Session M33: Quantum Simulation III

Optical-domain spectral super-resolution enabled by a quantum memory

Super-resolution methods of optical imaging hold a solid place as an application in biological and chemical sciences, but many new developments allow the beating of diffraction limit in better and more subtle ways by fully exploiting spatial information already present in the optical field. By analogy, full spectral information of the optical field leads to a super-resolution spectroscopy, in which we can detect frequency separation of two emitters with precision surpassing the Fourier limit. We employ an optical quantum memory with embedded time-frequency processing capabilities to implement a time-inversion interferometer for input light, thus projecting the optical field in the symmetric–antisymmetric mode basis. This is accomplished by engineering a frequency-dependent dispersion combined with time-dependent temporal phase modulation that allows us to split, rotate and interfere the signal pulses in the chronocyclic space. Analysis based on quantum metrology shows the advantage of our technique over both conventional spectroscopy as well as heterodyne measurements. Moreover, our work not only establishes a new super-resolution spectroscopy method but also provides an exceptionally good spectral resolution, not seen even in Fourier spectrometers.   

Quench dynamics of dipolar Bose-Hubbard model

A long-range interaction plays significant roles in Bose-particle systems leading to peculiar phenomena, e.g. spatially ordered structures and droplets in Bose-gases[1,2]. Especially in the dipolar Bose-Hubbard(BH) model, the dipole interaction gives rise to spatially ordered phases, which depends on anisotropy of the interaction [3]. This earlier study also pointed out the existence of an "unstable region" in the phase diagram of the dipolar BH system. In our earlier study, we have shown that in the unstable region, droplets emerge in the dipolar BH system [4]. In Ref. [4], we proposed a toy model that describes the size and shape of droplets. In this presentation, we will show the quench dynamics of the dipolar BH model induced by sudden change of the interaction parameter crossing the phase boundary. We find that the fluctuation of the initial state plays an important role in the relaxation of the system in quench dynamics. We will also discuss the effect of fluctuation on the formation of droplets.

[1] Ilzhöfer, P., et. al. Nat. Phys. 17(3), 356-361(2021).

[2] Léonard, J., et. al. Science 358(6369), 1415-1418(2017).

[3] Danshita, I., et. al. PRL 103(22) (2009).

[4] Tamura, K., et. al. arXiv:2110.01265.   

Using a quantum simulator to benchmark a novel efficient approximation algorithm for localized 1D Fermi-Hubbard systems

Identifying and understanding the applications of NISQ-era quantum simulators and quantum computers is a topical problem. Quantum many-body physics embodies a unique set of problems that are both computationally hard and physically pertinent and are therefore apt for applications of NISQ devices. While state-of-the art neutral atom quantum simulators have made remarkable progress in studying many-body dynamics, they are noisy and limited in the variability of initial state and the observables that can be measured. Here we show that despite these limitations, quantum simulators can be used to develop new numerical techniques to solve for the dynamics of many-body systems in regimes that are practically inaccessible to established numerical techniques [1]. Considering localized 1D Fermi-Hubbard systems, we use an approximation ansatz to develop a new numerical method that facilitates efficient classical simulations in such regimes. Since this new method does not have an error estimate and is not valid in general, we use a neutral-atom quantum simulator with L_exp = 290 lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to 700 tunnelling times. We then use this method to make a prediction of the behaviour of interacting dynamics for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.   

Quantum Matter Synthesizer: Seeing and Controlling Individual Atoms

We present progress on the construction of a "quantum matter synthesizer," a new experimental apparatus that integrates site-resolved imaging of atoms in a sub-micron lattice with dynamic control using a moveable tweezer array. Cold cesium atoms are first stochastically loaded into a static 2D triangular optical lattice. Subsequently, degenerate Raman sideband cooling is applied to the atoms and the resulting fluorescence is collected on a low-noise CCD to image the site occupancies. A re-arrangement algorithm computes tweezer trajectories to bring atoms to a desired configuration. The computed moves are streamed to a digital micromirror device (DMD), which projects the tweezer array with a fast switching speed of 2 kHz. After re-arrangement, the atoms are again cooled and their final distribution imaged. We characterize the single-site imaging fidelity and the DMD tweezer generation.   

Modelling the thermodynamics of ultracold atomic bubbles in space

With the recent observation of ultracold atomic bubbles in microgravity using the NASA Cold Atom Lab (CAL) aboard the International Space Station, we discuss modelling the thermodynamic properties of shell-shaped quantum fluids and directly compare to the data obtained from the experiment. We calculate the critical temperature required to achieve Bose-Einstein condensation (BEC) in the novel hollowed-out bubble geometries generated on CAL and, in line with experiment, model how the temperature evolves as an initially condensed gas is inflated into a bubble adiabatically. Using a simplified isotropic `bubble-trap' potential, we show that standard semiclassical methods overestimate the BEC critical temperature for atoms confined in quasi-2D thin shells and with this insight carry out our analysis of the anisotropic CAL trap using a hybrid spectral and semiclassical approach. We conclude by discussing the near-future possibility of achieving large condensed bubbles on CAL.   

