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

Atom interferometry in a blue-detuned guiding optical potential

We propose and demonstrate a novel, to the best of our knowledge, scheme for atom interferometry along the direction deviating an angle from gravity, using slender light pulses that nest around a blue-detuned guiding optical potential (BDGOP). Cold atoms could be uniformly transported through guiding optical potential and interacted coherently by slender light pulses. We analyze the coherence of cold atoms in BDGOP using the Ramsey interference. In comparison to free-falling atom interferometry, the rapid exponential decay of fringe contrast is changed to slower linear decay when subjected to a tilting angle. The contrast could be enhanced approximately fourfold by BDGOP. Our work paves the way for inertial vector measurements based on BDGOP.

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.

Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential

In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.

Dynamical Localization Transition of String Breaking in Quantum Spin Chains

The fission of a string connecting two charges is an astounding phenomenon in confining gauge theories. The dynamics of this process have been studied intensively in recent years, with plenty of numerical results yielding a dichotomy: the confining string can decay relatively fast or persist up to extremely long times. Here, we put forward a dynamical localization transition as the mechanism underlying this dichotomy. To this end, we derive an effective string breaking description in the light-meson sector of a confined spin chain and show that the problem can be regarded as a dynamical localization transition in Fock space. Fast and suppressed string breaking dynamics are identified with delocalized and localized behavior, respectively. We then provide a further reduction of the dynamical string breaking problem onto a quantum impurity model, where the string is represented as an "impurity" immersed in a meson bath. It is shown that this model features a localization-delocalization transition, giving a general and simple physical basis to understand the qualitatively distinct string breaking regimes. These findings are directly relevant for a wider class of confining lattice models in any dimension and could be realized on present-day Rydberg quantum simulators.

Formation, propagation, and excitation of matter solitons and rogue waves in chiral BECs with a current nonlinearity trapped in external potentials

In this paper, we investigate formation and propagation of matter solitons and rogue waves (RWs) in chiral Bose-Einstein condensates modulated by different external potentials, modeled by the chiral Gross-Pitaevskii (GP) equation with the current nonlinearity and external potentials. On the one hand, the introduction of two potentials (Pöschl-Teller and harmonic-Gaussian potentials) enables the discovery of exact soliton solutions in both focusing and defocusing cases. We analyze the interplay effects of current nonlinearity and potential on soliton stability via associated Bogoliubov-de Gennes equations. Moreover, multiple families of numerical solitons (ground-state and dipole modes) trapped in potentials are found, exhibiting distinctive structures. The interactions between solitons trapped in potentials are studied, which exhibit the inelastic trajectories and repulsive interactions. On the other hand, we introduce the time-dependent potentials such that the controlled RWs are found in both focusing and defocusing GP equations with current nonlinearity. Furthermore, through the interaction between potentials and current nonlinearity, it is possible to enlarge the region of modulational instability, leading to the generation of RWs and chiral solitons. High-order RWs are generated from several Gaussian perturbations on a continuous wave. The presence of current nonlinearity disrupts the structures of these high-order RWs, causing them to undergo a transform into chiral lower-amplitude solitons. Finally, various types of soliton excitations are investigated by varying the strengths of potential and current nonlinearity, showing the abundant dynamic transforms of chrital matter solitons.

Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, Ω_{cr}, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the Ω_{cr} values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional s-wave scattering lengths through the strength of nonlinear rotation, C, such that Ω_{cr}(C>0)<Ω_{cr}(C=0)<Ω_{cr}(C<0). In an analogous manner, the critical ellipticity (ε_{cr}) for vortex nucleation during an adiabatic introduction of trap ellipticity (ε) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.

Stability of trapped Bose-Einstein condensate under a density-dependent gauge field

We study the ground-state stability of the trapped one-dimensional Bose-Einstein condensate under a density-dependent gauge field by variational and numerical methods. The competition of density-dependent gauge field and mean-field atomic interaction induces the instability of the ground state, which results in irregular dynamics. The threshold of the gauge field for exciting the instability is obtained analytically and confirmed numerically. When the gauge field is less than the threshold, the system is stable, and the gauge field induces chiral dynamics of the wave packet. When the gauge field is greater than the threshold, the system is unstable, and the ground-state wave packet will be deformed and fragmented. Interestingly, we find that as the gauge field approaches the threshold, strong dipolar and breathing dynamics take place, and strong modes mixing occurs, the instability of the system sets in. In addition, we show that the stability of the system can be well controlled by periodical modulation of the trapping potential. We provide theoretical evidence to understand and control the irregular dynamics associated with chiral superfluid induced by density-dependent gauge field.

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.

