Session K55: Ultracold Quantum Gases

Imaging and Probing Spin Polarons in Kinetically Frustrated Lattices

Kinetically frustrated lattices, even in the absence of superexchange interactions, are predicted to have magnetism appear in the form of itinerant spin polarons — bound states of magnons and charge dopants. Although signatures of this kinetic magnetism have recently been observed in doped van der Waals heterostructures, a microscopic observation is still lacking. Here, we present new results directly imaging itinerant spin polarons in a triangular lattice Hubbard system using a quantum gas microscope, where full spin-charge readout allows measurement of arbitrary n-point correlation functions. Around a hole dopant, we see enhanced antiferromagnetic spin correlations. Furthermore, we see enhanced ferromagnetic correlations in the presence of a charge dopant, a manifestation of the Nagaoka effect. We study the evolution of these correlations with density and interaction, and are able to use 4-point correlations to show the relative contributions of the kinetic and superexchange magnetisms. The robustness of kinetic magnetism at experimental temperatures allows for the exploration of potential mechanisms of hole pairing and superconductivity in frustrated systems. Additionally, we may be able to directly measure the binding energy of itinerant spin polarons in frustrated systems using Raman spectroscopy.   

BCS-BEC crossover in atomic Fermi gases in quasi-two-dimensional Lieb lattices: Effect of flat band at finite temperature

The superfluid behavior of ultracold atomic Fermi gases with a short  range attractive interaction in quasi-two-dimensional Lieb lattices  is studied using a pairing fluctuation theory, within the context of  BCS-BEC crossover, with a focus on the interplay of finite  temperature and flat band.  As the Fermi level enters the flat band,  the evolution of $T_c$ as a function of interaction strength $g$  changes from the conventional exponential behavior to power law,  along with strongly enhanced quantum geometric effects. The  temperature dependence of both the superfluid order parameter and  the high superfluid density also undergoes a similar  change due to the influence of flat band. At relatively high  densities and moderate or strong pairing interaction, a pair density   wave emerges. In addition, hole-like pairing occurs when the Fermi   level crosses the van Hove singularity, leading to nonmonotonic dependence  of the chemical potential $mu(g)$ on $g$..   

Flat band effects on the ground-state BCS-BEC crossover in atomic Fermi gases in a quasi-two-dimensional Lieb lattice

The ground-state superfluid behavior of ultracold atomic Fermi gases with an on-site attractive interaction in a quasi-two-dimensional Lieb lattice is studied using BCS mean-field theory, within the context of BCS-BEC crossover.  We find that the flat band leads to nontrivial exotic effects.  As the Fermi level enters the flat band, both the gap and the in-plane superfluid density exhibit an unusual power law as a function of interaction strength, in addition to a dramatic increase of compressibility as the interaction approaches the BCS limit as well as strongly enhanced quantum geometric effect. As the Fermi level crosses the van Hove singularities, the character of pairing changes from particle-like to hole-like or vice versa. We present the computed phase diagram, in which a pair density wave state emerges at high densities away from half filling and relatively strong interaction strength.   

Ultracold bosons in the flat band of an optical kagome lattice

The kagome lattice hosts a flat band resulting from extensive geometric frustration. For fermions, this makes the kagome antiferromagnet a candidate for studying the quantum spin liquid phase. But even for weakly interacting scalar bosons, the many-body physics in a flat band is complex and not fully understood. Stable loading of ultracold atoms into the flat band of an optical kagome is challenging, as it is not the ground band. For the first time, we load bosonic ³⁹K atoms into the flat band of the kagome lattice using a negative absolute temperature scheme. I will report on recent progress in identifying the many-body physics that comes into play as we melt a kagome Mott insulator into the flat band.   

Effect of disorder on multifractality and hyperuniformity in quasicrystalline Bose-Hubbard models

Despite the aperiodic structures of quasicrystals, we sometimes find quantum phenomena similar to those of crystals. However, the difference of quantum phenomena in crystals and quasicrystals has yet to be clearly understood. To quantitatively distinguish them, we apply multifractality and hyperuniformity to the characterization of nonuniform spatial patterns in the Bose-Hubbard model on the Penrose and Ammann-Beenker tilings. Based on the mean-field approximation, we obtain real-space distributions in the expectation values of bosonic condensate and number operators. In both Mott insulating and superfluid phases, the distributions are hyperuniform. Moreover, analyzing the order metric that quantifies the complexity of nonuniform spatial patterns, we find that the Penrose and Ammann-Beenker tilings show a divergence of the order metric at a phase boundary between the Mott insulating and superfluid phases, in stark contrast to the case of a periodic square lattice. Our results suggest that hyperuniformity is a useful method to differentiate between crystalline and quasicrystalline Bosonic systems. Next, we introduce on-site random potentials into the quasicrystalline Bose-Hubbard models, leading to a Bose glass phase. Contrary to the Mott insulating and superfluid phases, we find that the Bose glass phase is multifractal. We find that the same multifractality also appears on a Bose glass phase in the periodic square lattice. Therefore, multifractality is common in a Bose glass phase irrespective of the periodicity of systems.   

