.

Rare-earth ion doped crystals, owing to the protected optical transition of Lanthanides, offer unique potential to build fully integrated quantum information devices. We investigate atom-light interactions in Pr:YSO solid state crystal to develop efficient single photon storage devices. We use broadband atomic frequency comb (AFC) protocol to spectrally shape the inhomogenously broadened optical transition of Praseodymium ions. W study the effects of hyperfine splitting to generate high quality atomic frequency combs for quantum memory devices. We further utilize rephasing effect of atomic dipoles to demonstrate efficient storage and retrieval of optical pulses through photon echo measurements.   

Locally addressable cold atomic gas coupled to a high finesse optical cavity

The study of many-body quantum systems via weak measurement and at the single atom level enables better understanding and control of such systems. Here we report on the first calibrations of an experimental apparatus 1) in which an atomic quantum gas is strongly coupled to an optical cavity and 2) with which we will locally address individual components of the gas for read out and control. The optical cavity is in a near concentric geometry with small radius of curvature mirrors to ensure high cooperativity while preserving transverse numerical aperture for local optical addressing. Optical addressing will be achieved by the trapping of atoms in individual far off-resonant optical tweezers imaged onto the atoms through a high numerical aperture objective. We plan to destructively image the atomic cloud through the high resolution objective as well as to non-destructively monitoring the cloud dynamics though the dispersive interaction between the atoms and the cavity photonic mode by measuring the cavity output with a heterodyne detector. The combination of local addressability with non-destructive measurement presents the opportunity to use this apparatus to explore local Hamiltonian engineering, quantum measurement, open many body quantum dynamics, and quantum feedback.   

Rydberg entanglement and clock operation in alkaline-earth atom arrays~

Alkaline-earth atoms individually trapped in optical tweezers have gained prominence in recent years for their potential to combine quantum metrology, simulation, and computation in a single platform. Here we present our recent results in these directions with a dynamically reconfigurable 1D array of strontium atoms, showing both high-fidelity entanglement and detection of Rydberg states, and separate development of an atomic-array optical clock. Both results exploit the clock state, which we use as a metastable groundstate~to achieve single-photon Rydberg excitation and commensurately high Rabi frequencies. We observe both non-blockaded and blockaded Rabi oscillations with high-fidelity (\textgreater 0.99) and detect the Rydberg state with similarly high fidelity through auto-ionization of the Rydberg electron. These results set the stage for current investigations into many-body physics and the development of quantum gates.   

Real-time tracking and stabilization of cavity-coupled atomic gases

Ultracold atoms dispersively coupled to optical cavities are an ideal testbed for studying quantum measurement and control. Through sensitivity to the atomic state, an optical field in cavity can apply coherent backaction, modifying the dynamics of an atomic ensemble. In addition, photons leaving the cavity carry information about the real-time dynamics of the atomic ensemble. Here, we show how tracking of the dispersive cavity shift enables the non-invasive study of the time evolution of the atom number. We track the real-time evolution of the atom number during evaporative cooling in a cloud of laser-cooled atoms. The minimally-invasive measurement allows for extracting two-time atom number correlation functions, which provide further insight into the evaporation dynamics. Using feedback, we demonstrate the preparation of atomic ensembles with sub-Poissonian shot-to-shot atom number fluctuations. In a different set of experiments, we investigate dynamics of the collective spin of an atomic ensemble. Tracking the real-time energy exchange between light and spin reveals autonomous stabilization of the spin to the cavity drive. Our results illustrate the interplay of measurement and feedback in optical cavities and pave the way for future studies of feedback-stabilized atomic systems.   

Experimental study of Spontaneous Emission in the Quantum Walk

We have recently realized a quantum walk of a Bose-Einstein Condensate (BEC) of Rubidium 87 atoms by applying a periodic kicking potential to change the momentum state of the atoms and using microwave pulses to control the internal state. This periodic potential was generated by two counter-propagating, off-resonant frequency stabilized laser beams. This setup is stable to generate a quantum walk for tens of steps, however, it is affected by spontaneous emission induced by the same laser beams used to generate the kicking potential. We have investigated this spontaneous emission by varying a few parameters including the power of the kicking laser beams. The results of this study allow us to determine the robustness of the quantum walk during the experiment. These findings can also be used in other related experiments involving the use of BECs as a basis.   

Steady-state phase diagram of a weakly driven chiral-coupled atomic chain

A chiral-coupled atomic chain of two-level quantum emitters allows strong resonant dipole-dipole interactions, which enables significant collective couplings between every other emitters. This chiral-coupled system can be made of an atom-nanofiber or atom-waveguide interface, where nonreciprocal decay channels emerge. We theoretically study distinct interaction-driven quantum phases of matter with chiral couplings and infinite-range dipole-dipole interactions mediated by one-dimensional nanophotonics systems. The steady-state phase diagram in the low saturation limit involves states with extended distributions, crystalline orders, bi-edge/hole excitations, and a region of chiral-flow dichotomy. We distinguish these phases and regions by participation ratios and structure factors, and find two critical points which relate to decoherence-free subradiant sectors of the system. We further investigate the transport of excitations and emergence of crystalline orders under spatially-varying excitation detunings, and present non-ergodic butterfly-like system dynamics in the phase of extended hole excitations with a signature of persistent subharmonic oscillations. Our results pave the way toward simulations of many-body states in nonreciprocal quantum optical systems.   

Strong coupling of two individually controlled atoms via a nanophotonic cavity

We demonstrate photon-mediated interactions between two individually trapped atoms coupled to a nanophotonic cavity. Specifically, we observe collective enhancement when the atoms are resonant with the cavity, and level repulsion when the cavity is coupled to the atoms in the dispersive regime. Our approach makes use of individual control over the internal states of the atoms, their position with respect to the cavity mode, as well as the light shifts to tune atomic transitions individually, allowing us to directly observe the anti-crossing of the bright and dark two-atom states. These observations open the door for realizing quantum networks and studying quantum many-body physics based onatom arrays coupled to nanophotonic devices.   

Light-Atom Interfaces from $10^9$ to $10^14$ Hz

The character of specific light-atom interactions is a critical aspect to nearly all quantum technologies, from sensors to simulators to memories and repeaters. We consider the design of this interface for two ongoing experiments in our lab: a Rydberg electric field sensor and a multiplexed quantum memory. Rydberg electric field sensors suffer in sensitivity from the limited coupling strength to free-space modes as compared to antenna-based sensors. We will present our progress at increasing this coupling by orders of magnitude, opening the door to truly quantum-optical regimes. Our cold-atom quantum memory experiment takes advantage of a unique ring-cavity design to achieve strong coupling. Furthermore, our system is able to write, store, and readout hundreds of holograms in our atoms. This unique combination of large multiplexing capacity with efficient strong coupling to a single optical mode enables a path to a functional quantum repeater.   

Mechanical modes of an `Alligator' photonic crystal waveguide.

We present our experimental observations on opto-mechanical coupling for guided optical light fields of an `Alligator' photonic crystal waveguide (APCW). Quasi-odd harmonics of the fundamental mechanical mode are observed for optical light frequency in the waveguide regime, while both quasi-odd and quasi-even harmonics are observed for optical light frequency near the band-edge of the APCW. A novel theoretical model of transduction mechanisms is developed to explain the experimental observations.   

Engineering Atom-Photon and Atom-Atom Interactions with Silicon Nano-Photonics

Interfacing thermal atomic vapors with Nano-photonics on a chip provides a unique testbed for manipulating the interaction of atoms with photons and other atoms on a miniaturized scale. We studied an integrated silicon photonic chip, composed of several sub-wavelength ridge and slot waveguides, immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observed that the guided mode transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. The tight confinement of the field around the waveguide leads to a large optical non-linearity at the telecom wavelength within the Femto-Watt power range. To benefit further from the small mode volume below the difraction achievable in Nano-devices, we investigated the coupling of atomic vapor to slot waveguides. The slot mode constrains the probed atomic density to an effective one-dimension hence leading to geometry dependent atom-light and atom-atom interactions. The results of this study help to understand the capabilities and limits of hybrid systems of thermal atoms and Nano-photonics and pave the way towards on-chip, integrated and atom-based quantum technologies.   

Microring Resonators on a Suspended Membrane Circuit for Atom–Light Interactions

Atoms that are trapped and interfaced with light in nanophotonic circuits form an exciting new platform for applications and fundamental research in quantum optics and many-body physics. The ability to induce tunable long-range atom-atom interactions with photons, and the formation of an organized atom–nanophotonic hybrid lattice presents a novel opportunity to explore collective quantum optics and many-body physics. Our system is based on high quality silicon nitride microring resonators fabricated on a transparent membrane substrate. This platform is compatible with laser cooling and trapping with cold atoms and with potentially high cooperativity parameters C $\approx$ 500, thus holding great promises as an on-chip atom cavity QED platform. We present our on-going experiment effort for coupling atoms to a micro-ring and further fabrication improvements for quality factor for creating strong atom-photon coupling.   

Reduced volume and reflection for optical tweezers with radial Laguerre-Gauss beams

Our progress to develop advanced capabilities for the integration of cold atoms and nanophotonics is documented at https://doi.org/10.1364/OPTICA.384408. At DAMOP we will describe a critical new component of this effort related to coherent superpositions of radial Laguerre-Gauss beams that lead to tightly focused optical tweezers with reduced volume and increased particle trapping frequency. Beyond free-space, such superpositions can enable the efficient transport of atoms via optical tweezers directly to trap sites near the surfaces of nanoscopic optical devices. More generally, the rapid variation of the Gouy phase for wavelength-scale focal regions could enable phase-contrast microscopy within heterogeneous sample volumes.   

Topological Quantum Matter Made of Light

Topological states of matter can be realized using cavity Rydberg polaritons, quasiparticles composed partly of cavity photons and partly of atomic Rydberg excitations. These polaritons interact strongly thanks to the Rydberg excitations and have individual particle behaviors determined by their photonic degree of freedom and shaped through a twisted optical cavity. We recently demonstrated that this hybrid system is a fruitful platform for building strongly correlated quantum states in an artificial gauge field by preparing a synthetic two-particle Laughlin state of photons for the first time. Building on this pioneering work, we describe our recent efforts to enable larger systems by designing a highly degenerate cavity in combination with improved state readout through Rydberg enhanced imaging.   

Doing more with Fabry-Perot resonators: low-loss intracavity optics and real-time dynamics

Recent developments have shown that Fabry-Perot resonators are a powerful tool for manipulating and characterizing light, and present unique opportunities to tailor the dispersion of strongly interacting photons when combined with Rydberg EIT. To extend these exciting possibilities, we are exploring the limits of optical resonators, demonstrating that intracavity lenses and electro-optic crystals can be incorporated without significantly impacting the resonator finesse (${>10}^{3})$. Introduction of lenses opens avenues for aberration-compensation and stronger light-matter coupling, while electro-optics present possibilities to explore Floquet physics with optical photons. We also employ the intracavity electro-optic modulator to achieve MHz-bandwidth resonator locking. Finally, we demonstrate space-time-resolved measurement of the transverse motional dynamics of intracavity photons, paving the way for exploring curved space dynamics of photons on multiply connected surfaces.   

