Superradiant Topological Peierls Insulator inside an Optical Cavity

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.

Controlling the Dynamics of Atomic Correlations via the Coupling to a Dissipative Cavity

We analyze the relaxation dynamics in an open system, composed by a quantum gas of bosons in a lattice interacting via both contact and global interactions. We report the onset of periodic oscillations of the atomic coherences exhibiting hallmarks of synchronization after a quantum quench. The dynamical behavior exhibits the many-body collapse and revival of atomic coherences and emerges from the interplay of the quantum dissipative nature of the cavity field and the presence of a (approximate) strong symmetry in the dissipative system. We further show that the approximate symmetry can dynamically self-organize. We argue that the approximate symmetry can be tailored to obtain long-lived coherences. These insights provide a general recipe to engineer the dynamics of globally interacting systems.

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering¹, pairing and superfluidity², and the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate³. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen-Cooper-Schrieffer superfluid and Bose-Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

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.

Self-oscillating pump in a topological dissipative atom-cavity system

Pumps are transport mechanisms in which direct currents result from a cyclic evolution of the potential^1,2. As Thouless showed, the pumping process can have topological origins, when considering the motion of quantum particles in spatially and temporally periodic potentials³. However, the periodic evolution that drives these pumps has always been assumed to be imparted from outside, as has been the case in the experimental systems studied so far^4-12. Here we report on an emergent mechanism for pumping in a quantum gas coupled to an optical resonator, where we observe a particle current without applying a periodic drive. The pumping potential experienced by the atoms is formed by the self-consistent cavity field interfering with the static laser field driving the atoms. Owing to dissipation, the cavity field evolves between its two quadratures¹³, each corresponding to a different centrosymmetric crystal configuration¹⁴. This self-oscillation results in a time-periodic potential analogous to that describing the transport of electrons in topological tight-binding models, such as the paradigmatic Rice-Mele pump¹⁵. In the experiment, we directly follow the evolution by measuring the phase winding of the cavity field with respect to the driving field and observing the atomic motion in situ. The observed mechanism combines the dynamics of topological and open systems, and features characteristics of continuous dissipative time crystals.

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].

Numerically Exact Treatment of Many-Body Self-Organization in a Cavity

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many-body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. In particular, for large dissipation strengths a steady state with a fully mixed atomic sector is obtained crucially different from the predicted mean-field state.

Photoinduced Electron Pairing in a Driven Cavity

We demonstrate how virtual scattering of laser photons inside a cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that laser light that is red (blue) detuned from the cavity yields attractive (repulsive) interactions whose strength is proportional to the laser intensity. Furthermore, we find that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, laser-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results provide a novel route for engineering electron interactions in a wide range of two-dimensional materials including AB-stacked bilayer graphene and the conducting interface between LaAlO_{3} and SrTiO_{3}.

Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition

Feedback is a general idea of modifying system behavior depending on the measurement outcomes. It spreads from natural sciences, engineering, and artificial intelligence to contemporary classical and rock music. Recently, feedback has been suggested as a tool to induce phase transitions beyond the dissipative ones and tune their universality class. Here, we propose and theoretically investigate a system possessing such a feedback-induced phase transition. The system contains a Bose-Einstein condensate placed in an optical potential with the depth that is feedback-controlled according to the intensity of the Bragg-reflected probe light. We show that there is a critical value of the feedback gain where the uniform gas distribution loses its stability and the ordered periodic density distribution emerges. Due to the external feedback, the presence of a cavity is not necessary for this type of atomic self-organization. We analyze the dynamics after a sudden change of the feedback control parameter. The feedback time constant is shown to determine the relaxation above the critical point. We show as well that the control algorithm with the derivative of the measured signal dramatically decreases the transient time.

Strongly correlated Fermions strongly coupled to light

Strong quantum correlations in matter are responsible for some of the most extraordinary properties of materials, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interactions, have thus far been strongly coupled with photons. Here we report on the strong coupling of a quantum-degenerate unitary Fermi gas with light in a high finesse cavity. We map out the spectrum of the coupled system and observe well resolved dressed states, resulting from the strong coupling of cavity photons with each spin component of the gas. We investigate spin-balanced and spin-polarized gases and find quantitative agreement with ab initio calculation describing light-matter interaction. Our system offers complete and simultaneous control of atom-atom and atom-photon interactions in the quantum degenerate regime, opening a wide range of perspectives for quantum simulation.

Extended Bose-Hubbard Model with Cavity-Mediated Infinite-Range Interactions at Finite Temperatures

We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short- and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures. At a fixed chemical potential, we map out the distributions of the superfluid order parameters and number densities with respect to the temperatures. For a charge density wave, we find that the global-range interaction enhances the charge order by increasing the transition temperature at which the charge order melts out, while for a supersolid phase, we find that the disappearance of the charge order and the superfluid order occurs at different temperature. At a fixed number-density filling factor, we extract the temperature dependence of the thermodynamic functions such as internal energy, specific heat and entropy. Across the superfluid phase transition, the specific heat has a discontinuous jump.

Topological supersolidity of dipolar Fermi gases in a spin-dependent optical lattice

We investigate the topological supersolid states of dipolar Fermi gases trapped in a spin-dependent 2D optical lattice. Our results show that topological supersolid states can be achieved via the combination of topological superfluid states with the stripe order. Different from the general held belief that supersolid state in fermionic system can only survive with simultaneous coexistence of the repulsive and attractive dipolar interaction. We demonstrate that it can be maintained when the dipolar interaction is attractive in both x and y direction. By adjusting the ratio of hopping amplitude between different directions and dipolar interaction strength U, the system will undergo a phase transition among p _x + ip _y superfluid state, p _y -wave superfluid state, and the topological supersolid state. The supersolid state in the attractive environment is proved to be stable by the positive sign of the inverse compressibility. We also design an experimental protocol to realize the staggered next-next-nearest-neighbor hopping via the laser assisted tunneling technique, which is the key to simulate the spin-dependent potential.

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.

P-Band Induced Self-Organization and Dynamics with Repulsively Driven Ultracold Atoms in an Optical Cavity

We investigate a Bose-Einstein condensate strongly coupled to an optical cavity via a repulsive optical lattice. We detect a stable self-ordered phase in this regime, and show that the atoms order through an antisymmetric coupling to the P band of the lattice, limiting the extent of the phase and changing the geometry of the emergent density modulation. Furthermore, we find a nonequilibrium phase with repeated intense bursts of the intracavity photon number, indicating nontrivial driven-dissipative dynamics.

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.

Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms

We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of 500  μm are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the m_{f}=0 Zeeman state, we observe correlated pair creation in the m_{f}=±1 states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.

Strongly Correlated Bosons on a Dynamical Lattice

We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.

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.