Observing Dynamical Currents in a Non-Hermitian Momentum Lattice

We report on the experimental realization and detection of dynamical currents in a spin-textured lattice in momentum space. Collective tunneling is implemented via cavity-assisted Raman scattering of photons by a spinor Bose-Einstein condensate into an optical cavity. The photon field inducing the tunneling processes is subject to cavity dissipation, resulting in effective directional dynamics in a non-Hermitian setting. We observe that the individual tunneling events are superradiant in nature and locally resolve them in the lattice by performing real-time, frequency-resolved measurements of the leaking cavity field. The results can be extended to a regime exhibiting a cascade of currents and simultaneous coherences between multiple lattice sites, where numerical simulations provide further understanding of the dynamics. Our observations showcase dynamical tunneling in momentum-space lattices and provide prospects to realize dynamical gauge fields in driven-dissipative settings.

Open Quantum System Simulation of Faraday's Induction Law via Dynamical Instabilities

We propose a novel type of a Bose-Hubbard ladder model based on an open quantum-gas-cavity-QED setup to study the physics of dynamical gauge potentials. Atomic tunneling along opposite directions in the two legs of the ladder is mediated by photon scattering from transverse pump lasers to two distinct cavity modes. The resulting interplay between cavity photon dissipation and the optomechanical atomic backaction then induces an average-density-dependent dynamical gauge field. The dissipation-stabilized steady-state atomic motion along the legs of the ladder leads either to a pure chiral current, screening the induced dynamical magnetic field as in the Meissner effect, or generates simultaneously chiral and particle currents. For a sufficiently strong pump the system enters into a dynamically unstable regime exhibiting limit-cycle and period-doubled oscillations. Intriguingly, an electromotive force is induced in this dynamical regime as expected from an interpretation based on Faraday's law of induction for the time-dependent synthetic magnetic flux.

Domain-wall dynamics in Bose-Einstein condensates with synthetic gauge fields

Interactions in many-body physical systems, from condensed matter to high-energy physics, lead to the emergence of exotic particles. Examples are mesons in quantum chromodynamics and composite fermions in fractional quantum Hall systems, which arise from the dynamical coupling between matter and gauge fields^1,2. The challenge of understanding the complexity of matter-gauge interaction can be aided by quantum simulations, for which ultracold atoms offer a versatile platform via the creation of artificial gauge fields. An important step towards simulating the physics of exotic emergent particles is the synthesis of artificial gauge fields whose state depends dynamically on the presence of matter. Here we demonstrate deterministic formation of domain walls in a stable Bose-Einstein condensate with a gauge field that is determined by the atomic density. The density-dependent gauge field is created by simultaneous modulations of an optical lattice potential and interatomic interactions, and results in domains of atoms condensed into two different momenta. Modelling the domain walls as elementary excitations, we find that the domain walls respond to synthetic electric field with a charge-to-mass ratio larger than and opposite to that of the bare atoms. Our work offers promising prospects to simulate the dynamics and interactions of previously undescribed excitations in quantum systems with dynamical gauge fields.

Atom-optically synthetic gauge fields for a noninteracting Bose gas

Synthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of ¹³³Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.

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.

Modulational instability and soliton generation in chiral Bose-Einstein condensates with zero-energy nonlinearity

By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskii equation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a single traveling solitary wave. The sign of the current nonlinearity determines the direction of propagation of the emerging solitons.

Novel Quantum Phases of Two-Component Bosons with Pair Hopping in Synthetic Dimension

We study two-component (or pseudospin-1/2) bosons with pair hopping interactions in synthetic dimension, for which a feasible experimental scheme on a square optical lattice is also presented. Previous studies have shown that two-component bosons with on-site interspecies interaction can only generate nontrivial interspecies paired superfluid (super-counter-fluidity or pair-superfluid) states. In contrast, apart from interspecies paired superfluid, we reveal two new phases by considering this additional pair hopping interaction. These novel phases are intraspecies paired superfluid (molecular superfluid) and an exotic noninteger Mott insulator which shows a noninteger atom number at each site for each species, but an integer for total atom number.

Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator

The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories¹. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss's law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task², which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices^3-6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry^7,8, realized mappings onto effective models to integrate out either matter or electric fields^9-12, or were limited to very small systems^13-16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter-gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss's law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.

Jet Substructure in Fireworks Emission from Nonuniform and Rotating Bose-Einstein Condensates

We show that jet emission from a Bose condensate with periodically driven interactions, also known as "Bose fireworks", contains essential information on the condensate wave function, which is difficult to obtain using standard detection methods. We illustrate the underlying physics with two examples. When condensates acquire phase patterns from external potentials or from vortices, the jets display novel substructure, such as oscillations or spirals, in their correlations. Through a comparison of theory, numerical simulations, and experiments, we show how one can quantitatively extract the phase and the helicity of a condensate from the emission pattern. Our work, demonstrating the strong link between jet emission and the underlying quantum system, bears on the recent emphasis on jet substructure in particle physics.