3D Printing an External Cavity Diode Laser Housing

The ability to control the frequency of an external cavity diode laser is an essential component for undergraduate laboratories through atomic research. Typically the housing for the diffraction grating and piezo is either commercially purchased or milled from metal. Here we present an alternative to these more expensive options using 3D printing, a commonly available tool in many physics departments. We have examined the laser performance using atomic spectroscopy and self-heterodyne interferometry. The performance and affordability of these designs make them an appealing option for future use.   

Dual-wavelength laser frequency stabilization on a single ULE cavity for strontium Rydberg experiments

A narrow-linewidth stable laser is crucial for both laser cooling and Rydberg-atom creation in cold atomic gases. Here we present a dual-wavelength laser frequency stabilization system based on a single ultra low expansion (ULE) reference cavity that is suitable for laser cooling on the strontium $^1S_0$-$^3P_1$ intercombination line and exciting atoms to the triplet Rydberg series. The standard Pound-Drever-Hall (PDH) technique is used to lock a 689nm diode laser and a 640nm optical parametric oscillator seeded by a 1064nm fiber laser. The 689nm laser is used for laser cooling on the $^1S_0$-$^3P_1$ line and also provides the first photon in the two-photon Rydberg excitation. The 640nm light is frequency doubled to excite the $^3P_1$ state to a Rydberg level. The frequencies of both lasers are tunable while locked by adjusting the offset frequencies (provided by electro-optic modulators) between the lasers and the cavity modes. A servo bandwidth of 1.2MHz is achieved for the 689nm system while the 640nm laser has a target lock bandwidth of 30kHz due to the slower response of the fiber master. Long-term drift of the ULE cavity is measured to be $\sim$25kHz/day and is compensated by continual offset-frequency adjustment.   

An Optically-Locked Interferometer for Attosecond Pump Probe Setups

Ultrafast pump-probe measurements at the attosecond time scale are generally achieved by exposing the target to both an attosecond pump pulse and a phase-locked IR probe field, with a variable time delay between the two. To fully exploit the temporal resolution of attosecond pulses for time-resolved studies, the time delay between the pump and probe pulses must be controlled with attosecond resolution as well. This requires the ability to linearly vary the delay with time steps of the order of the pulse duration (or less), and maintain it to any desired value over extended periods of time. We present the design and performance of an active stabilization system for attosecond pump-probe setups based on a Mach- Zehnder interferometer configuration. The system employs a CW laser propagating coaxially with the pump and probe beams in the interferometer. The stabilization is achieved with a standalone feedback controller that adjusts the length of one of its arms to maintain a constant relative phase between the CW beams. With this system, the time delay between the pump and probe beams is stabilized within 10 as rms over several hours.   

Cavity-enhanced detection of transient absorption signals

We present a simple, high-duty-cycle, cavity-enhanced optical absorption measurement technique based on a delay-limited Pound-Drever-Hall sideband locking technique. The chosen circuit naturally provides real-time readout of the amplitude quadrature, which can be mapped onto the cavity's internal loss rate. Our proof-of-concept device comprises a 5-cm-long Fabry-Perot cavity with a 400 kHz bandwidth (finesse 7000, 400 ns power ringdown), and a feedback bandwidth of several MHz, limited primarily by the group delay of our electronics. This technique could readily be applied to other optical resonators such as fiber cavities, with potential applications in radiation dosimetry.   

A robust, field-deployable, low-cost mode-locked laser oscillator for deployed optical atomic clocks.

Frequency combs have been investigated in the laboratory over the course of the last 25 years in a wide range of implementations and applications including but not limited to optical atomic clocks, precision metrology, precision spectroscopy, LIDAR, and low-phase-noise RF generation. While the Nobel prize winning technology of frequency combs have shown their usefulness in a variety of applications, there have been few demonstrations of this technology in real-world applications. Here we present a mode-locked oscillator that has been designed to be environmentally robust and low cost, while maintaining suitability for use in frequency comb applications. Vescent Photonics has designed environmentally robust oscillators and frequency combs for government programs including satellites and terrestrial moving platforms. These designs allow for repetition rate matching at the time of manufacture, which is an important consideration for integration of this technology into several key applications. Vescent Photonics will report on the performance, environmental robustness, and cost of these fiber laser systems.   

Generating High-Power Bragg Pulses for Atom Interferometry

Achieving lower systematic errors in atom interferometry calls for greater optical power. To this end, we are building a high-power quasi CW laser system, generating 150-$\mu$s pulses with a 100-Hz repetition rate of light near the 852 nm D2 line of Cesium by amplifying a 500-mW Nd:YAG CW seed to produce up to 10 kW peak power at 1064 nm in 1 J pulses. This is converted to several kW of peak power at 532 nm using second harmonic generation in LBO. We will use this to pump optical parametric amplification in periodically poled SLT, seeded by spectroscopically stabilized 852 nm light. This system is designed to deliver more than 1 kW peak power and should allow us to realize higher-order Bragg diffraction in our atomic fountain, a major step towards a higher precision measurement of the fine structure constant.   

Generating Greenberger-Horne-Zeilinger States in Remote Trapped Ions

Quantum networks promise ultra-secure lines of communications that are both tamper proof and tamper evident. Remote entanglement, the required first-step towards a quantum network, has been demonstrated in a number of systems. Here we describe a protocol to extend two-qubit remote entanglement to generate a Greenberger-Horne-Zeilinger (GHZ) state comprising three remote trapped-ion qubits. Two-particle remote entanglement combined with local operations and communication of classical bits can generate large-scale, network-sized, multi-particle entanglement for distributing quantum information. Quantum communication channels are desirable as they may enable secure links that could reveal the presence of eavesdroppers and protect critical information.   

Measurement of Dicke-narrowed optical transitions in warm alkali vapor for different buffer gas pressures

We demonstrate the quadratic dependence on the relative pump-probe beam angle of the electromagnetically induced transparency narrowed transition linewidth - a defining signature of Dicke narrowing of the optical transition linewidth. We vary the buffer gas pressure thus varying the atomic spatial localization and hence the size of the “quantization box” causing the Dicke narrowing. By carefully defining the zero-value for the relative angle where the linewidth is measured to be a minimum, we find that our data agrees with the theory better than ever before, with no fit-parameters. A Ramsey-like measurement of ground state decay rates between hyperfine and Zeeman sub-levels is performed to investigate the lower limit on the EIT linewidth for case where the pump and probe are perfectly collinear.   

Yb Rydberg Atom Arrays

Arrays of laser-cooled neutral atoms in optical tweezers are a promising platform for quantum science, because of their flexibility and the potential for strong interactions via Rydberg states. Recent experiments with alkaline-earth atoms have demonstrated significant advantages in terms of coherence and control. We will present recent results with Yb Rydberg atoms in optical tweezer arrays, including novel spectroscopy of Yb Rydberg states, trapping Yb Rydberg atoms in tweezers using the polarizability of the Yb+ ion core, and progress towards qubit operations using the $^{171}$Yb nuclear spin levels.   

Dynamics of entanglement entropy and particle number distribution in disordered, free fermionic systems

The information contained in a quantum state $\rho$ is quantified by the entanglement entropy $S=-\textrm{tr}(\rho \ln \rho)$, which is difficult to measure. For systems with particle number conservation, $S$ is the sum of the number entropy, $S_N$, and the configuration entropy, $S_{conf}$, which have been measured recently in a cold-gas experiment [1]. We here show that for systems of non-interacting fermions, including the case of disorder, the time evolution of the second Renyi entropy $S^{(2)}=-\ln\textrm{tr}(\rho^2)$ is determined by the exponent of corresponding number entropies. As a consequence in free fermionic systems a dynamical growth of entanglement is always related to a slower growth of the number entropy. We numerically illustrate this for different tight-binding fermionic models including the case of off-diagonal disorder for which the entanglement entropy shows an ultra slow, double logarithmic growth in time and give an outlook to interacting systems showing many-body localization.\\ [1] A. Lukin, \textit{et al.} \textit{Probing entanglement in a many-body localized system}, Science \textbf{364}, 256 (2019).   

Measurement-Induced Phase Transitions in Long-range Quantum Circuits

Recent theoretical work has demonstrated a phase transition in the dynamics of quantum entanglement, originating from competition between scrambling unitary evolution and unwanted coupling to a classical bath, represented by measurements. In realistic systems, the presence of long-range interactions often allows for parametrically faster scrambling dynamics, which may qualitatively modify the transition. In this poster, we show this is indeed the case: long-range interactions change the universality of the transition. More specifically, we study 1D long-range quantum circuits, interspersed with projective measurements, where each unitary is a random two-qubit Clifford gate with range sampled from a $1/r^\alpha$ power law distribution. We find that the parameter 𝛼 of the interaction has a dramatic effect: for $\alpha>3$, the critical exponents agree with studies of nearest-neighbor hybrid circuits, while for $\alpha<3$ the critical exponents change continuously with $\alpha$. Moreover, for $\alpha<2$ the area-law scaling crosses over to a sub-volume law scaling in which entanglement entropy grows with system size, even under high measurement rates. We conclude with a resource analysis of realizing the transition in several AMO quantum simulators.   

Observation of nanoscale hydrodynamics in a strongly interacting dipolar spin ensemble in diamond

Bridging the gap between the microscopic description of quantum many-body dynamics and its macroscopic emergent phenomena remains an important open problem. We experimentally tackle this challenge by probing the nanoscale diffusion in strongly interacting solid-state spin ensembles in diamond. More specifically, we harness nitrogen-vacancy (NV) centers as effective nanoscale quantum probes to initialize and detect the local spin polarization in a high-density ensemble of substitutional nitrogen defects (P1 centers). After preparing an out-of-equilibrium initial state of the P1 ensemble, we monitor its quantum quench dynamics and observe that the late time behavior can be described by emergent hydrodynamics, from which we extract the diffusion coefficients. To establish a quantitative connection between the observed hydrodynamics and the underlying microscopic Hamiltonian, we develop an effective semi-classical description for the spin dynamics. Crucially, this description allows us to understand how the interplay between disorder and long-range interactions leads to diffusive---yet non-gaussian---dynamics in the experimental observations.   

Non-equilibrium dynamics of a superfluid Fermi gas with time-periodic modulation: Higgs mode and higher-order harmonic excitation

Motivated by the recent experiment on observation of the Higgs mode in a strongly interacting superfluid Fermi gas [A. Behrle \textit{et al}., Nat. Phys. \textbf{14}, 781 (2018)], we study the non-equilibrium dynamics of a superfluid Fermi gas with a time-periodic modulation in the BCS-BEC crossover by solving the time-dependent Bogoliubov-de Gennes (BdG) equations. By tuning the modulation amplitude and frequency of the coupling constant, we have demonstrated that the Higgs mode can be excited with the time-periodic modulation. For a small modulation amplitude, the long-lived Higgs mode comparing to the current experimental result exists when the modulation frequency is slightly red-detuned. When the modulation frequency is blue-detuned, the single-particle excitation appears along with the Higgs mode. For a large modulation amplitude, the higher-order harmonic excitation is generated due to the nonlinearity. The exploration of other optimal ways of exciting the Higgs mode in a superfluid Fermi gas is also discussed.   

Towards quantum gas microscopy of fermions in p-bands

Quantum gas microscopy is a novel technique which can realize single-site and single-atom resolved detection of strongly correlated quantum gas in optical lattices. We report our recent progress on constructing a quantum gas microscope enabling the imaging of Lithium 6 in p-bands. In addition to the ground band, higher bands are an essential ingredient in Hubbard models for real materials leading to important new effects like orbital ordering which are not well studied up to now. Exotic quantum phases arise by competition between orbital ordering and spin-ordering. Here, we present our latest progress towards the preparation of a two-dimensional Fermi gas and discuss our approach to implementing a two-dimensional optical lattice and loading the atoms into this lattice.   