Confined states of a spinon gas in a mixed-dimensional XXZ model

Here we study a two-dimensional system where we consider the usual XXZ interactions in the x-direction and a simple Ising interaction in the y-direction, which we refer to as a mixed-dimensional XXZ model. This is in analog to the mixed-dimensional t-J models where hopping is restricted to one dimension. By using DMRG we study phase diagrams at different magnetizations of the system and uncover an extended region of an AFM ordered state at the zero magnetization, and a spin-stripe order at finite magnetization. By considering spin-spin correlations in the ground state and at finite temperature, we uncover melting of the stripes into a meson gas at low but finite temperature. Our research is motivated by the recent advancement of quantum simulation with cold atoms that carry magnetic dipoles, where such systems could be simulated. Dipole-dipole interactions in such systems could be used to engineer two-dimensional spin systems with tunable interactions in different spatial directions. In addition, we find a mapping of our spin system to a one-dimensional lattice gauge theory (LGT) with superconducting pairing terms, by considering the spin domain walls as hard-core bosons. We show that the confining term in the LGT basis emerges from the short-ranged spin-spin correlations on a mean-field level, and thus explain the confining signatures of the meson gas. Interpretation of the mixed-dimensional XXZ model in terms of LTGs thus provides simple understanding of the rich phase diagrams of these systems. In addition, we sample snapshots from our numerical calculations and study which experimental observables are best suited to probe confinement in a cold atom setup.   

Magnetoelectric response in bosonic insulators

In the absence of inversion and time-reversal symmetry, insulators exhibit a non-quantized magneto-electric response. For fermionic band insulators, it is well-known how to compute the corresponding linear response tensor from the band structure and Berry connection. We adapt this analysis to the case of gapped bosonic systems with a U(1) charge, and find a formula for the magneto-electric response in terms of the Berry connection on the bosonic modes. Such responses could be observed in Mott insulators coupled to synthetic gauge fields. Our formulae also permit the computation of the effective axion couplings in quantum spin ice coupled to appropriate antiferromagnetic orders.   

Structural complexity of Fermi Hubbard model snapshots

The structural complexity is a recently introduced unbiased measure to analyze images. This measure aggregates information about different scales present in the problem by performing a series of coarse-graining steps on concatenated samples, which at the end of the procedure produces a single number which encodes properties of the image whose connection the physics we wish to determine. In this work we study the evolution of the structural complexity in projective measurements (snapshots) of the two-dimensional Fermi Hubbard model across different filling fractions and temperatures spanning the antiferromagnetic regime and the strange metallic regions. We demonstrate that the complexity measure is linked to relevant physical observables of the model, such as the entropy and the double occupancy, and provides an immediately useful tool for ultra cold atom experiments. In addition, we further explore the application of this method to quantities other than projective measurements.   

Stability of a molecular Bose-Einstein condensate in atomic Bose gases

Recently a molecular BEC has been created out of a bosonic-atom condensate through application of a Feshbach resonance [1]. This observation makes it finally possible to probe a 

bosonic analogue of the widely studied BCS-BEC crossover seen in fermionic systems and allows access to a rich variety of phenomena. In this talk, using a two-channel Feshbach Hamiltonian, we theoretically characterize the associated stability. We do so here in the context of a many-body variational ground state which contains both condensates as well

as depletion and Cooper-pair contributions. We address both wide and narrow Feshbach resonances and show that for a sufficiently narrow resonance a molecular superfluid is stable except for a small region of magnetic fields in the immediate vicinity of the Feshbach resonance [2]; this applies to the resonance of ¹³³Cs atoms at B=19.849 G. By contrast

for more typical broad resonances such as those in ⁸⁵Rb, ⁷Li and ³⁹K the region of instability is substantial and there is little access to the purported quantum critical point phenomena.   

Study of the Interaction of Static Impurity within a Dipolar Environment

Information on the relaxation dynamics in quantum systems is essential to understand many-body systems. These dynamics are not only necessary for quantum mechanics but also important to understand several open questions in areas like high-energy physics, cosmology, and quantum data processing [1]. In the present work, we explore these dynamics using a static impurity in a quantum environment as our model. We delve into this by placing a static impurity in a three-dimensional Bose-Einstein Condensate made of dipolar gases. The Hamiltonian of the system was transformed in the frame of impurity, which led to a modified Gross-Pitavskii equation (GPE) [2]. This modified GPE was then solved using both analytical methods and numerical solutions through the split-step Crank-Nicolson method. We then calculated different properties of the static impurity, including its self-energy and density distribution. Additionally, we examined the effects of anisotropic impurities on density results by deforming the impurity. Further, by changing the orientation of the impurity at different deformations, we observed the density profile at several angles, revealing unique shifts due to the impurity's shape changes, emphasizing its complex interaction with the surrounding condensate.

References:

[1]        T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold Atoms out of Equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).

[2]        R. K. Kumar, L. E. Young-S., D. Vudragović, A. Balaž, P. Muruganandam, and S. K. Adhikari, Fortran and C Programs for the Time-Dependent Dipolar Gross-Pitaevskii Equation in an Anisotropic Trap, Comput. Phys. Commun. 195, 117 (2015).   

