Session G33: Quantum Simulation II

Suppression of phonon propagation in a Bose superfluid immersed in a degenerate Fermi gas

We investigate the behavior of sound propagation in a Bose-Einstein condensate (BEC) immersed in a degenerate Fermi gas (DFG). The interaction between the bosons and the surrounding fermions modifies the phonon dispersion with density perturbations of the DFG. Sound waves in the interacting mixture propagate with modified velocity as coupled excitations of the two species.

Our experiments utilize mixtures of bosonic ¹³³Cs and fermionic ⁶Li atoms cooled to quantum degeneracy and prepared in a linear optical trap. Using a microscope objective, we optically excite sound wave-packets and observe the resulting BEC dynamics in situ. We control the interspecies interaction and study its effect on the speed and decay rate of the phonons. We observe significant reduction of the sound speed in the presence of strong interspecies attraction. Our observations help develop more accurate theoretical models and lay groundwork for future applications of Bose-Fermi mixtures for quantum simulation.   

Non-adiabatic mapping from Fermi-Hubbard to t-J model via optical lattice ramps

The t-J model is believed to contain the essential physics of the doped Fermi-Hubbard model, relevant to the studies of high-Tc superconductivity. We propose a protocol to directly measure correlators in the t-J model using a fermionic quantum gas microscope. We can non-adiabatically map to the t-J model by preparing a Fermi-Hubbard state and simply ramping up the depth of the optical lattice, at a rate comparable to the initial tunneling strength. We perform exact diagonalization and sparse time-evolution on 1D and 2D Fermi-Hubbard systems and find that for the optimal ramp speed, various correlators measured in the ramped state approach the value expected for the corresponding t-J model. The slow lattice ramp allows doublon-hole pairs to recombine, effectively mapping to the restricted Hilbert space of the t-J model while preserving the spin-spin correlations coming from the super-exchange mechanism. We compare our numerics to a simplified 2-site analytical model as well as experimental data from our Lithium-6 fermionic quantum gas microscope and find good agreement. Further, we study the effect of slow ramps on estimating temperatures from spin-spin correlations in a Fermi-Hubbard experiment.   

Universal thermodynamics of an SU(N) Fermi-Hubbard Model

The SU(N) Fermi-Hubbard model can be engineered by loading ultracold alkaline-earth-like atoms (AEAs) in optical lattices, and N can span N=1,…,10. In previous numerical results using determinant Quantum Monte Carlo and numerical linked cluster expansion (NLCE) [PRA 104 043316 (2021)] we found that in a homogeneous square lattice with one particle per site on average, thermodynamic observables as a function of temperature obey a universal scaling with N. Since experiments do not have access to temperature but rather entropy and densities typically vary in the trap, it is an open question how the universal scaling manifests in more accessible experimental observables. We will describe our progress answering this question, and routes to accessing the universal scaling experimentally.   

Assessing the Accuracy of Random Phase Approximation for Dynamical Structure Factors in Cold Atoms with Quantum Monte Carlo

Cold atomic gases provide an excellent test ground to study the exotic and counterintuitive behavior of quantum many-body physics. Of particular interest is the appearance of collective excitations in these systems, such as the Goldstone and Higgs mode. To make progress, we need to assess the robustness of the theoretical and computational techniques commonly used to study the properties of cold atoms. We exploit the fact that, in some cases, exact numerical predictions can be obtained through Quantum Monte Carlo for the dynamical properties of cold atoms. We use these predictions to assess the accuracy of the Generalized Random Phase Approximation, which is widely considered the method of choice for studying collective excitations in cold atomic Fermi gases modeled with a Fermi-Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamical properties, especially for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential.    

Variational study of interacting 1D mixtures of bosons and fermions

We revisit the case for paired coherent states in one-dimensional Bose-Fermi mixtures of cold atomic gases in the presence of attractive interactions. We do so by updating the continuum formulation of the Matrix Product States (cMPS) ansatz to deal with the specific scenario of mixed statistics. Our results complement previous studies done using tools like DMRG and bosonization, and build a more comprehensive picture of the different concomitant ground-state pairing orders.   

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a detailed theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we discover first-order transitions from the disordered paramagnetic phase to the density-wave-ordered star and striated phases. We develop an understanding of these first-order transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that with open boundary conditions, the boundary itself  undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important insights for the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.   