Search for the FFLO Phase in the 1D-3D Crossover of a Spin-Imbalanced Fermi Gas

The Fulde-–Ferrell-–Larkin-–Ovchinnikov (FFLO) type superconductor is exotic since it simultaneously supports superfluid and magnetic order, and thus, is a supersolid. This phase has yet to be conclusively observed either in condensed matter or in ultracold atomic gases. In one-dimension (1D), the FFLO phase is found in a large region of the phase diagram\footnote{Y.-A. Liao et al. Nature. 467, 567-569 (2010)} - unlike in 3D where it is believed to occupy only a small region, if any. The FFLO phase is expected to be more robust against quantum and thermal fluctuations, however, in higher dimensions. These considerations motivated the proposal to search for FFLO near the 1D-3D dimensional crossover\footnote{M. M. Parish et al. Phys. Rev. Lett. 99, 250403 (2007).}, which we have identified and characterized\footnote{M. C. Revelle et al. Phys. Rev. Lett. 117, 235301 (2016).}. We confine a spin-imbalanced Fermi gas of $^6$Li to 1D tubes using a 2D optical lattice. By increasing the inter-tube tunneling rate, we bring the system into the dimensional crossover, while interactions are tuned via an s-wave Feshbach resonance. We present our progress towards direct observation of the periodic domain walls which would be a definitive signature of the FFLO phase.   

Measurement of spin susceptibility in ultracold lithium-6 gases by a radiofrequency method

Cold atoms have been widely applied in simulating material systems, and in particular ``pseudogap'' effects in the BEC-BCS crossover model make for interesting comparisons to the high-Tc cuprates. We present a radiofrequency (RF) method to create imbalances between equilibrium RF-dressed states and measure the equilibrium spin susceptibility of lithium-6 atoms in a trap with a magnetic gradient. We will present a conceptual overview of this method, which relies on the small but non-zero difference in the magnetic moment between hyperfine states. For this purpose, the second lowest two hyperfine states of lithium-6 are chosen so that we can take advantage of their large magnetic differential moment. Here we emphasize the experimental setup, including the imaging system, and show benchmarking measurements for the spin susceptibility of weakly interacting gases, the dressed-spin relaxation time, and discuss possible parasitic effects.   

Controlling spin and thermoelectric transport in an atomic transport experiment

We report on the control of the thermoelectric transport properties of a strongly interacting Fermi gas flowing through a quasi-two-dimensional contact and second on the control of spin inside a quantum point contact (QPC) and the effects of dissipation on a superfluid. The versatility of cold-atom techniques allows us to precisely define a QPC using light potentials, to directly measure particle, heat and spin currents and to tune interatomic interactions. In a first experiment, we probe the thermoelectric effects induced by a temperature difference across a two-dimensional channel. We use an attractive gate beam as well as an repulsive wall beam to change the relative strength of channel and reservoir contributions to the thermoelectric transport. This allows us to tune the particle transport going from hot to cold to going from cold to hot. In a second experiment, we locally lift the spin degeneracy of atoms inside the QPC usingan optical tweezer tuned very close to atomic resonance. Tuning the laser further away from the atomic resonance we also look at how a superfluid is reacting to dissipation and how its transport properties are effected. These results open the way to the quantum simulation of the coupling between spin, heat and particle currents with cold atoms.   

Observation of Phase Coherence and Superfluidity in a Strongly Interacting Two-dimensional Fermi Gas

We present our studies of phase coherence and superfluidity in strongly interacting two-dimensional Fermi gases. We observe phase coherence by creating a tunnel junction in a homogeneous 2D Fermi gas and measuring the frequency of Josephson oscillations as a function of the phase difference across the junction. We find excellent agreement with the sinusoidal current phase relation of an ideal Josephson junction. We probe superfluidity by dragging a periodic potential through a homogeneous 2D gas and observing the characteristic onset of dissipation above a critical velocity $v_c$. We measure the excitation spectrum of a low-temperature system as a function of interaction strength and find that for a gas of tightly bound molecules there is a well-defined phononic excitation at the speed of sound, as expected from the Landau criterion. This phononic excitation persists into the crossover regime until pair breaking becomes the primary mechanism of dissipation on the BCS side of the resonance. We also present our progress towards studying the temperature dependence of the excitation spectrum to determine the critical temperature for superfluidity of a 2D Fermi gas as a function of interaction strength.   

Transport dynamics of fermions in an optical lattice

We measure the conductivity spectrum of ultracold fermionic atoms in an optical lattice through high-resolution imaging in a quantum gas microscope. By applying a time-varying force to atoms confined to the lattice, we sample their current response at multiple frequencies. We observe that the current response scales linearly with the forcing, providing an experimental demonstration of Ohm's Law for neutral atoms. Broadening of the conductivity spectrum under varying external parameters elucidates how the dissipation of current is affected by fermion-fermion collisions. Furthermore, the spectral weight of the response satisfies a sum rule in the limit of small lattice depth, but diminishes as the depth or temperature increase, reflecting an increase in the band-averaged effective mass. This spectral weight characterizes the strength of the current response to an impulse, and therefore underpins the resistivity. As our measurements approach a high-temperature regime, its inverse is shown to approach T-linear behaviour. The recent implementation of a DMD in the system allows for further flexibility in studying and probing the dynamics. This tool enables the creation of customizable local potentials for both initiating and modifying current response.   

SU(N) enhanced interactions and reduced number fluctuations in a quantum degenerate Fermi gas

We study theoretically and experimentally an interacting $SU(N)$ Fermi gas of $\,{}^{87}$Sr, where N can be as large as 10, in the quantum degenerate regime. The presence of $N$ distinct spin species results in an enhanced interaction due to the larger number of available scattering partners, thus, leading to significant interaction effects even for a nominally weakly interacting gas. Using all 10 spin states during evaporation allows to have efficient sample preparation while reaching deep degeneracy, with $T/T_F = 0.07$ in under 3 s. We employ a kinetic approach and scaling ansatz to obtain the equilibrium and out of equilibrium phase space distribution of the interacting harmonically trapped gas, which allow us to extract the in-situ and time-of-flight density profiles as well as the isothermal compressibility. While generically the effects of lower temperature or interactions are difficult to disentangle, we demonstrate the interacting nature of the system via the time-of-flight density anisotropy. The experimentally measured density profiles and number fluctuations are in good agreement with the theoretical predictions, and enable a precise thermometry and characterisation of the interacting quantum gas.   

High-power optical transport of ultracold fermions using focus-tunable lens

We present an all-optical setup designed to transport a trapped cold cloud of $^6$Li over a macroscopic distance of 30 cm, based on a focus-tunable lens. We transport the atoms from the initial preparation chamber to a dedicated glass cell with increased optical access by displacing the focus of the focus-tunable lens. We estimate the transport efficiency by measuring the atom number and temperature both before and after the transfer. We further characterize the loading and post-transport focus stability. We show that the atom number and focus fluctuation amplitudes can be greatly reduced by an stabilization of lens temperature and the focus-tunable lens control current. We demonstrate the robustness of the optical transport by preparing a molecular BEC after transporting the atoms to the glass cell.   

Quantum Turbulence: Generation and Evolution in Bosonic and Fermionic Superfluids

Interactions between quantized vortices govern the generation and decay of quantum turbulence. Accurate simulation of the vortex dynamics employing models like time-dependent Superfluid Local Density Approximation (TDSLDA) can be computationally quite expensive for a macroscopically large Fermionic sample. To understand these interactions and the instabilities inherent to the turbulent regimes, we propose using Extended Thomas Fermi (ETF) model, similar to the Gross-Pitaevskii (GPE) with a finite temperature extension. In this work, we investigate the role of temperature in the evolution of turbulence in the Unitary Fermi Gas (UFG) and validate against TDSLDA.   

Homogeneous Fermi Gases in the BEC-BCS Crossover

Recently, the realization of homogeneous quantum gases has opened up exciting new playgrounds for studying complex quantum many-body problems. By directly producing gases with a uniform density, we can now avoid many issues associated with the spatial variation of the density of harmonically-trapped gases. We demonstrate the creation of a homogeneous degenerate gas of $^{6}\mathrm{Li}$ atoms trapped in a cylindrical light box created by a combination of axicons and digital micromirror devices. We will report the measurement of the \emph{in-situ} atomic momentum distributions of the uniform Fermi gas across BEC-BCS crossover, and the study of its expansion dynamics from the uniform box trap.   

Spin-oscillation dynamics beyond the single-mode approximation for a harmonically trapped spin-1 Bose-Einstein condensate

Compared to single-component Bose-Einstein condensates, spinor Bose-Einstein condensates display much richer dynamics. In addition to density oscillations, spinor Bose-Einstein condensates exhibit intriguing spin dynamics that is associated with population transfer between different hyperfine components. This work analyzes the validity of the widely employed single-mode approximation when describing the spin dynamics in response to a quench of the system Hamiltonian. The single-mode approximation assumes that the different hyperfine states all share the same time-independent spatial mode, i.e., the field operator for each of the hyperfine states is expanded in terms of one and the same spatial basis state. This implies that the resulting spin Hamiltonian only depends on the spin interaction strength and not on the density interaction strength. Taking the spinor sodium Bose-Einstein condensate in the $f=1$ hyperfine manifold as an example, it is found that the single-mode approximation misses, in some parameter regimes, intricate details of the spin and spatial dynamics. Our results have implications for a variety of published and planned experimental studies.   

On Demand

Many-body spin singlet states have been widely suggested as ideal candidates in investigating quantum metrology and quantum memory. In this poster, several experimental sequences for producing spin singlets in an antiferromagnetic spinor condensate confined by a cubic optical lattice are presented. We demonstrate how to optimize spin singlet production efficiency by properly varying the initial atom number distributions, which are precisely measured from non-equilibrium spin dynamics. Two experimental methods for detecting spin singlet states are also discussed.   

Microwave Control of Spin Dynamics in F=1 Sodium Spinor Bose-Einstein Condensates

We present our latest experimental data on controlling spin dynamics in F=1 sodium spinor Bose-Einstein condensates via microwave dressing. By applying quenches and time-dependent microwave pulse sequences, we implement nonlinear atom interferometry in spin-space in the long evolution time regime, $t \gg h/c$, where $c$ is the spin-dependent interaction energy. We also investigate the breakdown of commonly made approximations such as the single-mode approximation and the undepleted pump approximation for certain parameters.   

Creation of a Skyrmion in a Biaxial-Nematic Magnetic Phase

Spin-2 Bose-Einstein condensates exhibit several magnetic phases with symmetries different from those of the spin-1 case, extending the variety of possible topological excitations. For example, three-dimensional skyrmions in the spin-2 biaxial nematic (BN) phase involve a topologically nontrivial winding in the order parameter, where the space is described at each point by the orientation of a square . We present evidence for the creation of a three-dimensional BN half-skyrmion using magnetic imprinting techniques, as well as progress towards the experimental realization of a full BN skyrmion   

Bulk Viscosity and the Virial Expansion for a Three-Component Fermi Gas in One Dimension

We explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance, similar to two-body interactions in two dimensions. The anomaly will naturally lead to a finite viscosity, as scale invariance is broken. We calculate the bulk viscosity in the high-temperature limit and compare the result to the two-body anomalous interaction in two dimensions. We show there is an exact mapping between these two anomalous systems in the high temperature limit.   