Deconfining Disordered Phase in Two-Dimensional Quantum Link Models

We explore the ground-state physics of two-dimensional spin-1/2 U(1) quantum link models, one of the simplest nontrivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that, whereas the striped phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms.

A scalable realization of local U(1) gauge invariance in cold atomic mixtures

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

Dynamical Spin-Orbit Coupling of a Quantum Gas

We realize the dynamical 1D spin-orbit coupling (SOC) of a Bose-Einstein condensate confined within an optical cavity. The SOC emerges through spin-correlated momentum impulses delivered to the atoms via Raman transitions. These are effected by classical pump fields acting in concert with the quantum dynamical cavity field. Above a critical pump power, the Raman coupling emerges as the atoms superradiantly populate the cavity mode with photons. Concomitantly, these photons cause a backaction onto the atoms, forcing them to order their spin-spatial state. This SOC-inducing superradiant Dicke phase transition results in a spinor-helix polariton condensate. We observe emergent SOC through spin-resolved atomic momentum imaging and temporal heterodyne measurement of the cavity-field emission. Dynamical SOC in quantum gas cavity QED, and the extension to dynamical gauge fields, may enable the creation of Meissner-like effects, topological superfluids, and exotic quantum Hall states in coupled light-matter systems.

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.

Quantum Entropic Self-Localization with Ultracold Fermions

We study a driven, spin-orbit coupled fermionic system in a lattice at the resonant regime where the drive frequency equals the Hubbard repulsion, for which nontrivial constrained dynamics emerge at fast timescales. An effective density-dependent tunneling model is derived, and it is examined in the sparse filling regime in one dimension. The system exhibits entropic self-localization, where while even numbers of atoms propagate ballistically, odd numbers form localized bound states induced by an effective attraction from a higher configurational entropy. These phenomena occur in the strong coupling limit where interactions impose only a constraint with no explicit Hamiltonian term. We show how the constrained dynamics lead to quantum few-body scars and map to an Anderson impurity model with an additional intriguing feature of nonreciprocal scattering. Connections to many-body scars and localization are also discussed.

Interacting Floquet polaritons

Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions^1,2, raising the prospect of forming synthetic materials³ and quantum information systems^4-7 from photons. One promising approach combines highly excited Rydberg atoms^8-12 with the enhanced light-matter coupling of an optical cavity to convert photons into strongly interacting polaritons^13-15. However, quantum materials made of optical photons have not yet been realized, because the experimental challenge of coupling a suitable atomic sample with a degenerate cavity has constrained cavity polaritons to a single spatial mode that is resonant with an atomic transition. Here we use Floquet engineering^16,17-the periodic modulation of a quantum system-to enable strongly interacting polaritons to access multiple spatial modes of an optical cavity. First, we show that periodically modulating an excited state of rubidium splits its spectral weight to generate new lines-beyond those that are ordinarily characteristic of the atom-separated by multiples of the modulation frequency. Second, we use this capability to simultaneously generate spectral lines that are resonant with two chosen spatial modes of a non-degenerate optical cavity, enabling what we name 'Floquet polaritons' to exist in both modes. Because both spectral lines correspond to the same Floquet-engineered atomic state, adding a single-frequency field is sufficient to couple both modes to a Rydberg excitation. We demonstrate that the resulting polaritons interact strongly in both cavity modes simultaneously. The production of Floquet polaritons provides a promising new route to the realization of ordered states of strongly correlated photons, including crystals and topological fluids, as well as quantum information technologies such as multimode photon-by-photon switching.

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.

Density Waves and Jet Emission Asymmetry in Bose Fireworks

A Bose condensate, subject to periodic modulation of the two-body interactions, was recently observed to emit matter-wave jets resembling fireworks [Nature (London) 551, 356 (2017)NATUAS0028-083610.1038/nature24272]. In this Letter, combining experiment with numerical simulation, we demonstrate that these "Bose fireworks" represent a late stage in a complex time evolution of the driven condensate. We identify a "density wave" stage which precedes jet emission and results from the interference of matter waves. The density waves self-organize and self-amplify without breaking long range translational symmetry. This density wave structure deterministically establishes the template for the subsequent patterns of the emitted jets. Moreover, our simulations, in good agreement with experiment, address an apparent asymmetry in the jet pattern, and show that it is fully consistent with momentum conservation.