Topological Superradiant States in a Degenerate Fermi Gas

Fluctuation-Induced Bistability of Fermionic Atoms Coupled to a Dissipative Cavity

We investigate the steady state phase diagram of fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. The coupling between the atoms and the cavity field is induced by a transverse pump beam. Taking fluctuations around the mean-field solutions into account, we find that a transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths two self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a bistability. We show that the bistable behavior is induced by the atoms-cavity fluctuations and is not captured by the mean-field approach.

Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition

We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a nonanalytical frequency dependence of the damping ∝|ω|^{2/3}. Standard cavity probes could allow us to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.

Long-Range Photon Fluctuations Enhance Photon-Mediated Electron Pairing and Superconductivity

Recently, the possibility of inducing superconductivity for electrons in two-dimensional materials has been proposed via cavity-mediated pairing. The cavity-mediated electron-electron interactions are long range, which has two main effects: firstly, within the standard BCS-type pairing mediated by adiabatic photons, the superconducting critical temperature depends polynomially on the coupling strength, instead of the exponential dependence characterizing the phonon-mediated pairing; secondly, as we show here, the effect of photon fluctuations is significantly enhanced. These mediate novel non-BCS-type pairing processes, via nonadiabatic photons, which are not sensitive to the electron occupation but rather to the electron dispersion and lifetime at the Fermi surface. Therefore, while the leading temperature dependence of BCS pairing comes from the smoothening of the Fermi-Dirac distribution, the temperature dependence of the fluctuation-induced pairing comes from the electron lifetime. For realistic parameters, also including cavity loss, this results in a critical temperature which can be more than 1 order of magnitude larger than the BCS prediction. Moreover, a finite average number of photons (as can be achieved by incoherently pumping the cavity) adds to the fluctuations and leads to a further enhancement of the critical temperature.

Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas

[Figure: see text].

Realization and Detection of Nonergodic Critical Phases in an Optical Raman Lattice

The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.

Spin-Momentum-Locked Edge Mode for Topological Vortex Lasing

Spin-momentum locking is a direct consequence of bulk topological order and provides a basic concept to control a carrier's spin and charge flow for new exotic phenomena in condensed matter physics. However, up to date the research on spin-momentum locking solely focuses on its in-plane transport properties. Here, we report an emerging out-of-plane radiation feature of spin-momentum locking in a non-Hermitian topological photonic system and demonstrate a high performance topological vortex laser based on it. We find that the gain saturation effect lifts the degeneracy of the paired counterpropagating spin-momentum-locked edge modes enabling lasing from a single topological edge mode. The near-field spin and orbital angular momentum of the topological edge mode lasing has a one-to-one far-field radiation correspondence. The methodology of probing the near-field topology feature by far-field lasing emission can be used to study other exotic phenomena. The device can lead to applications in superresolution imaging, optical tweezers, free-space optical sensing, and communication.

Localization Driven Superradiant Instability

The prominent Dicke superradiant phase arises from coupling an ensemble of atoms to a cavity optical field when an external optical pumping exceeds a threshold strength. Here we report a prediction of the superradiant instability driven by Anderson localization, realized with a hybrid system of the Dicke and Aubry-André (DAA) model for bosons trapped in a one-dimensional (1D) quasiperiodic optical lattice and coupled to a cavity. Our central finding is that for bosons condensed in a localized phase given by the DAA model, the resonant superradiant scattering is induced, for which the critical optical pumping of the superradiant phase transition approaches zero, giving an instability driven by the Anderson localization. The superradiant phase for the DAA model with or without a mobility edge is investigated, showing that the localization driven superradiant instability is in sharp contrast to the superradiance as widely observed for a Bose-Einstein condensate in extended states, and should be insensitive to the temperature of the system. This study unveils a novel effect of localization on the Dicke superradiance, and is well accessible based on the current experiments.

Topologically Protected Quantum Coherence in a Superatom

Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.

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.

Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms

We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.

Self-Adapted Floquet Dynamics of Ultracold Bosons in a Cavity

Floquet dynamics of a quantum system subject to periodic modulations of system parameters provides a powerful tool for engineering new quantum matter with exotic properties. While system dynamics is significantly altered, the periodic modulation itself is usually induced externally and independent of Floquet dynamics. Here we propose a new type of Floquet physics for a Bose-Einstein condensate (BEC) subject to a shaken lattice generated inside a cavity, where the shaken lattice and atomic Floquet bands are mutually dependent, resulting in self-adapted Floquet dynamics. In particular, the shaken lattice induces Floquet quasienergy bands for the BEC, whose backaction leads to a self-adapted dynamical normal-superradiant phase transition for the shaken lattice. Such self-adapted Floquet dynamics shows two surprising and unique features: (i) The normal-superradiant phase transition possesses a hysteresis even without atom interactions. (ii) The dynamical atom-cavity steady state could exist at free energy maxima. The atom interactions strongly affect the phase transition of the BEC from zero to finite momenta. Our results provide a powerful platform for exploring self-adapted Floquet physics, which may open an avenue for engineering novel quantum materials.