Methods for Loading Heavy Metals into the Clemson EBIT

The Clemson University EBIT (CUEBIT) facility allows for the creation and study of highly charged ions (HCIs). Up until now, only elements existing as gases at room temperature have been loaded and studied in the CUEBIT (e.g. Ar, O, C from CO2). However, for studying metal HCIs of interest to astronomers (e.g. Fe, Ag, Au), it is necessary to find a method to load these solids into the CUEBIT. We investigated two methods, laser ablation and thermal evaporation, which allow for the loading of neutral metals into the CUEBIT. A time-of-flight mass spectrometer and a quartz crystal microbalance were used to evaluate the particle yield of each of these methods.   

Towards Qudit-Based Quantum Computing

We present recent progresses in realizing qudit-based quantum computing with barium ions. Quantum state manipulations and measurements are paramount to quantum computation. In our proposed qudit measurement scheme, high fidelity is achieved by shelving computational qudit states in the 6S$_{\mathrm{1/2}}$ level to the meta-stable 5D$_{\mathrm{5/2}}$ level, which has transition wavelength of approximately 1762 nm. Therefore, spectroscopy of 6S$_{\mathrm{1/2}}$ to 5D$_{\mathrm{5/2}}$ states is a crucial preparatory data for our qudit-based computing scheme, and we report on our recent progress on this experiment. From our prior theoretical investigation, qudit manipulation can be done practically with either direct transitions with microwave or Raman transition. As a preliminary experiment, we have chosen microwave-driven control. To have sufficient control on qudit manipulation, phase, frequency and amplitude control of microwave radiation are required. We report on the architecture of this infrastructure and our progress on this experiment.   

Background-Free State Detection of $^{88}$Sr$^{+}$ Optical Qubits

State-dependent fluorescence detection schemes that rely on optical excitation and detection at the same wavelength are subject to undesirable background counts due to, for example, excitation light scattered by nearby optics. Here, we eliminate scattered light background counts for an optical $^{88}$Sr$^{+}$ qubit by implementing a two-step excitation protocol and detecting light at a wavelength separated by hundreds of nanometers from that of the excitation lasers. This technique uses the $4D_{3/2}$ and $5P_{1/2}$ levels to detect the $5S_{1/2}$ qubit state without populating the $4D_{5/2}$ qubit state. With increased laser intensity to quickly drive the dipole-forbidden $S_{1/2}\to D_{3/2}$ transition and two laser frequencies to address both ground state Zeeman sublevels, we achieve photon count rates that permit high-fidelity state detection and also demonstrate motional state cooling using this pathway. Additionally, this two-step readout scheme may find use in applications, such as in integrated photonic devices, where visible and NIR excitation light is preferred to the blue and UV light used in single-wavelength state detection.   

An Experimental Apparatus for Generation and Isolation of Highly Charged Ions with Low Ionization Thresholds

Access to highly charged ions (HCIs) for various applications has been somewhat limited by the need to use expensive, dedicated facilities such as electron beam ion traps (EBITs). The use of high-field permanent magnets has made it possible to construct smaller EBITs and other ion traps. Such low-maintenance systems will be useful in applications such as the development of x-ray transition-edge-sensors [1]. Other potential uses include creating certain HCIs, such as Pr$^{\mathrm{9+}}$ and Nd$^{\mathrm{10+}}$, proposed for the development of next-generation atomic clocks, or the search for variation in the fine-structure constant [2]. At NIST, a miniaturized EBIT using NdFeB magnets has been built as a source of ions with relatively low ionization thresholds (\textless 1000 eV). To isolate ions of interest, we are building a permanent magnet Penning trap with a trap center magnetic field of $\approx $ 0.75 T. Preliminary ion extraction results with noble gas HCIs are presented. Measurements of the lifetimes in metastable states of Sn-like Pr$^{\mathrm{9+}}$ are planned after the laser-ablation-based metal loading system becomes operational. The mobility of the apparatus would facilitate its use in various experiments. [1] P. Szypryt, et al., Rev. Sci. In. 90, 123107 (2019), [2] M. Safronova, et al., PRL 113, 030801 (2014)   

Metastable qubits in trapped Calcium-43 ions

While all of the basic primitives required for universal \newline quantum computing (QC) have been demonstrated in trapped-ion qubits with high fidelity, it is currently not possible to simultaneously realize the highest achieved fidelities in a single ion species. This can be a serious impediment to the development of practical quantum computers. However, there are possibilities for achieving high-fidelity and full functionality in a single species with the use of multiple internal levels: augmenting existing species with new functionality. Specifically, essential dual-species capabilities can be developed in the Calcium-43$+$ ion through novel encoding schemes in metastable states, allowing user-selectable, ion-specific activation of the necessary functions on demand (e.g. storage, coupling to motion, cooling, and state preparation and measurement). I will present simulation results and progress towards experimental implementation of high-fidelity preparation and readout procedures in metastable states of Calcium-43$+$.   

Ion-trapping lab setup for quantum information experiments

The Allcock group at the University of Oregon is in the process of setting up a new ion trap lab. The broad purpose of our setup is to trap $+$Ca43 ions and use them for quantum information experiments. We are currently building and integrating: a macroscopic, linear Paul trap that will operate at room temperature; an ultra-high vacuum system; and a compact, rack-mounted laser system for ion cooling, state preparation, state readout, and logic gates. The apparatus includes an imaging system for collecting light from trapped ions for either counting photons or imaging individual ions, and a control system, based on ARTIQ hardware, gateware, and software, for managing and analyzing experiments.   

On direct geneation of ion-photon entanglement at telecom wavelengths in 171Yb+

Entanglement between small-scale quantum processors and flying qubits is the building block of quantum networking. Leading ion-photon entanglement demonstrations at telecom wavelengths achieve high-fidelity over distances up to 50 km [0,1]. These demonstrations used quantum frequency conversion and 40Ca+ ions. Here, we explore entanglement between 171Yb+ ions and photon polarization states at 1350 nm (P3/2-D3/2) and 1650 nm (P3/2-D5/2). A cavity-mediated Raman interaction increases IR photon generation and collection efficiency. Driving the S-D quadrupole transition can map D-state coherences to the long-lived HF qubit. We also consider photon frequency qubits as an approach that decreases sensitivity to birefringence. Relative to two-species proposals, our approach avoids QFC, secondary ion species and swap gates [2]. [0] M. Bock, et al, Nature Communications (2018)9:1998 [1] V. Krutyanskiy, et al, NPJ Quantum Information (2019)5:72 [2] C. Crocker, et al, Optics Express(2019)27:20:28143   

Towards Building an Open-access Trapped Ion Quantum Information Processor for the Research Community

Trapped ions are a leading platform for quantum information processing with pristine qubits, fully connected interaction graphs, and long coherence times. Trapped ion NISQ processors have enabled an immense variety of research in academic and private sector groups, and are highly oversubscribed. A shared open-access processor would facilitate many research programs, particularly those requiring fine control over low-level hardware. In this poster, we present the progress towards developing QuantumIon - an open-access trapped-ion quantum information processor at University of Waterloo. We present innovative approaches to the optical, mechanical, and control challenges. A guided-light platform which combines state-of-the-art glass micro-machining technologies will provide fully controllable individual addressing for up to 16 Ba+ ions. The control system will use a distributed configuration of fast commercial FPGAs capable of providing real time branching decision logic. Using established networking protocols pulled from a variety of industries this control system straightforwardly scales to increasing numbers of qubits and even increasing numbers of networked traps.   

Towards a large scale fully-programmable trapped-ion quantum spin simulator

A trapped-ion quantum simulator can simulate models of quantum many-particle systems that may be otherwise intractable, such as frustrated spin systems and fundamental forces in high energy physics. Our trapping architecture is based on a multi-segmented `blade electrode' Paul trap, capable of producing anharmonic confining potentials to trap and control a long chain ($>$50) of Ytterbium ions with near-uniform spacing. A holographic optical addressing system is integrated for aberration-corrected optical engineering, providing the capability to exert programmable and dynamic control over non-trivial many-body Hamiltonians at the level of individual ion-spins and interactions between them. Leveraging powerful modern machine-learning tools [1], the quantum simulator can in principle be programmed to realize an arbitrarily connected spin network, allowing the simulation of dynamical spin systems on arbitrary lattice geometries in higher dimensions. \\ \text{[1]} Yi Hong Teoh , Marina Drygala, Roger G. Melko, and Rajibul Islam, \textit{Quantum Science and Technology} \textbf{5}, 024001 (2020)   

Ultra-long-range molecules and ultracold heavy Rydberg systems

Ultralong-range Rydberg molecules (ULRMs) are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. Heavy Rydberg systems (HRS) are highly excited, binary atomic systems, which consist of a positive and a negative ion. The large reduced mass leads to high principal quantum numbers up to several thousand, which can be achieved in ultracold samples. We here propose an experimentally feasible and efficient protocol to create HRS via photoassociation to an intermediate ULRM. The Rabi coupling is typically in the MHz range and the permanent electric dipole moments of the HRS can be as large as one kilo-Debye. We identify specific transitions which place the creation of the heavy Rydberg system within immediate reach of experimental realization.   

Non-adiabatic Quantum Interference Effects and Chaoticity in the Ultracold Li + LiNa $\to$ Li$_2$ + Na Reaction

Quantum reactive scattering calculations for the ultracold Li + LiNa $\to$ Li$_2$ + Na reaction are presented which include both the ground and first excited doublet electronic states. In the interaction region the excited electronic state exhibits a conical intersection with the ground electronic state. This intersection is energetically accessible even in the ultracold regime for Li + LiNa collisions with ground state reactants. A numerically exact full-dimensional time-independent scattering method based on hyperspherical coordinates is used to compute the total, vibrationally, and rotationally resolved non-thermal rate coefficients for collision energies between $1\,{\rm nK}$ and $0.3\,{\rm K}$. A significant enhancement or suppression of up to two orders of magnitude is observed in many of the rotationally resolved rate coefficients. These effects are due to constructive or destructive quantum interference between the two scattering amplitudes which encircle the conical intersection. A statistical analysis of the rotational distributions shows a Poisson behavior which is indicative of the underlying classically chaotic dynamics.   

A few interacting fermions near the unitarity limit

Interacting few-fermion systems have been extensively studied in atomic physics, and their behavior at very large scattering lengths continues to pose stringent theoretical challenges. One naturally occurring class of systems that are close to unitarity arises in the nuclear few-body problem: key examples are the few-neutron systems that interact through the strong force. The $n$-$n$ two body $s$-wave scattering length is large ($\simeq$ $-18.9$ fm) compared to the range of the interaction ($\simeq$ 1-2 fm), which provides good criteria for studying near-unitarity physics. Low-energy scattering of the three neutron (3$n$) and four neutron (4$n$) systems are studied in the framework of the adiabatic hyperspherical method using an Explicitly-Correlated Gaussian basis. The 4$n$ problem is treated in the symmetry $J^{\pi}=0^{+}$ and $J^{\pi}=\frac{3}{2}^-$ for the 3$n$ system. These symmetries lead to the strongest attraction between the neutrons due to the large, negative two-body singlet $s$-wave scattering length. The nuclear interaction considered is a version of the Argonne nuclear potentials, the AV$8'$ potential, fitted to gaussians. The lowest few potentials are obtained and the energy-depenent phaseshift and time delay are computed for the lowest potential in each case.   

