Session Z04: Quantum Gases in Optical Lattices II

Spatial correlations in fermionic triangular lattice Hubbard systems

Ultracold atoms in triangular optical lattices provide a versatile platform to study strongly correlated systems in which the interplay of motion, interactions and spin gives rise to new states of matter. The interesting feature for triangular lattices is the geometric frustration that three spins with antiferromagnetic interactions cannot be antiparallel, leading to large degeneracies in the many-body ground state [1]. The superposition of the degeneracies could result in a quantum spin liquid which is numerically predicted to occur between the metallic and ordered magnetic phases [2]. In this talk, we present a Mott insulator of lithium-6 on a symmetric triangular lattice with a lattice spacing of 1003 nm. The lattice is imaged using Raman sideband cooling technique with an imaging fidelity of 98% [3]. We calibrated tunneling and interaction by extracting lattice depth from band excitation. The temperature of our atoms is below one-fifth of the Fermi temperature before loading to the lattice and the temperature scale is less than the tunneling in the lattice. We performed spin removal technique [4] to resolve either spin up or down using on-resonance imaging light to detect spin-spin correlations. We compare the results to a numerical linked cluster expansion calculation and plan to investigate 120° Neel ordering in Heisenberg antiferromagnets and search for quantum spin liquids in the triangular lattice Hubbard system.

[1] L. Balents, Nature 464, 7286 (2010)

[2] M. Laubach, Phys. Rev. B 91, 245125 (2015)

[3] J. Yang, PRX Quantum 2, 020344 (2021)

[4] M. F. Parsons, Science 353, 1253-1256 (2016)

    

Fermi-Hubbard Model in Tunable-Geometry Lattices

Ultracold atoms in optical lattices provide new perspectives into the study of strongly correlated systems. Fermi gas microscopes, in particular, offer single site-resolved readout and manipulation to elucidate the intricate quantum phases in the Fermi Hubbard model such as pseudo gap, strange metal and High-Tc superconductivity. We demonstrate this capability by studying the time- and site-resolved dynamics of a hole dopant after a quench and how it scrambles the spin environment. We also report on progress towards an upgraded optical lattice. By interfering and phase-locking the lattice beams, the lattice geometry can be tuned to triangular, honeycomb and non-bipartite square geometries. This would allow introducing geometric frustration in quantum magnetism and studying the Fermi Hubbard model beyond the square lattice band structure. The dynamical tunability would also facilitate adiabatic state preparation of low entropy strongly-correlated quantum phases.   

Bilayer Fermi-Hubbard physics under a quantum gas microscope

Two crucial goals of experiments on strongly-correlated fermions in optical lattices are to understand how fermion pairing depends on dimensionality, and to understand how pairing is altered when the lattice is doped with excess charge and spin. In this talk, we introduce an experimental platform to address these questions. We realize a bilayer two-dimensional Fermi-Hubbard system under a quantum gas microscope through the use of a coherent, out-of-plane, double-well superlattice. This double-well superlattice is also used to reveal the full spin and charge configuration of a single layer system through a two-step process of out-of-plane Stern Gerlach separation, followed by bilayer-selective illumination. These advances represent steps toward quantum simulators which closely mimic and inform the properties of real materials.   

Engineering of lattice models with local control in quantum microscopes

Optical lattices provide a robust platform for quantum simulations in simple geometries, and the use of superlattices and digital mirror devices (DMDs) vastly extends the control over the microscopic behavior. We use these methods to prepare exciting starting states, modify the lattice Hamiltonian, and reach full spin resolution in our quantum microscope. In particular, I will present our realization of the spin-1 Haldane model in a fermionic ladder system by engineering antiferromagnetic leg and ferromagnetic rung couplings. We measure the topological structure of the Haldane phase via the string correlations and compare them to the trivial case. Upon doping, we can use our local control to restrict the motion of holes to one dimension while keeping the spin-exchange two-dimensional. This greatly enhances hole-hole attraction leading to bound hole pairs.     