Supersolid phases of lattice dipoles tilted in three-dimensions

By means of large-scale quantum Monte Carlo simulations, we study ground-state properties of dipolar bosons trapped in a two-dimensional lattice with dipoles tilted in three dimensions. We present ground-state phase diagrams of the above system at different tilt and azimuthal angles and find a variety of solid and supersolid phases. This work is an extension of Phys. Rev. A. $\mathbf{103}$. 043333 (2021).   

Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators

Interacting many-body systems combining confined and extended dimensions, such as ladders and few layer systems are characterized by enhanced quantum fluctuations, which often result in interesting collective properties. Recently two-dimensional bilayer systems, such as twisted bilayer graphene or ultracold atoms, have sparked a lot of interest because they can host rich phase diagrams, including unconventional superconductivity. Here we present a theoretical proposal for realizing high temperature pairing of fermions in a class of bilayer Hubbard models. We introduce a general, highly efficient pairing mechanism for mobile dopants in antiferromagnetic Mott insulators, which leads to binding energies proportional to t^{1/3}, where t is the hopping amplitude of the charge carriers. The pairing is caused by the energy that one charge gains when retracing a string of frustrated bonds created by another charge. Concretely, we show that this mechanism leads to the formation of highly mobile, but tightly bound pairs in the case of mixed-dimensional Fermi-Hubbard bilayer systems. This setting is closely related to the Fermi-Hubbard model believed to capture the physics of copper oxides, and can be realized by currently available ultracold atom experiments.   

The Ground State Properties of a spin-3/2 Fermi gas

Large spin (f ≥ 3/2) fermions have recently become a focus of a rapidly growing interest in the context of cold atom physics. Some pioneering theoretical studies had been performed before the experimental realization of large spin Fermi atomic gases. Ho and Yip studied normal Fermi liquid behaviors and Cooper pairing structures of fermions with arbitrary large spins early in 1999. Wu et al. proved that there exists a hidden SO(5) symmetry in the spin-3/2 Fermi atomic gas . A series of experimental progresses are achieved in recent years  and realization of degenerate large spin Fermi gases in Yb , Li and Sr atoms is reported. In contrast to spin-1/2 system, large spin Fermi systems have more spin components and interacting channels, including a spin-mixing interaction . Consequently the systems exhibit more intriguing properties in novel quantum phases , quantum magnetism and magnetic impurity, Cooper pairing and spin-mixing dynamics .Though present research interests are mainly laid on correlated properties of large spin fermions, the Fermi-liquid theory of normal-state Fermi gas is of most fundamental. Actually, this issue has already attracted many attentions. Theoretically, Yip et al. investigated properties of the SU(N) Fermi gas at zero and finite temperatures and found that the Fermi-liquid parameters can be enhanced by the number of components . Ramires developed Fermi liquid theory for a Fermi gas with SP(N) symmetry. On the other hand, Fermi parameters of ultracold Fermi atoms can be experimentally checked. Scazza et al. examined the effective mass, the residue, and the decay rate of quasiparticles of a polarized ultracold ⁶Li mixture.

In this paper, we study ground state properties of a generalized spin-3/2 Fermi model in which interactions are set to be spin-dependent and emphasize contributions of the spin-mixing interaction. The system with SU(N) or SP(N) symmetry is just the special case of the generalized model by supposing 

some interaction parameters to be related. Our treatment is different from but complementary to the methods used previously for the SU(N) and SP(N) systems. We calculate the effective interaction via Galitskii's equation and integrate the self-energy with the tricky method that was originally used to treat the uniform electron gas by Onsager  and Ziesche . The obtained results can be compared to previous studies. 

After the calculation , we find that the ground state energy and effective mass always increase with the spin-dependent interaction strengths in the spin-3/2 Fermi system with lower symmetry which is consistent with the conclusion of SP(N) and SU(N) Fermi liquid. We derive the effective interaction iterately by using the  Green's function and ladder diagrams. These techniques make it easier to get the higher-order approximation terms of each spin channel and avoid some redundant cross terms. We can get the contribution of spin-mixing term g_0 separately.  The numerical integration results of spin-1/2 system is approximately equal to the result calculated by Galitskii in 1958 , but the scattering length is spin-dependent because of the contact interaction. Otherwise, there are more interaction parameters especially the spin-mixing term that always strengthens the ground state energy and effective mass in spin-3/2 Fermi gas. Taking the value of scattering length as ( g_1=g_2=g_3=g_4=1/2 g), we obtain the result of effective mass for spin-3/2 system, which can recover the SU(2) and SU(N) results but add a spin-mixing term.The chemical potential, ground state energy and effective mass are calculated after elaborately dealing with the effective interaction and the self-energy. Contributions of each interaction term are derived within the second-order perturbation. It is found that the spin-mixing term always strengthens the ground state energy and effective mass.   