Optimization of Pulsed-Laser Ablation Production of AlCl for Laser Cooling and Trapping

Ultracold molecules offer opportunities for many areas of fundamental research, ranging from testing fundamental physics, probing for temporal variations of fundamental constants, quantum simulation of many-body systems, control of chemical reactions and quantum information processing. To realize many of these applications a high phase-space density of ultracold molecules is required. Molecules with highly diagonal Franck-Condon factors are particularly well-suited for this endeavour. Here, we report on our ab-initio calculations and our spectroscopy results, which confirm that AlCl has a Franck-Condon factor of 99.88%[1], which renders it an excellent candidate for laser cooling and trapping. In addition, we will present our results on optimizing the production of AlCl via laser ablation of various chemical precursors, including AlCl3, Al+KCl, Al+MgCl2, in a cryogenic buffer-gas beam cell[2] and give an update on our progress towards slowing and cooling AlCl.   

Information-theoretic description of superconductivity in a doped Mott insulator

Quantum information can be used to advance our understanding of phases of matter in many-body quantum systems. We use tools of quantum information to characterize the entanglement-related properties of unconventional superconductivity in a doped Mott insulator. We study the two-dimensional Hubbard model with cluster dynamical mean-field theory to show how key measures of correlations -local entropy, thermodynamic entropy and total mutual information- detect the superconducting phase obtained upon doping the Mott insulating phase. We find that the behavior of the difference in the local entropy between the normal and superconducting states follows that of the potential energy. In the superconducting state thermodynamic entropy is strongly suppressed near the Mott insulator, whereas the total mutual information is amplified and shows a peak versus doping.    

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Long-range interactions in optical lattices have been extensively studied for more than one decade. Two types of long-range interactions, dipolar interactions and cavity-mediated long-range interactions, have been realized in experiments, and the phase diagrams for both systems have been obtained. However, when two types long-range interactions are competing with each other, the phase diagram of the system is still obscure. By means of large-scale Monte Carlo simulations, we study the competition between cavity-mediated and dipolar interactions in a system of lattice bosons. We also briefly present how to experimentally realize the phases stabilized by the extended Bose-Hubbard model describing the system.    

Exotic Superfluid Phases in Spin Polarized Systems on Optical Lattices

Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly $500$ atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between interaction and superfluidity in an exotic phase of matter.   

Two types of BCS-BEC crossover of atomic Fermi superfluidin a spherical bubble trap

Inspired by the spherical bubble traps in microgravity, we derive and analyze the BCS-Leggett theory of atomic Fermi superfluid on a thin spherical shell. Despite the flat dispersion within each angular momentum number and jumps between adjacent levels of an ideal Ferm gas on a spherical shell, the properly normalized gap and chemical potential of Fermi superfluid exhibit universal behavior regardless of the planar or spherical geometry. By tuning the attractive interaction, an interaction-induced BCS-BEC crossover occurs. However, we consider a different scenario where the particle number and interaction strength are fixed but the sphere is shrinking. The increase of the curvature leads to an increase of the Fermi energy and causes a reduction of the ratio between the pairing and kinetic energies, pushing the system towards the BCS limit. The curvature-induced BCS-BEC crossover is made possible by the compact geometry, exemplified by the spherical bubble traps. The theory paves the way for a systematic study of atomic Fermi superfluid in spherical geometry.    

Superfluidity in the 1D Bose-Hubbard Model

Due to strong quantum fluctuations, superfluidity in one dimension is special:  The superfluid state is critical, with power-law-decaying correlation functions and no Bose-Einstein condensation. In a lattice, where one can find an interaction-driven Mott insulator, the physics is even more interesting. We compute the ground state superfluid density of the 1D Bose-Hubbard model using an infinite variational matrix product state technique. We explore the scaling relationships involving the correlation functions and entanglement entropy, explicitly demonstrating the connection between superfluid density and Luttinger parameters. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one of them (VUMPS) is more efficient than the other (iDMRG).   

Entanglement dynamics of bosons in an optical lattice

Entanglement structure characterizes quantum phases of many-body systems. Recently, entanglement entropy has been measured in a system of bosons in an optical lattice. Motivated by the experiment, we study entanglement dynamics of bosons in an optical lattice based on the Bose-Hubbard model and investigate how the dynamics of entanglement entropy characterizes the superfluid (SF) and Mott insulating (MI) phases. Specifically, we study quench dynamics from the deep MI regime by numerically calculating the Renyi entropy (RE) using the time-evolving block decimation algorithm. We find that the dynamics of RE exhibits distinct features depending on whether the system is quenched into the SF or the MI phases. When the system is quenched into the SF phase, thermalization occurs and the RE converges to a constant value in time evolution. On the other hand, when the system is quenched into the MI phase, the RE oscillates with a certain period that depends on the strength of the on-site interaction. We develop the effective theory in the strong-coupling regime and obtain an analytic expression for the time-evolution of the RE, which agrees very well with the numerical results. We thus find that the signature of the SF-MI phase transition appears in the dynamics of RE.   

Multi-magnon quantum many-body scars from tensor operators

We construct a family of three-body spin-1/2 Hamiltonians with a super-extensive set of infinitely long-lived multi-magnon states. A magnon in each such state carries either quasi-momentum zero or fixed p≠0, and energy Ω. These multi-magnon states provide an archetypal example of quantum many-body scars: they are eigenstates at finite energy density that violate the eigenstate thermalization hypothesis, and lead to persistent oscillations in local observables in certain quench experiments. On the technical side, we demonstrate the systematic derivation of scarred Hamiltonians that satisfy a restricted spectrum generating algebra using an operator basis built out of irreducible tensor operators. This operator basis can be constructed for any spin, spatial dimension or continuous non-Abelian symmetry that generates the scarred subspace