Using a Magneto-Optical Trap (MOT) to teach Experimental and Computational Methods in Undergraduate Physics.

We are using cold-atom physics to motivate our culminating undergraduate senior-level ``Experimental Methods in Physics'' course. Students continue to develop upon and refine previously-introduced computational methods by numerically solving a host of non-analytical problems, including a semi-classical simulation of atomic motion in a MOT. After an extensive literature review and basic laboratory instruction the student-teams endeavor to create a MOT. Previous experimental and theoretical coursework is reinforced through the hands-on setup of the cooling and repump laser systems and use of saturated absorption spectroscopy to observe the hyperfine structure of Rb. Finally, to form the MOT of $^{87}$Rb, students combine the light into a stand-alone vacuum cell that includes a Rb source and coils to establish an appropriate magnetic field gradient (manufactured by ColdQuanta). Time permitting, students then characterize the MOT by comparing their results to simulations. Updates and results from the second iteration of this new course will be presented at the meeting.   

Rovibrational optical cooling of $Rb_{2}$ in a supersonic beam

In this work, we propose to optically cool the rotation and the vibration of $Rb_{2}$ molecules in a supersonic beam by applying a broadband light source. Such source consists of a tapered amplifier laser with frequency-shifted feedback, around 682 nm, which can drive transitions from $\nu_{x}, J_{x}$ $X^{1}\Sigma_{g}^{+}$ ground state to the $b^{1}\Pi_{u}$ excited potential. The spectrum of our source is such that the $\nu_{x}, J_{x} = 0$ $X^{1}\Sigma_{g}^{+}$ ground state will be a dark state. The molecules will be observed by photoionization technique, through transitions from the $\nu_{x}, J_{x}$ to $\nu, J_{x}$ of the $b^{1}\Pi_{u}$ potential using a CW diode laser, and then photoionized by a 532 nm pulsed laser. Such technique will allow us to resolve the rotational distribution of the $\nu_{x}=0$. Theoretical simulations indicate that we should be able to perform the rovibrational cooling in less than 300 $\mu$s.   

On Demand

Cold molecular gases are the starting point for a large number of novel and interdisciplinary applications ranging from few- and many-body physics to cold chemistry and precision measurements. Especially heavy polar molecules, such as barium monofluoride, are perfect candidates for tests of fundamental symmetries and studies of complex quantum systems with strong, long-range interactions. However, in comparison to atoms, the preparation of molecular gases in the sub-Kelvin regime is complicated by their complex vibrational and rotational level structure and the lack of closed transitions for optical cycling. Nevertheless, thanks to favorable Franck-Condon factors and selection rules, quasi-cycling transitions can be identified for many molecular species, including barium monofluoride. In this contribution, we will report on our buffer gas beam source for slow and internally cold barium monofluoride molecules. Moreover, we will present our progress towards one-dimensional Doppler cooling of the molecular beam.   

$^{\mathrm{23}}$Na$^{\mathrm{87}}$Rb polar molecules in 3D optical lattice

In recent years, ultracold polar molecules have attracted more and more attentions due to their many potential applications. However, several recent experiments have observed strong inelastic losses even for ultracold molecules in their absolute ground states. While it is generally agreed that this unexpected loss is due to the formation of two-molecule complexes, no clear remedy to this issue is known other than isolating these molecules from each other. Here we report our progress on creating a sample of ground-state $^{\mathrm{23}}$Na$^{\mathrm{87}}$Rb molecules in 3D optical lattices. With a strong enough lattice potential, long-lived samples with lifetime of more than 10 seconds are observed. We will also discuss the investigation on the coherence between nuclear hyperfine levels and dipolar effects between adjacent lattice sites.   

Three-body collisions of ultracold dipolar molecules

A lot of effort is devoted nowadays to produce ground state ultracold molecules in high densities. Two-body collisions as well as three-body collisions can occur in those gases. In this poster, we present the hyperspherical formalism used to describe three-body collisions. We adapated the formalism of Kendrick et al. [1] to three identical particles such as dipolar molecules and including an electric field. To avoid numerical limits, we found a model to treat the dipolar molecules without their internal rotational structure. With this formalism, we can compute the adiabatic energies and rate coefficients for the three-body collisions. [1] B. K. Kendrick et al., J. Chem. Phys 110, 6673 (1999).   

Exotic dipole traps for $^{23}$Na$^{40}$K molecules

Mixing rotational states of dipolar molecules is essential to utilize their dipolar interaction and to simulate spin systems. We use a rotational-state-sensitive electronic transition to create a highly-tunable optical dipole trap for NaK molecules. By tuning the trapping light over a range of 10 GHz we can switch between a 'magic' and two 'tune-out' conditions for the states $|v=0, J=0\rangle$ and $|v=0, J=1\rangle$, while maintaining molecule lifetimes of about $1$ s or longer [1]. Here, $v$ is the vibrational and $J$ the rotational quantum number of the electronic ground state. The transition can be used to achieve long coherence times in superpositions of rotational states and to realize novel cooling schemes in optical lattices. [1] R. Bause et al., arXiv:1912.10452.   

Optical cycling, radiative deflection, and laser cooling of metal monohydride molecules

The past decade has seen major advances in direct laser cooling of diatomic and even polyatomic molecules, including trapping of ultracold samples for several species. A critical requirement for direct laser cooling is the demonstration of sustained optical cycling without loss to dark states, and control over the molecules spatial degrees of freedom using laser light. Here we present the first demonstration of optical cycling, radiative deflection, and Sisyphus cooling for barium monohydride molecules (BaH). This adds a new class of diatomic molecules, the alkaline earth monohydrides, to the rapidly expanding set of laser cooled molecules. Optical cycling rates are measured via depletion of the ground vibrational state and deflection of the molecular beam. Our results are consistent with the maximum scattering rate obtainable, based on a simulation of the Lindblad master equation for the complete system. Sisyphus cooling was carried out along one transverse dimension of a cryogenic buffer gas beam. Prospects for confinement in a magneto-optical trap will be discussed. We will also present preliminary results on optical cycling and manipulation of CaH, a lighter alternative to BaH.   

Toward non-destructive, dispersive imaging of ultracold molecules

There is currently a lack of high-fidelity and non-destructive imaging strategies for generic diatomic molecules, in particular for the commonly used bialkalis. Here, we propose and describe a technique to address this shortcoming using naturally occurring optical birefringence of excited rotational states. We will also discuss current experimental progress toward the creation of ground-state sodium-rubidium molecules and the demonstration of this proposed imaging scheme.   

Novel Laser-Coolable Molecular Species

Laser cooling techniques have recently been extended to diatomic and polyatomic molecules. The molecules that have so far been laser cooled are highly symmetric, linear molecules. Previous cooling schemes have relied crucially on these high symmetry states. Here, we identify several new classes of laser-coolable molecules with complex molecular and electronic structure. Among these are non-linear symmetric top molecules like CaOCH$_3$ [1], asymmetric rotors including CaSH and CaNH$_2$ [2], and exotic molecules with multiple optical cycling centers, such as CaCCSr [3]. We discuss ongoing experimental and theoretical work, including dispersed fluorescence spectroscopy, demonstrations of optical photon cycling, and structural calculations. The addition of such species to the laser-cooled molecular toolbox will lend itself to diverse applications ranging from quantum computing and simulation to quantum chemistry to precision measurements and fundamental physics. [1] Yu et. al., New J. Phys. 21, 093049 (2019). [2] Augenbraun et. al., arXiv:2001.11020 (2020). [3] Ivanov et. al., J. Phys. Chem. Lett. (2020).   

Magneto-optical forces applied to polyatomic molecules

In recent years, laser cooling has been successfully applied to diatomic molecular systems, resulting in robust magneto optical traps (MOTs) and grey molasses cooling to the $\mu$Kelvin temperature regime. Polyatomic molecules have additional (controllable) degrees of freedom, compared to their diatomic counterparts, that provide further advantages for a myriad of applications in quantum science [1-3]. Here we present the one-dimensional magneto-optical cooling and compression (1D MOT) of a cryogenic buffer-gas beam [4] of calcium monohydroxide (CaOH) molecules [5]. We establish a quasi-closed cycling transition and scatter 10$^3$ photons per molecule, with this number limited predominantly by interaction time. The resulting cooling and compression lead to an increase in on-axis molecular beam brightness and a reduction of temperature from 8.4 mK to 1.4 mK. This demonstration realizes a significant milestone on the route towards a 3D MOT of CaOH and the laser cooling of polyatomic molecules into the $\mu$Kelvin regime . [1] Kozyryev and Hutzler, PRL 119, 133002 (2017). [2] Yu et. al., New J. Phys. 21 093049 (2019) [3] Wall et. al., New J. Phys. 17, 025001 (2015). [4] Hutzler et. al., Chem. Rev. 112, 9 4803 (2012) [5] Baum et. al., arXiv 2001.10525   

Microwave control of ultracold molecular collisions

Microwaves can be used to engineer long-range interactions between ultracold polar molecules. Resonant dipole-dipole interactions induce strong interactions and high scattering rates in molecules collisions. Repulsive long-range interactions can be used to shield molecules from short-range loss.   

Observation of Magnetic Feshbach Resonances in Li-Yb Mixtures

We observe multiple interspecies magnetic Feshbach resonances between the open-shell Li and the closed-shell Yb ground state atom [1]. We resolve closely-located resonances that arise from a weak separation-dependent hyperfine coupling between the nuclear spin of ${}^{173}$Yb and the electronic spin of ${}^6$Li, and confirm their magnetic field spacing by ab initio electronic-structure calculations. Resonances are identified via trap-loss spectroscopy with the mixtures in a crossed optical dipole trap and varying magnetic field. The asymmetric loss profiles of the resonances show that three-body recombination in fermionic mixtures has a p-wave Wigner threshold. We plan to apply these resonances towards magnetoassociation of ultracold YbLi molecules in the electronic ground state. The ${}^2 \Sigma$ YbLi molecule possesses both electric and magnetic dipole moments that can be utilized towards ultracold chemistry, quantum many-body physics, and quantum information. [1] A. Green et al. arXiv: 1912.04874 (2019)   

Controlled Interactions of Polar Molecules in Two Dimensions

Degenerate polar molecules, which interact via long-range, anisotropic potentials, allow access to rich many-body physics. One challenge for realizing many-body interacting systems is the short molecular lifetime relative to the interaction energy, which is limited by chemical reactions and photo-induced loss of collision complexes. By confining potassium-rubidium molecules to two dimensions and applying an electric field to polarize the dipoles perpendicular to the plane of motion, we demonstrate strong suppression of inelastic loss and a corresponding enhancement of elastic collisions. We present preliminary results of direct evaporation of molecules, as well as progress towards single-site microwave addressing of molecules in an optical lattice and measurement of the dipolar interaction shift.   