Emergent symmetry at superradiance transition of a Bose condensate in two crossed beam cavities

Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87 (2017). The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U(1) symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U(1) symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.

Symmetry-Protected Topological States for Interacting Fermions in Alkaline-Earth-Like Atoms

We discuss the quantum simulation of symmetry-protected topological (SPT) states for interacting fermions in quasi-one-dimensional gases of alkaline-earth-like atoms such as ^{173}Yb. Taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these atoms, we consider Raman-assisted spin-orbit couplings in the clock states, which, together with the spin-exchange interactions in the clock-state manifolds, give rise to SPT states for interacting fermions. We numerically investigate the phase diagram of the system, and study the phase transitions between the SPT phase and the symmetry-breaking phases. The interaction-driven topological phase transition can be probed by measuring local density distribution of the topological edge modes.

Quantum mixed phases of a two-dimensional polarized degenerate Fermi gas in an optical cavity

The coupling of ultracold fermions to a high-finesse optical cavity can result in novel many-body phenomena, and has attracted significant interests at present. Here we consider a realization of the Fermi-Dicke model with controllable parameters, based on a two-dimensional polarized degenerate Fermi gas coupled to an optical cavity. We analytically investigate the ground-state properties of such system under the mean-field approximation. We find the system can exhibit a rich phase diagram depending on the fermion-photon coupling strength and the atomic resonant frequency. Contrasting to the bosonic counterpart, a first-order quantum phase transition between the superradiant phase and the normal phase featuring two Fermi surfaces can occur for the weak atomic resonant frequency, and there is a unique mixed phase where this normal phase and the superradiant phase coexist. The experimental detection of our results is also discussed.

Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity

We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.

Superradiant Topological Peierls Insulator inside an Optical Cavity

We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity, the homogeneous gas density breaks a Z_{2} symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization, the resulting Bloch bands can have a nontrivial topological structure characterized by a nonvanishing Zak phase. In the case where the Fermi momentum is close to half of the cavity-mode wave number, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be nondestructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well-defined frequency window of the cavity spectrum.

Meissner-like Effect for a Synthetic Gauge Field in Multimode Cavity QED

Previous realizations of synthetic gauge fields for ultracold atoms do not allow the spatial profile of the field to evolve freely. We propose a scheme which overcomes this restriction by using the light in a multimode cavity with many nearly degenerate transverse modes, in conjunction with Raman coupling, to realize an artificial magnetic field which acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution of such a system and present the results of numerical simulations which show dynamical coupling between the effective field and the matter on which it acts. Crucially, the freedom of the spatial profile of the field is sufficient to realize a close analogue of the Meissner effect, where the magnetic field is expelled from the superfluid. This backaction of the atoms on the synthetic field distinguishes the Meissner-like effect described here from the Hess-Fairbank suppression of rotation in a neutral superfluid observed elsewhere.

Superradiance Induced Particle Flow via Dynamical Gauge Coupling

We study fermions that are gauge coupled to a cavity mode via Raman-assisted hopping in a one-dimensional lattice. For an infinite lattice, we find a superradiant phase with an infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the nonequilibrium dynamics including fluctuation effects. The short-time dynamics is dominated by superradiance, while the long-time behavior is governed by cavity fluctuations. We show that the steady state in the finite lattice is not unique and can be understood in terms of coherent bosonic excitations above a Fermi surface in real space.

Semiclassical bifurcations and topological phase transitions in a one-dimensional lattice of coupled Lipkin-Meshkov-Glick models

In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean-field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with free open-boundary conditions.

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

We propose how a fermionic quantum gas confined to an optical lattice and coupled to an optical cavity can self-organize into a state where the spontaneously emerging cavity field amplitude induces an artificial magnetic field. The fermions form either a chiral insulator or a chiral liquid carrying chiral currents. The feedback mechanism via the dynamical cavity field enables robust and fast switching in time of the chiral phases, and the cavity output can be employed for a direct nondestructive measurement of the chiral current.