Anyon Hubbard Model in One-Dimensional Optical Lattices

Realization of one-dimensional anyons with arbitrary statistical phase

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons.

Quantum Walks and Correlated Dynamics in an Interacting Synthetic Rydberg Lattice

Coherent dynamics of interacting quantum particles plays a central role in the study of strongly correlated quantum matter and the pursuit of quantum information processors. Here, we present the state space of interacting Rydberg atoms as a synthetic landscape on which to control and observe coherent and correlated dynamics. With full control of the coupling strengths and energy offsets between the pairs of sites in a nine-site synthetic lattice, we realize quantum walks, Bloch oscillations, and dynamics in an Escher-type "continuous staircase." In the interacting regime, we observe correlated quantum walks, Bloch oscillations, and confinement of particle pairs. Additionally, we simultaneously tilt our lattice both up and down to achieve coherent pair oscillations. When combined with a few straightforward upgrades, this work establishes synthetic Rydberg lattices of interacting atom arrays as a promising platform for programmable quantum many-body dynamics with access to features that are difficult to realize in real-space lattices.

Density Dependent Gauge Field Inducing Emergent Su-Schrieffer-Heeger Physics, Solitons, and Condensates in a Discrete Nonlinear Schrödinger Equation

We investigate a discrete nonlinear Schrödinger equation with dynamical, density-difference-dependent gauge fields. We find a ground-state transition from a plane wave condensate to a localized soliton state as the gauge coupling is varied. Interestingly we find a regime in which the condensate and soliton are both stable. We identify an emergent chiral symmetry, which leads to the existence of a symmetry-protected zero-energy edge mode. The emergent chiral symmetry relates low and high energy solitons. These states indicate that the interaction acts both repulsively and attractively.

Interaction-Induced Non-Hermitian Topological Phases from a Dynamical Gauge Field

We present a minimal non-Hermitian model where a topologically nontrivial complex energy spectrum is induced by interparticle interactions. Our model consists of a one-dimensional chain with a dynamical non-Hermitian gauge field with density dependence. The model is topologically trivial for a single-particle system, but exhibits nontrivial non-Hermitian topology with a point gap when two or more particles are present in the system. We construct an effective doublon model to describe the nontrivial topology in the presence of two particles, which quantitatively agrees with the full interacting model. Our model can be realized by modulating hoppings of the Hatano-Nelson model; we provide a concrete Floquet protocol to realize the model in atomic and optical settings.

Realizing a 1D topological gauge theory in an optically dressed BEC

Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models^1,2. A prime example is the Chern-Simons theory of fractional quantum Hall states, where anyonic excitations emerge from the coupling between weakly interacting matter particles and a density-dependent gauge field³. Although in traditional solid-state platforms such gauge theories are only convenient theoretical constructions, engineered quantum systems enable their direct implementation and provide a fertile playground to investigate their phenomenology without the need for strong interactions⁴. Here, we report the quantum simulation of a topological gauge theory by realizing a one-dimensional reduction of the Chern-Simons theory (the chiral BF theory^5-7) in a Bose-Einstein condensate. Using the local conservation laws of the theory, we eliminate the gauge degrees of freedom in favour of chiral matter interactions^8-11, which we engineer by synthesizing optically dressed atomic states with momentum-dependent scattering properties. This allows us to reveal the key properties of the chiral BF theory: the formation of chiral solitons and the emergence of an electric field generated by the system itself. Our results expand the scope of quantum simulation to topological gauge theories and open a route to the implementation of analogous gauge theories in higher dimensions¹².

Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids

Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.

Bosonic Continuum Theory of One-Dimensional Lattice Anyons

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.

Quantum Simulation Meets Nonequilibrium Dynamical Mean-Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model

We perform an ab initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross validates the experimental and numerical approaches in a strongly correlated nonequilibrium system.

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ2 lattice gauge theories

From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying many-body physics. Here, we demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices, using a combination of coherent lattice modulation with strong interactions. Specifically, we propose implementation of ℤ2 lattice gauge theories coupled to matter, reminiscent of theories previously introduced in high-temperature superconductivity. We discuss a range of settings from zero-dimensional toy models to ladders featuring transitions in the gauge sector to extended two-dimensional systems. Mastering lattice gauge theories in optical lattices constitutes a new route toward the realization of strongly correlated systems, with properties dictated by an interplay of dynamical matter and gauge fields.

Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics

We study the nonequilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast to the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through nonequilibrium dynamics.

Observation of Density-Dependent Gauge Fields in a Bose-Einstein Condensate Based on Micromotion Control in a Shaken Two-Dimensional Lattice

We demonstrate a density-dependent gauge field, induced by atomic interactions, for quantum gases. The gauge field results from the synchronous coupling between the interactions and micromotion of the atoms in a modulated two-dimensional optical lattice. As a first step, we show that a coherent shaking of the lattice in two directions can couple the momentum and interactions of atoms and break the fourfold symmetry of the lattice. We then create a full interaction-induced gauge field by modulating the interaction strength in synchrony with the lattice shaking. When a condensate is loaded into this shaken lattice, the gauge field acts to preferentially prepare the system in different quasimomentum ground states depending on the modulation phase. We envision that these interaction-induced fields, created by fine control of micromotion, will provide a stepping stone to model new quantum phenomena within and beyond condensed matter physics.

Generalized lattice Wilson-Dirac fermions in (1 + 1) dimensions for atomic quantum simulation and topological phases

The Dirac fermion is an important fundamental particle appearing in high-energy physics and topological insulator physics. In particular, a Dirac fermion in a one-dimensional lattice system exhibits the essential properties of topological physics. However, the system has not been quantum simulated in experiments yet. Herein, we propose a one-dimensional generalized lattice Wilson-Dirac fermion model and study its topological phase structure. We show the experimental setups of an atomic quantum simulator for the model, in which two parallel optical lattices with the same tilt for trapping cold fermion atoms and a laser-assisted hopping scheme are used. Interestingly, we find that the model exhibits nontrivial topological phases characterized by gapless edge modes and a finite winding number in the broad regime of the parameter space. Some of the phase diagrams closely resemble those of the Haldane model. We also discuss topological charge pumping and a lattice Gross-Neveu model in the system of generalized Wilson-Dirac fermions.

Perfect Spin Filter by Periodic Drive of a Ferromagnetic Quantum Barrier

We consider the problem of particle tunneling through a periodically driven ferromagnetic quantum barrier connected to two leads. The barrier is modeled by an impurity site representing a ferromagnetic layer or a quantum dot in a tight-binding Hamiltonian with a local magnetic field and an ac-driven potential, which is solved using the Floquet formalism. The repulsive interactions in the quantum barrier are also taken into account. Our results show that the time-periodic potential causes sharp resonances of perfect transmission and reflection, which can be tuned by the frequency, the driving strength, and the magnetic field. We demonstrate that a device based on this configuration could act as a highly tunable spin valve for spintronic applications.

Anyonic Haldane Insulator in One Dimension

We demonstrate numerically the existence of a nontrivial topological Haldane phase for the one-dimensional extended (U-V) Hubbard model with a mean density of one particle per site, not only for bosons but also for anyons, despite a broken reflection parity symmetry. The Haldane insulator, surrounded by superfluid, Mott insulator, and density-wave phases in the V-U parameter plane, is protected by combined (modified) spatial-inversion and time-reversal symmetries, which is verified within our matrix-product-state based infinite density-matrix renormalization group scheme by analyzing generalized transfer matrices. With regard to an experimental verification of the anyonic Haldane insulator state the calculated asymmetry of the dynamical density structure factor should be of particular importance.

Floquet Realization and Signatures of One-Dimensional Anyons in an Optical Lattice

We propose a simple scheme for mimicking the physics of one-dimensional anyons in an optical-lattice experiment. It relies on a bosonic representation of the anyonic Hubbard model to be realized via lattice-shaking-induced resonant tunneling against potential offsets, which are created by a combination of a lattice tilt and strong on-site interactions. No lasers additional to those used for the creation of the optical lattice are required. We also discuss experimental signatures of the continuous interpolation between bosons and fermions when the statistical angle θ is varied from 0 to π. Whereas the real-space density of the bosonic atoms corresponds directly to that of the simulated anyonic model, this is not the case for the momentum distribution. Therefore, we propose to use Friedel oscillations in the density as a probe for continuous fermionization of the bosonic atoms.