Joint first-order superfluid transition of a strongly ferromagnetic spin-1 Bose gas

The strongly ferromagnetic spin-1 Bose-Einstein condensate (BEC) has recently been realized with atomic ⁷Li [1]. It was earlier predicted that the ferromagnetic interaction, if sufficiently strong relativet to the spin-independent part of the potential, can drive the normal gas into a magnetized phase at a temperature above the superfluid transition [2]. In light of our recent negative result in the context of an unconventional superconductor [3], we re-examine this theoretical proposal and conclude that there exists no stable normal, magnetized phase for a dilute ferromagnetic Bose gas. For ⁷Li, we predict that the normal gas undergoes a joint first order transition and jump directly into a state with finite superfluid density. We estimate the size of the first order jump, and examine how a non-zero initial magnetic moment of the gas affects the first order transition.

[1] Huh, Kim, Kwon, and Choi. 2020, Physical Review Research 2 (3): 033471.

[2] Natu and Mueller 2011,  Physical Review. A 84 (5): 053625.

[3] How and Yip. 2023. Physical Review. B, Condensed Matter 107 (10): 104514.   

Fractional angular momentum quantization in Atomtronic circuits

In this talk, I showcase the latest results for bosonic and fermionic matter-wave circuits in the context of Atomtronics. For attractively interacting bosons, the system sees the formation of bound states, which are the quantum analogs of bright solitons found in the mean-field regime. Considering the full many-body regime allows us access to a new phenomenology arising from the strong correlations in the system. Specifically, for a ring geometry pierced by a synthetic gauge field, we find that the angular momentum quantization per particle acquires fractional values depending on the number of particles constituting the bound state [1]. The phenomenon of fractionalization manifests as new plateaus in the angular momentum and presents potentially important applications in the field of metrology and sensing. Analogous phenomenology is found in SU(N)-symmetric fermionic systems in a similar configuration. However, the physical origin of the angular momentum quantization present in these systems depends on the nature of the interactions, be they repulsive or attractive [2-3]. The feature of

fractionalization has promising applications to interferometry using these massive bound states in fermionic and bosonic systems.   

Characterization of NASA Cold Atom Laboratory potentials using variational techniques

In a recent atom-interferometry (AI) experiment, conducted aboard the NASA cold atom laboratory, a Bose-Einstein condensate (BEC) was formed too near to the atom chip wall for the AI experiment to be carried out [1]. The intent was to modify the BEC confining potential so as to move the BEC away from the atom-chip wall by tuning the external magnetic field and atom-chip currents. Unfortunately, instead of moving away from the wall, the condensate split into two pieces and the pieces flew out of the trap. Image data from the one available camera provided enough information for an estimate of an assumed unexpected stray magnetic field to match the motion captured by this camera. This estimate of the stray magnetic did not use the condensate width information contained in the images. We have used a variational approximation model for the solutions of the Gross-Pitaevskii equations [2] to refine the estimate of the stray magnetic field. We present the experimental data, the initial estimate of the stray magnetic field, our refined estimate and a program of tuning the external magnetic field and atom-chip currents that can be used to produce the intended intended motion of the condensate with the stray field present.   

Chiral current of Bose-Einstein Condensates via asymmetric tunneling

Tunnelling is one of the most well studied phenomena in quantum physics, and its implementations can be seen across many different fields. For example, the experimental creation of synthetic gauge fields, whose unique physics have opened new horizons in topological quantum matter and technology, is made much more complex due to the assumption that tunneling is symmetric. However, we computationally show the breaking of left-right tunneling symmetry using Bose-Einstein condensates (BEC) in 1D modeled by the Gross-Pitaevskii equation (GPE). These asymmetric tunneling dynamics suggests a simpler implementation for creating synthetic gauge fields: a trapped BEC in a quasi-1D ring-shaped potential comprised of periodic, asymmetric barriers. This trap exhibits left-right asymmetry in the transmission probability, thereby inducing a chiral motion of the BEC via directionally biased momentum. This is a signature of synthetic gauge fields, with the chiral current appearing as if it were induced by a magnetic field. Our computations employ experimentally feasible parameters such that these results may be experimentally demonstrated in the near future.   

Thermocrystallization in Lattice Dipolar Bosons Coupled to a High-finesse Cavity

Ultracold bosons trapped in optical lattices and coupled to a high-finesse cavity have been theoretically shown to stabilize supersolid phases at zero temperature for a vast range of densities ADD REF. In this talk, we will address the robustness of superfluidity and density-density correlations against temperature fluctuations. Our results our based on path-integral Monte Carlo by the Worm algorithm. Interestingly, we observe that the presence of cavity-mediated interactions is responsible for thermocrystallization. Indeed, with increasing temperature, density-density correlations are observed at densities and Hamiltonian parameters for which the ground state does feature such correlations. Our results provide valuable insights into the parameter space and temperature range for the detection of solid and supersolid phases.