Dynamical preparation of the t-J model in a Fermi-Hubbard simulator via optical lattice ramps

The t-J model describes the low-energy properties of the doped Fermi-Hubbard model, relevant to the studies of high-Tc superconductivity. The "simpler" t-J model can be derived from the Fermi-Hubbard model by performing a Schrieffer-Wolff basis transformation and restricting the Hilbert space to exclude doubly occupied sites. We propose a protocol for cold atom experiments to dynamically prepare the t-J model ground (thermal) state in an optical lattice starting from the Fermi-Hubbard ground (thermal) state. Our simple protocol involves performing a slow linear ramp of the optical lattice depth just before fluorescence imaging, which acts as an approximate Schrieffer-Wolff transformation on low energy Fermi-Hubbard eigenstates and eliminates the doublon-hole fluctuations. This lattice ramp maps the Fermi-Hubbard eigenstates onto eigenstates of the t−J model which can then be imaged in the natural Fock basis of cold atom experiments.  We perform a numerical study using exact diagonalization and find an optimal ramp speed for which the state after the lattice ramp has maximal overlap with the t-J model state and shows correlations approaching those for the t-J model. We also compare our numerics to existing experimental data from our Lithium-6 fermionic quantum gas microscope and show a proof-of-principle demonstration of this protocol. More generally, this protocol enables the study of low energy effective Hamiltonians derived via the Schrieffer-Wolff transformation frequently encountered in particle physics.   

Out-of-equilibrium dynamics of the two component Bose-Hubbard model

Cold atoms in optical lattices can be used as quantum simulators to study the temporal evolution of quantum systems, which has lead to increasing interest in the out-of-equilibrium dynamics of multi-component bosons in optical lattices. We study the Bose-Hubbard model for two component bosons using a strong-coupling approach within the closed time path formalism. We develop an effective theory for the action of this problem and obtain equations of motion for the superfluid order parameter. We study these equations of motion in the low-frequency, long wavelength limit for various initial conditions.   

Formation of matter-wave polaritons in an optical lattice

The polariton is a quasiparticle formed by strong light-matter coupling. It has been exploited to achieve superfluids of light as well as strongly correlated phases in photonic quantum systems. Recently, we have implemented an ultracold-atom polariton analog, where light and matter are replaced by matter waves and excitations in an optical lattice [1, 2]. In our tunable and dissipation-free system, we have spectroscopically accessed the polariton band structure and studied transport behavior in the superfluid and Mott-insulating regimes. Our work opens up novel possibilities for exploring exciton-polariton physics and polaritonic quantum matter.   

Snapshot-based detection of ½-Laughlin states: coupled chains and central charge

Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and characterization of such states, where novel detection schemes enable an unprecedented microscopic understanding.

Here, I discuss how the central charge can be directly measured in current cold atom experiments using the number entropy as a proxy for the entanglement entropy. I present DMRG simulations of Hubbard-interacting bosons on coupled chains subject to a magnetic field. Tuning the inter-chain hopping, we found a transition from a trivial quasi-one dimensional phase to the topologically ordered Laughlin state at magnetic filling factor ν=1/2 for systems of three or more chains. We resolve the transition using the central charge, on-site correlations, momentum distributions and the many-body Chern number. Finally, we propose a scheme to experimentally estimate the central charge from Fock basis snapshots. Related settings will also be discussed.

The model is realizable with current cold atom techniques and the proposed observables pave the way for the detection and classification of a larger class of interacting topological states of matter.   

Strongly interacting fluids in a Bose-Hubbard circuit: Adiabatic preparation

​​In recent years, circuit QED has proven to be a rich testbed for studying quantum many-body phenomena in synthetic photonic materials. We assemble a 1D Bose Hubbard lattice for microwave photons using a chain of capacitively coupled transmon qubits, with strong photon interactions mediated by the transmon anharmonicity. In this part of the talk we manipulate the on-site energy to explore themes of adiabatic state preparation: melting localized single particles in disordered lattices to quasi-momentum states in ordered lattices, preparing a strongly interacting superfluid state, studying the transition between diabatic and adiabatic regime, and quantifying the reversibility of the state preparation as a measure of adiabaticity.   

Strongly interacting fluids in a Bose-Hubbard circuit: Observables

In recent years, circuit QED has proven to be a rich testbed for studying many-body phenomena in synthetic photonic materials. We assemble a 1D Bose Hubbard lattice for microwave photons using a chain of capacitively coupled transmon qubits, with strong photon interactions mediated by the transmon anharmonicity. In this second part of the talk, we discuss our results in probing the static and dynamical properties of the adiabatically prepared fluid. We characterize the long-range order in the lattice by measuring two-body density correlations, highlighting the statistics for the separation between two photons. Going beyond nonlocal correlations, we probe the global entanglement from single-site tomography and average the purity over the whole lattice. Finally, we access out-of-equilibrium transport properties by locally modulating the lattice potential and measuring the spectral response in terms of heat absorption and AC susceptibility, offering a direct probe of the low lying density of states of the strongly interacting fluid.