Towards Scalable Generation and Control of Ultracold Singly-Trapped NaK Molecules

Ultracold polar molecules have been shown to possess long-lived coherent states and long-range electric dipole interactions, making them ideal candidates for applications in large-scale quantum information processing and quantum memory. The generation of these molecules involves starting from arrays of two atomic species cooled to the ground motional state of tightly focused optical dipole traps, before merging the atoms using Feshbach interactions and performing stimulated Raman adiabatic transfer into the molecular ground state. When combined with reconfigurable dipole trap arrays, a high degree of control over system Hamiltonians can be achieved, which is ideal for quantum simulation. We present the experimental progress made towards achieving this goal, primarily the efforts in cooling and trapping of single Na and K atoms for eventual generation of NaK molecules.   

Singlet Pathway to the Ground State of Ultracold Polar Molecules

We demonstrate a two-photon pathway to the ground state of $^{\mathrm{6}}$Li$^{\mathrm{40}}$K molecules that involves only singlet-to-singlet optical transitions. We start from a molecular state which contains a significant admixture from the singlet ground state potential by selecting the Feshbach resonance for molecule association. With the only contributing singlet state to the molecular state being fully stretched and with control over the lasers polarization we address a sole hyperfine component of the excited A$^{\mathrm{1}}\Sigma^{\mathrm{+}}$ potential without resolving its hyperfine structure. This scheme ensures access to only one ground state hyperfine component with sufficient Franck-Condon factors and moderate laser powers for both coupling transitions. Its implementation results in large and balanced Rabi frequencies, a favorable condition for the coherent transfer to the ground state. We perform dark resonance spectroscopy to precisely determine the transition frequencies of the states involved. The strong dipolar nature of $^{\mathrm{6}}$Li$^{\mathrm{40}}$K is revealed by Stark spectroscopy, as it is necessary for the study of dipolar interactions in an optical lattice.   

The diatomic molecular spectroscopic database

The spectroscopic constants of molecules contain crucial information regarding the electronic structure and properties of molecules and hence are of great interest in the atomic, molecular, and optical physics community. In this work, we develop a user-friendly and interactive website in which the user can get access to the spectroscopic constants and Franck-Condon factors of polar diatomic molecules. The spectroscopic constants are retrieved directly from the website or through our application programming interface. The registered users can also upload data to the database after authorization. This data-driven website may help to target the possible candidates for a range of applications, such as molecular laser cooling.   

Towards strongly correlated 2D gases of ultracold dipolar NaCs molecules

Ultracold dipolar ground state molecules open up new avenues to study many-body quantum systems with long-range dipole-dipole interactions and promise to become a novel platform for quantum simulation. In this project, we aim to use ultracold molecules of sodium-cesium (NaCs) to study strongly correlated quantum phases. Sodium-cesium molecules feature chemical stability in the ground state and an electric dipole moment of 4.6 Debye. We plan to create these molecules from ultracold mixtures of sodium and cesium and will report on progress towards simultaneous cooling of the two atomic species to quantum degeneracy, as well as preliminary studies of interactions in this new atomic mixture. We will trap the mixture in two dimensions using an accordion lattice potential, explore intra- and interspecies Feshbach resonances, study the impact of reduced dimensionality on molecule formation, and identify a pathway towards the molecular ground state of NaCs.   

Toward Microscopy of a Degenerate Bose Gas of Polar Molecules

Recent years have seen rapid progress in creating and studying ultracold gases of polar molecules. These molecules are attractive candidates for quantum simulation of many-body systems, such as the XXZ model of quantum magnetism, due to their long-range anisotropic interactions and rich internal structure. Here we present our progress toward a new apparatus to perform site-resolved microscopy of a degenerate Bose gas of polar $^{\mathrm{23}}$Na$^{\mathrm{87}}$Rb molecules confined within a 2D optical lattice. We have constructed a rubidium quantum gas microscope, and we are currently working toward the production of ground-state NaRb molecules. We plan to overlap dual 2D Mott insulators of sodium and rubidium atoms before adiabatically sweeping across the Feshbach resonance to form weakly-bound molecules. Following STIRAP to the molecular ground state, evaporation can then proceed using in-vacuum electrodes to generate a strong electric field orthogonal to the lattice plane, suppressing inelastic collisions. These electrodes also allow us to tune the interactions between the molecules. We will perform quantum gas microscopy by dissociating the molecules and performing site-resolved fluorescence imaging of the constituent atoms.   

Towards a Quantum Gas Microscope for Laser-Cooled Molecules

Ultracold molecules, with their rich internal structure and long-range dipolar interactions, could be a powerful platform for applications ranging from quantum simulation and information processing to ultracold chemistry. Here we report on progress towards a new apparatus for laser-cooled CaF molecules. Our apparatus is designed to produce large samples of trapped molecules while allowing detection and control at the single molecule level. These capabilities could be important for future explorations in quantum science, such as simulating spin models and building molecular qubits.   

Coherent spin-rotation state transfer in TlF

The aim of CeNTREX (Cold molecule Nuclear Time-Reversal Experiment) is to search for the proton’s electric dipole moment by exploiting the Schiff moment of $^{205}$TlF in the polar molecule thallium fluoride (TlF). To maximize the molecular flux, an electrostatic quadrupole lens is employed to collimate a TlF beam. After rotational cooling, the first few rotational ground states of a cold TlF beam have been emptied into a single J=0 hyperfine level in the $^1\Sigma^+$ electronic ground state. In order to populate a weak-field seeking state that the lens can optimally affect, microwaves are required to transfer TlF from J=0 to J=2. Transitioning from this state preparation region into the electrostatic quadrupole field of the lens will induce non-adiabatic transitions to unwanted states due to rapidly changing fields. This poster describes the recent progress in efficient, coherent spin-rotation state transfer in TlF.   

Development of the Axion Resonant InterAction DetectioN Experiment (ARIADNE)

The Axion Resonant Interaction Detection Experiment (ARIADNE) will look for monopole-dipole interactions mediated by the QCD axion field in the mass range of 1$\mu $eV to 6meV. Modulating an unpolarized Tungsten mass in close proximity to polarized helium-3 gas creates an effective transverse magnetic field as seen by the He-3 spins, which drives a nuclear magnetic resonance transition. The experimental principles, the expected challenges of the experiment, as well as the latest updates will be discussed.   

On Demand

The baryon asymmetry of the universe—the presence of matter in far greater abundance than antimatter—is an ongoing scientific mystery. Since the Big Bang is expected to have produced matter and antimatter in equal amounts, physicists have developed theories to account for the processes that have led to this asymmetry. Many of these theories predict a violation of the T (time reversal) symmetry at levels that exceed the Standard Model predictions. The existence of a nuclear Schiff moment is an example of such a T violating phenomenon. Our experiment, the Cold Molecule Time Reversal Experiment, or CeNTREX, is designed to measure the Schiff moment of the thallium nucleus. I present progress towards this measurement, including a cryogenic buffer gas beam of thallium fluoride (TlF) molecules and spectroscopic characterization of TlF with an ultraviolet laser system. Additionally, I report on future steps and the experimental layout for measuring the Schiff moment of thallium using TlF.   

Upgrading the ACME electron EDM search with a molecular lens

Measurements~of the electron~electric dipole moment (EDM) using cold molecules~set very powerful constraints on T-violating new physics beyond the Standard Model. The best upper limit on the electron EDM was recently set by the ACME collaboration: \textbar de\textbar \textless 1.1E-29 e\textbullet cm [Nature~562,~355 (2018)], using thorium~monoxide (ThO). A major upgrade in statistics for next generation of ACME is now underway, using a molecular lens to focus molecule flux into the EDM measurement region. Here, we report the first measurements [arXiv:1911.03015] of relevant properties of the Q state, which appears ideal for molecular lensing. Also, we demonstrate a double-STIRAP procedure that transfers population into and out of the Q state with 90{\%} efficiency. These combined with trajectory simulations on an electrostatic hexapole allow us to project a signal rate improvement by over an order of magnitude relative to an unfocused molecular beam.   

Progress towards improved precision of the electron and positron magnetic moment measurement

The measurement of the electron magnetic moment, measured to a precision of 0.28 ppt [1], gives one of the most stringent tests of the standard model, with an intriguing discrepancy of 2.4 standard deviations between the measurement and the prediction [2,3]. An apparatus has been developed~which reduces the effects from external magnetic and vibration noise, thought to have caused the largest systematic uncertainty in the previous measurement. These advances and new techniques are aimed at~obtaining a measurement an order of magnitude more precise [4]. Positrons from a student safe source will be used to measure the positron magnetic moment two orders of magnitude more precisely and give the most precise lepton test of CPT invariance.~ 1. D. Hanneke, S. Fogwell, and G. Gabrielse,~Physical Review Letters~100~(2008) 120801 2. T. Aoyama, T. Kinoshita, M. Nio, Atoms 7 (2019) 28. 3. R. H. Parker,~C. Yu,~W. Zhong, B. Estey, and H. M\"{u}ller,~Science~360~(2018) 191 4. G. Gabrielse, S. E. Fayer, T.G. Myers, X. Fan, Atoms 7 (2019) 45.~~   

Search for Axion topological defects using the Global Network of Optical Magnetometers for Exotic physics (GNOME)

The Global Network of Optical Magnetometers for Exotic physics (GNOME) is a network of geographically separated, time-synchronized atomic magnetometers and co-magnetometers in magnetically shielded environments. This configuration allows monitoring the energy splitting of Zeemann sublevels in an atomic ensemble continuously and simultaneously at different places all over the Earth. Axion-like particles could form topological defects that couple to atomic spins. Such an interaction would alter the Zeeman sublevel energy splitting producing a transient signal in the magnetometer network. The Earth’s movement is used to probe different regions of the galaxy for such defects. Possible candidates for the topological defects are domain walls which would be observed as an event plane crossing the earth following a predictable signal pattern. A time-domain analysis method was developed to look for correlations between the different magnetometers compatible with an axion domain-wall$^2$ . These methods are applied to the data gathered by GNOME in order to identify possible axion domain-wall events. $^2$ H.Masia-Roig, J. A. Smiga et al., arXiv:1912.0872   

Spin-Exchange Relaxation Free Magnetometer for the Global Network of Optical Magnetometers for Exotic Physics (GNOME)

Ultralight axion-like particles are a possible candidate for dark matter. These particles could result in cosmic topological defects such as domain walls or axion stars. The Global Network of Optical Magnetometers to search for Exotic Physics (GNOME) is looking for a transient signal caused by exotic-spin couplings as the Earth passes through such topological defects. We describe the Oberlin magnetometer station and present its performance during the latest GNOME science run. The magnetometer consists of a single-beam, spin-exchange relaxation-free (SERF) magnetometer that uses a vapor cell of potassium atoms with helium as a buffer gas. The cell is housed inside a four-layer magnetic shield. We use circularly polarized light resonant with $D_1$ transition to optical pump the atoms into a magnetically sensitive dark state. The transmission through the vapor cell is monitored and fed back to magnetic field coils to maintain zero field inside the cell. We also discuss the implementation of a co-magnetometer configuration that has the potential to improve the sensitivity of the detector.   

Local dark matter density estimation using Doppler spectroscopy of stars and pulsar timing

Doppler spectroscopy of stars has been extremely successful in the detection of exoplanets. We show that this technique can also be used to directly measure the gravitational potential of the Milky Way galaxy, and thereby determine the local dark matter density without any assumptions of dynamic equilibrium. In our work, we present a realistic strategy to observe the differential accelerations of stars in our Galactic neighborhood with next-generation telescopes, and provide numerical simulations of the expected sensitivity of such a program. We also present preliminary results of similar acceleration measurements derived from pulsar timing data, with an analysis of systematic errors.   