Robust stripes in mixed-dimensional variants of the t-J model

The interplay of spin and motional degrees of freedom is at the heart of many strongly correlated quantum materials. In the underdoped Hubbard model, there exists strong evidence for the formation of inhomogeneous order in the ground sate, such as stripes, close to optimal doping and in subtle competition with superconductivity. However, critical temperatures for stripe formation are too low to be reached with current state-of-the-art experiments. Motivated from the versatility of ultracold atoms in optical lattices, we shall look at stripe order of the t-J model of mixed dimensionality (mixD), where charge carriers are restricted to move only in one direction, whereas magnetic interactions are two-dimensional. Using finite temperature density matrix renormalization group methods via symmetry conserving purification schemes, we analyze the order of the mixD setting for various hole densities and map out the phase diagram. Below critical temperatures in the range of the magnetic coupling J, we predict a stable stripe phase, featuring incommensurate magnetic order and oscillating hole density profiles in the hopping direction over the whole range of the simulated system size. We further characterize the striped ground state under inhomogeneous hole doping in the ladder legs, leading to the formation of chargon-chargon and chargon-spinon bound states in the mixD t-Jz and t-J model, respectively.   

Pushing quantum-gas microscopes to their limit; understading the limits of deconvolution in single atom imaging.

Quantum-gas microscopes have provided many new insights into many-body physics in the past decade. In these setups, atoms are detected in a two-dimensional optical lattice via fluorescence imaging by a high-NA microscope objective. In our study, we compare three different deconvolution techniques to reconstruct the atomic lattice occupation, using simulated quantum-gas microscope images of single atoms in an optical lattice. Using a local iterative deconvolution algorithm, Wiener deconvolution and the Lucy-Richardson deconvolution algorithm, we investigate which deconvolution method is best capable of resolving the atomic lattice occupation as a function of signal-to-noise ratio and lattice filling. To test the limits of these techniques we then study the impact of inhomogeneous fluorescence and vary the imaging resolution and lattice spacing. We will also compare our simulation results with images of Mott insulators and thermal samples of from our two quantum-gas microscopes using bosonic ⁸⁷Rb and fermionic ⁴⁰K.     

Superfluid drag and quantum correlations in a binary Bose-Hubbard mixture

We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.   

Inelastic confinement-induced resonances in mixed-dimensional optical traps

Inelastic Confinement-Induced Resonances (ICIRs) were first observed in a fascinating experiment conducted in Innsbruck. ICIRs were observed in an ultracold quantum gas confined in a quasi-1D optical trap. More recently, the same group has also observed ICIRs in a 3D lattice. In both cases, the origin of ICIRs lies on the coupling between the center-of-mass and relative-motion coordinates due to the anharmonicities of the trapping potential.

In this communication, we present a mixed dimensional model, where the influence of the dimension on the ICIRs can be effectively described. ICIRs are identified by studying the energy spectra of two ultracold atoms one confined in a cuasi-1D trap or quasi-2D trap, and the other one in a 3D trap. A comparison to cuasi-1D and 3D traps is also performed.   

One-dimensional Bose-Fermi mixture under local and next-neighbor interactions.

We investigate a mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering local interspecies and intraspecies interactions as well as the next-neighbor interactions between fermions or bosons. It is well known that the interplay between commensurability and local repulsive interactions generates diverse Mott insulator states in Bose-Fermi mixtures [PRA 100, 063620 (19); PRA 102, 033341 (2020); PRA 103, 023304 (2021)]. Also in the absence of bosons, the ground state of two-color fermions with local and next-neighbor interactions exhibit a rich phase diagram. Here, we explore the ground state of Bose-Fermi mixture considering local and next-neighbor couplings, finding that the mixed Mott insulator and the spin-selective one are strongly affect by the no local interactions.