Update on the search for dark matter transient signatures using the GPS atomic clocks

A network of quantum sensors, such as the network of 32 Rb and Cs atomic clocks suited aboard the Global Positioning System (GPS), have shown to be a capable aperture for searching for exotic physics, such as clumpy dark matter. Topological Defect dark matter (DM) is an example of clumpy dark matter, which may take the form of a 0D monopoles or Q-balls, 1D strings, or 2D domain walls. For a 2D domain wall, the expected DM signal in the atomic clock data is a sweeping chirp in the clock data as the DM wall propagates the GPS constellation. A Bayesian statistical method is employed to search the 20 years of archival GPS data for transient dark matter signatures from 2D thin domain walls. For each potential dark matter candidate event, we carry out parameter estimation for the velocity, and geometry of the DM encounter. If no dark matter events are observed then powerful constraints may be placed on these models by computing the posterior distribution for the coupling strength.   

Searching for a relaxion halo with the Global Network of Optical Magnetometers for Exotic physics (GNOME)

The relaxion is a hypothetical ultralight boson proposed to solve the hierarchy problem [Graham, Kaplan, and Rajendran, Phys. Rev. Lett. {\textbf{115}}, 221801 (2015)]. Relaxions are also a dark matter candidate. The relaxion field couples to atomic spins and would lead to an oscillating signal detectable with atomic magnetometers. It is possible that relaxions collect in a halo in the gravitational potential of the Earth or Sun. In this scenario, the relaxion density is much greater than the average dark matter density in the Milky Way, resulting in enhanced signals [Banerjee et al., Communications Phys. {\textbf{3}}, 1 (2020)]. The Global Network of Optical Magnetometers for Exotic physics (GNOME) is an array of geographically separated, time-synchronized, atomic magnetometers whose purpose is to search for correlated signals heralding exotic physics [Afach et al., Physics of the Dark Universe {\textbf{22}}, 162 (2018)]. We discuss a search algorithm for GNOME data based on cross-correlation analysis that targets signals produced by a relaxion halo.   

Search for Axion Stars Using the Global Network of Optical Magnetometers for Exotic Physics (GNOME)

The Global Network of Optical Magnetometers for Exotic physics (GNOME) searches for evidence of exotic spin coupling between elementary particle spins and topological defects in a field of ultra-light axion-like particles (a possible candidate for dark matter). One of the network's search targets is a proposed dark matter structure known as an axion star or Q-ball. We present an analysis method designed to search for evidence of such structures. The analysis includes an initial stage based on the excess power technique that identifies transient oscillatory signals coincident across multiple detectors. This is followed by a consistency check in which the relative signal amplitudes in each station and the sensitive axis of each detector are used to establish the most likely magnitude and direction of the event.   

Noise characterization of atomic magnetometers on the GNOME network

The GNOME (Global network of atomic magnetometers for exotic physics) experiment comprises a network of shielded atomic magnetometers designed to search for spin interactions with fields that have been proposed in various extensions of the standard model such as axions. The experiment relies on the stable operation of the sensors over long ($\sim$ months) intervals. Our goal is to develop a noise model for each sensor on the network which can be used in subsequent analyses. We report on (1.) a characterization of the noise non-Gaussianity during a dedicated observational run, and (2.) an excess power analysis of the data in search of signals coincident with known astrophysical events.   

Search for Exotic Field Emission from the GW170817 Binary Neutron Star Merger Using GPS Atomic Clocks

Bosonic fields beyond the standard model of particles are proposed as constituents of dark matter and dark energy, and they appear as potential solutions to the strong-CP and hierarchy problems. These fields interact feebly with the standard model particles and fields; therefore, precision quantum sensors are an ideal candidate for detection. We focus on fields generated from highly energetic astrophysical events such as binary neutron star and binary black hole mergers and look for their signatures in GPS atomic clock data. For these signatures to be correlated with LIGO triggers, the fields must be ultrarelativistic and ultralight. We implement the excess power statistic method and search for exotic field signatures in GPS clock data near the binary neutron star merger measured by LIGO in August of 2017 (GW170817).   

A Multiplexed Strontium Optical Lattice Clock for Tests of Fundamental Physics

Optical lattice clocks are amongst the most accurate and precise devices ever built. Their remarkable stability is now giving rise to a number of novel applications. We are building a “multiplexed” strontium optical lattice clock, which will enable high precision differential measurements between two ensembles of ultracold strontium atoms confined in independently addressable lattices. In this poster, we will present recent progress in building an ultra-high vacuum chamber reaching pressures of low 10$^{-12}$ Torr and lifetime measurements of strontium atoms magnetically trapped in the $^3$P$_2$ state in our apparatus. Updates on a two-stage magneto-optical trap for laser cooling to $\mu$K temperatures and demonstration of sequential trapping of all stable strontium isotopes will be shared. We will then discuss our plans to study fundamental physics by performing new test of general relativity. We also propose new methods for evaluating clock systematics, studying isotope shifts, and achieving quantum enhanced clocks via Rydberg interactions with our multiplexed clock.   

MEMS uniform non-magnetic heating device for miniaturized atomic magnetometer

Miniaturized atomic magnetometer can be used for magnetoencephalogram source localization. The key technology of atomic magnetometer, vapor cell contained alkali metal atoms, requires a uniform temperature field to achieve superior sensitivity. In this study, ITO (Indium Tin Oxide) which is transparent and conductive is proposed as heating resistance wires to fabricate the heating films. A 300nm thick ITO film can transmit 95{\%} of light without affecting the polarization state of the light. Consequently, the vapor cell can be heated in five surfaces to achieve the uniform temperature field without considering the impact to the optical path. According to the experimental results, the proposed heating films can achieve 200 degrees Celsius, which can support alkali metal atoms such as potassium and rubidium sufficiently. Furthermore, two ITO layers with the same shaped island by insulation layer that configures the current to double back on itself to reduce the magnetic field caused by heating current. In addition, in the condition of the input bias of 50kHz AC, low-frequency magnetic field noise can be reduced. The proposed MEMS uniform non-magnetic heating device can be used in atomic devices such as chip scale atomic magnetometer and gyroscope.   

An Atomic Gradiometer with Two Parallel Elliptically Polarized Laser-pumped Used for Magnetocardiography

A new type of compact atomic gradiometer was designed and integrated. The gradiometer utilizes two parallel elliptically polarized light beams to optically pump atoms. To achieve higher sensitivity, the gradiometer works in the SERF regime. The circularly polarized components of both elliptical laser beams are used to polarize atoms, while the linearly polarized components are used to detect the atoms' spin polarization state. These two parallel beams of the gradiometer do not interfere with each other and can work independently in the magnetometer mode or constitute a gradiometer. The sensitivity of the magnetometer is near 22 fT/$\sqrt{\mathrm{Hz}} $, and the corresponding gradient sensitivity can reach 14 fT/cm/$ \sqrt{\mathrm{Hz}} $ on a 1 cm baseline. Using this gradiometer, magnetocardiography measurement was successfully performed. The experimental results show that in a poor magnetic shielding environment, the magnetometer cannot clearly measure the magnetocardiography signals due to the fluctuations of the environmental magnetic field, while the gradiometer can successfully extract clear magnetocardiography signals. The common-mode rejection ratio, bandwidth and working range of the magnetic gradiometer were also measured and explained.   

MEMS non-magnetic electric heating chip for integrated atomic sensors

The alkali metal vapor cell of most atomic devices requires high temperature and non-magnetic environment, while the heating current will introduce additional magnetic field and unexpected magnetic flux density gradient. It is necessary to develop a non-magnetic heater for atomic devices. In this paper, a new design for non-magnetic heating chip, fabricated by the MEMS technique, is proposed for the integrated atomic sensors. Platinum (Pt) is chosen as the material of resistance. The chip is composed of two layers of the same serpentine-shaped resistors to cancel the magnetic flux density. There are two sets of wires in each layer used as a thermometer resistor and a heating resistor forming a feedback loop of temperature control. The integration of heating and temperature measurement is beneficial for the miniaturization of physics package. The simulation results show that magnetic effect between layers can be reduced by 4 orders than in one layer. The experiment results show that the temperature coefficient of resistance (TCR) is approximately 0.224{\%}/K. The consistency of the resistance is better than 97.7{\%}. The fluctuation of temperature at 383.15 K is under 10 mK. The magnetic flux density introduced by the current in the Z direction is 0.22146 nT/mA.   

A method to measure the residual magnetic field in the magnetic shields of a compact nuclear spin co-magnetometer

The compact co-magnetometers are widely used because of its advantage to suppress the error induced by magnetic field fluctuation. The measurement of the residual magnetic field is valuable in the development of co-magnetometers. However, it is difficult to put external sensors into the small magnetic shields, and the direct in-situ measurement is affected by light shifts and nuclear polarization. In this paper, we put forward a method to eliminate these effects and obtain the real magnetic field in the magnetic shields. Firstly, the measured residual magnetic field orthogonal to the pump beam has linear relationship to the probe intensity, and the real residual field is the intercept on y axis. Then this field can be compensated to zero, and finally we get the residual magnetic field parallel to the pump beam by measuring the resonance frequency shift when the main magnetic field and pumping light are flipped simultaneously. The experiment is implemented on a set of compact cylinder magnetic shields, and the results show that the axial and radial residual magnetic field is 58 nT and 8.5 nT, respectively. This method can obtain the real residual magnetic field in the compact magnetic shields, which is useful for the research of magnetic shields design and demagnetization.   

The K-Rb-3He co-magnetometer for the GNOME

Atomic magnetometers are used to search for exotic physics. Yet, to limit the role of the magnetic field, such devices are typically operated as co-magnetometers. A specific example of the co-magnetomer is the system based on the mixture of a noble gas and alkali-metal vapor occupying the same glass cell. Coupled evolution of these spin samples at a specific magnetic field (so-called self-compensation mode) enables suppression of magnetic noise leaving nonmagnetic-coupling sensitivity unaffected. We describe the progress in construction of a K-Rb-3He magnetometer at the Jagiellonian University in Kraków. Due to operation in the spin-exchange relaxation free regime at the self-compensating mode, the comagnetometer is characterized with high sensitivity to nonmagnetic coupling. Careful investigation of the role of various experimental parameters will be presented. Future application of the comagnetometer in the Global Network of Optical Magnetometers for Exotic physics searches, searching for topological dark matter, will be also discussed. In the future, the comagnetometer will be used to search for domain walls of axion-like fields and axion planets or stars, which, within various models, are viable dark-matter candidates.   

Not Participating

Velocity map imaging (VMI) is a standard technique of gas-phase chemistry enabling the detailed investigation of molecular structure and reaction dynamics with an energy resolution that can exceed $h \times 1\;\mathrm{GHz}$. In typical VMI, the species of interest are initially neutral. We describe progress towards realizing a new type of VMI technology in which the species of interest are trapped, cold atomic and molecular cations. This extension of the VMI technique could be used to explore new realms of ion and plasma chemistry and bring to bear the many established advantages of ion traps, including long interaction times, single-particle addressability, and the ability to prepare pure-state ultracold reactants. We present preliminary data on VMI of photodissociated cold BaCl${}^+$ from a linear quadrupole ion trap.   

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Many common chemical sensors for environmental contaminants are based on a change in optical absorbance. The gold standard for measuring optical absorbance is UV/VIS spectrometry, but this typically requires an expensive bench-top instrument. Here we present a hand-held low resolution filter-based spectrometer that measures optical absorbance in six wavelength bands of the visible spectrum, built for less than \$100. This is sufficient to quantify the absorbance of several common color-based chemical sensors used for the detection of contaminants in water. We demonstrate our device by measuring fluoride concentrations in drinking water samples using an EPA-approved protocol (EPA-NERL 340.1) and show that our 6-channel device outperforms single-wavelength photometric measurements taken with an industry-standard commercial photometer in both detection threshold and sensitivity.   

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Cool (molecular) plasmas are ubiquitous throughout the Universe. Practically all opacity and emissivity studies of molecular plasmas are conducted utilizing data or codes taken from several different sources. To this end, we are developing a fully generalizable self-consistent approach to model cool hydrogen (H$_2$ and H$_2^+$) plasmas opacity and emissivity. Here we present results of cool hydrogen plasmas emission, and investigate the importance of electronic excited states.   

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We show a new multi-pump four-wave mixing configuration, with a potentially useful phase-dependence. We find that, for certain phase values of the input probes, the intensity noise of any output mode can be lower than that of its phase-insensitive counterpart. This lower-noise amplification has been demonstrated previously in atomic four wave mixing, but only with the use of significantly more complex experimental configurations, e.g. dual homodyne detection or cascaded vapor cells. Additionally, our method naturally results in four beams that can be squeezed or quantum correlated with one another. This result has obvious applications in the simplification of quantum optical experiments that involve the generation or amplification of more than two correlated modes. We describe how our findings may further be employed in a ``touchless'' or interaction-free SU(1,1) interferometry scheme, wherein a phase measurement may be made remotely on a pair of modes without introducing loss or destroying any squeezing between them.   

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A multi-component Fermi gas with SU($N$) symmetry is expected to behave like spinless bosons when the number of internal states $N$ becomes large weakening constraints from the Pauli exclusion principle. In this poster, we report direct evidence for bosonization by the measurement of contacts in a three-dimensional (3D) SU($N$) fermionic gas of $^{173}$Yb with tunable $N$. Imaging the column integrated momentum distribution with a high signal-to-noise ratio, we find that the contact per spin approaches a constant with a $1/N$ scaling in the low fugacity regime. This scaling reveals the vanishing role of the fermionic statistics in thermodynamics, and unfolds the intriguing nature of bosonization in 3D SU($N$) fermions. In addition, we will discuss complementary characterization of SU($N$) fermions including the collective modes and the machine learning aided study of a three-dimensional gas of SU($N$), which could be alternative route to reveal bosonization.   

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Driving quantum systems out of equilibrium can generate exotic and novel phases of matter. Floquet engineering focuses on the realization of effective, static Hamiltonians by driving systems periodically in time. In the pursuit of simulating lattice gauge theories in the laboratory, we present the successful implementation of a two-frequency driving scheme in a Hubbard dimer, which explicitly breaks time-reversal symmetry and allows to engineer density-dependent Peierls phases. We demonstrate the winding structure of this phase around a Dirac point in the driving parameter space. In Floquet schemes, in general, the choice of driving frequencies for the implementation of effective Hamiltonians is limited by resonances to energetically higher-lying modes, e.g. transitions to higher Bloch bands of an optical lattice. We implement a coherent control scheme by which we overcome this frequency constraint. By adding a second drive at twice the frequency and tuning the relative phase between the two drives we achieve destructive interference of the two paths. This extends the lifetime of the spin correlations in our many-body system by more than two orders of magnitude compared to the singly-driven system.   

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Lieb and Mattis have shown that ferromagnetism is impossible to achieve in the ground state of fermionic systems, our work focusses on identifying stable ferromagnetic correlations emanating in the excited states of 1D ultracold systems of few fermions. The stability of such correlations can be attributed to the Hund exchange interaction inherent in those setups. However, these ferromagnetic correlations are connected to neither the stability of the magnetization nor the phase separation of the spin-components, contrary to the well enstablished framework of the Stoner instability.   

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The more complicated quantum phase space of spin-1 atoms compared to the spin-1/2 case offers unique capabilities, but also provides unique challenges for quantum control and measurement. Our work with ultracold, spin-1, rubidium 87 atoms in an all-optical trap has given us insight into how holonomic-type schemes could be realized in an atomic system. We demonstrate the creation and readout of a non-Abelian geometric phase in a spin-1 quantum system. Furthermore, by implementing microwave techniques to selectively isolate hyperfine states, we are able to construct multi-level transitions with an accuracy of 99.5{\%}. We will discuss how these techniques can be applied to quantum metrology, quantum gates, and quantum tomography with spin-1 systems.   

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Two-dimensional arrays of ions in individual microtraps are a promising technology for quantum computation and simulation. In collaboration with Sandia National Laboratories, we have developed micro-fabricated surface electrode traps that confine three ions on the vertices of equilateral triangles, with each ion confined in a separate potential well. This feature, and the small inter-ion distance (30 $\mu$m), allows for selective coupling between ions that can be dynamically changed during single experiments. In principle, this approach enables simulation of arbitrary, tunable spin-lattice Hamiltonians. Quantum simulations of bosons in synthetic magnetic fields can also be performed using motional excitation of the ions (phonons), and not internal ion states, as the controllable quantum system of interest. In an effort to reduce motional decoherence of the ions, as desired for these simulations, the traps are operated at cryogenic temperatures ($\sim$4 K). We report progress on trapping and manipulating ions in these 2D-array traps.   

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Molecular ions are proposed to be promising candidates for high precision measurements of fundamental constants, cold chemistry dynamics control, and quantum information processing. Particularly with regards to quantum computer engineering, the rich internal structures and long range dipole-dipole interactions between molecular ions offer a means of potentially overcoming some of the current problems of atomic ion platforms. \footnote{E. Hudson and W. Campbell, 10.1103/PhysRevA.98.040302.}\footnote{ W. Campbell and E. Hudson, arXiv:1909.02668.}. Here, we report our progress towards dipole-phonon interaction with molecular and atomic ions. A Calcium ion is cooled near its motional ground state and is used to excite a dipole transition of a co-trapped molecular ion by delicately controlling the phonons. Progress towards dipole-phonon logic gate is also presented.   

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We present a general formulation of multichannel quantum-defect theory (MQDT) for anisotropic long-range potentials. The theory greatly expands the types of interactions, including complex interactions involving molecules, that can be treated and understood systematically. It promotes MQDT into a general theory of interactions and establishes a foundation for new classes of quantum theories for chemical reactions, few-body systems, and many-body systems.   

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We discuss the concept of ``arrangement'', traditionally found in the context of few-body rearrangement collisions, in a more general context of an $N$-body quantum system. We show that for an $N$-body quantum system with attractive interactions that can bind the constituent particles, the concept of arrangement provides both a necessary and an important basis for understanding its complexity and the general structure of its Hilbert space. The concept is a necessary part of a foundation for a more complete understanding of $N$-body quantum systems, especially those made of atoms and molecules.   

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We report progress towards the building of a quantum gas microscope for molecules that has the flexibility to produce RbCs or KCs diatomic molecules. A quantum gas microscope for molecules combines the state-of-the-art imaging and addressing techniques currently employed in atomic quantum gas microscopes and applies them to molecule experiments. The long-range dipole-dipole interactions between heteronuclear polar molecules will allow for studies, all with single lattice-site resolution, of extended Hubbard models, which are expected to exhibit much richer many-body physics, including novel checkerboard, star, and stripe phases.   

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Ultracold polar molecules are actively being explored as potential candidates for quantum simulation, quantum information processing, and precision testing of fundamental physics. Polar molecules involving alkaline earth atoms such as CaF have attracted considerable attention and direct laser cooling and trapping of CaF have recently been reported. A second-stage cooling may involve sympathetic collisions with ultracold alkali metal atoms such as Li but its applicability may be limited by exothermic reactive scattering. Here we explore elastic and inelastic (reactive) collisions of Li with CaF molecules in the cold and ultracold regime. In particular, we report the characteristics of highly anisotropic potential energy surface of Li+CaF and LiF+Ca obtained from extensive ab initio calculations and quantum scattering calculations of the ultracold Li+CaF$\to$ LiF+Ca chemical reaction using hyperspherical coordinates.   

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Cold polyatomic molecules provide fascinating research possibilities in physics and chemistry. The workhorse for producing cold molecules is buffer-gas cooling. Here, we present a comprehensive theoretical and experimental study of molecule flux from a buffer-gas cell, operating in the effusive regime. Technical details of improvements to the cell design and temperature are shown. In addition, an investigation into both molecule-molecule boosting and helium boosting effects is also presented. By decreasing the cell length [1], reducing boosting into the cell and improving the temperature of our system, we have increased our signal by more than a factor two. In combination with our centrifuge decelerator, these molecule fluxes are now sufficient to study cold collisions between trapped polyatomic molecules. [1] Gantner et al., arXiv:2001.07759   

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A proposed diamond-based detector for weakly interacting massive particle (WIMP) dark matter would combine the advantages of solid-state semiconductor detectors with directional detection capability, allowing WIMP searches below the neutrino floor. This crucially relies on the ability to detect and map damage to the diamond crystal lattice at the nanoscale, to determine the direction of incoming WIMP candidates. Nitrogen vacancy (NV) centers are a prime candidate to enable this because of their strain sensitivity and well-characterized quantum properties. We present recent progress on techniques using NV centers to locate and map nuclear-recoil-induced damage, including crystal lattice strain and induced lattice vacancies.   

A Multi-Ion Photonic Integrated Optical Clock

Optical atomic clocks based on single trapped ions boast impressive stability and accuracy, but extension to multiple co-trapped ions is hindered by their strong Coulomb repulsion and associated quadrupole shifts. An alternative path is to multiplex the entire trapping apparatus, a feat made accessible by chip scale traps with photonic integration. This multiplicity brings new opportunities for improved short-term stability, Dick-noise suppression, and simultaneous Zeeman sublevel interrogation. While chip traps bring challenges for clock operation, particularly with regard to motional excitation, they also offer greater control over blackbody radiation and a clearer path towards portability. We explore these new opportunities with multiple $^{88}$Sr$^+$ ions loaded in separate zones of a fully photonic integrated chip trap and clocked on the $^5S_{1/2}$ to $^4D_{5/2}$ forbidden optical transition.   

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We describe a $^{\mathrm{\thinspace 87}}$Rb scalar gradiometer using two multipass cells which increase the path length of the probe beam by one order of magnitude. This gives a much higher optical depth on resonance, which is crucial for quantum-nondemolition (QND) measurements. As a result, we can directly record a large optical rotation. When the optical rotation exceeds $\pi $/4 radians, the optical rotation signal wraps around, showing multiple zero-crossings in a single Larmor period. This exotic signal gains a higher signal intensity, which indicates that a single photon can interact with higher number of alkali atoms. The magnetic field sensitivity then can reach beyond the naive Cramer-Rao lower bound, the minimum bound for the estimated frequency variance of a sine wave in the presence of photon shot noise. The lower probe power consumption is also critical for development of a miniaturized magnetometer. We have implemented a novel method of zero-crossing detection of the wrapped signals. We report a magnetic sensitivity of 7 fT/$\surd $Hz in the geomagnetic field range, which agrees well with the quantum spin noise limit.