Abstract We study superradiant phase transitions in a hybrid system of a two-dimensional Bose–Einstein condensate of atoms and two cavities arranged with a tilt angle. By adjusting the loss rate of cavities, we map out the phase diagram of steady states within a mean field framework. It is found that when the loss rates of the two cavities are different, superradiant transitions may not occur at the same time in the two cavities. A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance. In the case that both cavities are superradiant, a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate. The photon current shows a non-monotonic dependence on the loss rate difference, owing to the competition of photon number difference and cavity field phase difference. Our findings can be realized and detected in experiments.
Abstract We study superradiant phase transitions in a hybrid system of a two-dimensional Bose–Einstein condensate of atoms and two cavities arranged with a tilt angle. By adjusting the loss rate of cavities, we map out the phase diagram of steady states within a mean field framework. It is found that when the loss rates of the two cavities are different, superradiant transitions may not occur at the same time in the two cavities. A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance. In the case that both cavities are superradiant, a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate. The photon current shows a non-monotonic dependence on the loss rate difference, owing to the competition of photon number difference and cavity field phase difference. Our findings can be realized and detected in experiments.
Abstract We consider a Bose–Einstein condensate loaded inside an optical cavity and exposed to two crossed coherent pump fields with same imbalance parameter γ . We identify different effects between pure standing wave fields ( γ = 1) and the pump beams combining standing wave and running wave ( γ ≠ 1). In particular, for γ = 1, the system only hosts a normal phase and a superradiant phase. In contrast, for γ ≠ 1, the system features three distinctive phases: the normal phase (NP), superradiant phase 1 (SR 1 ), and superradiant phase 2 (SR 2 ). Importantly, the superradiance is subdivided into different types characterized by the photon phase. Furthermore, we determine perturbatively the phase boundary separating the normal phase and the superradiant phases, and find that there exists a competitive relationship of energy minimum on the overlapping region between SR 1 and SR 2 . Interestingly, the transition between the normal phase to SR 1 or SR 2 is identified to be a second-order phase transition, while the transition between SR 1 and SR 2 is a first-order transition. When the first-order phase transition occurs, the phase of the photons changes abruptly from 0 to π /2.
We consider a Bose-Einstein condensate inside an optical cavity and two crossed coherent pump fields. We determine perturbatively the phase boundary separating the normal superfluid phase and the superradiance phase. In the regime of negative cavity detuning, we map out the phase diagrams for both an attractive and a repulsive optical lattice. It turns out that the situation is quite different in the two cases. Specifically, in the case of an attractive lattice, if a system is in the superradiant phase with one pump laser, adding another pump does not drive the system out of the superradiance phase, while for the repulsive lattice, increasing another pump potential has suppressive effects on the superradiance. We also find that, in the case of an attractive lattice, equally increasing two pump lattice potentials can induce a transition from the normal phase to the superradiance phase. In stark contrast, for the repulsive lattice, the system will remain in the normal phase as the pump depths are tuned within a wide range, independently of the cavity detuning and the decay rate.
We present a theoretical model for a transversally driven Bose-Einstein condensate coupled to an optical cavity. We focus on the interplay between different coherent couplings, which can trigger a structural phase transition, known as the superradiant phase transition. Our approach, based on band structure theory and a mean-field description, enables a comprehensive analysis of the nature of the system's excited modes, precursing the phase transitions. By incorporating dissipative couplings, intrinsic to these systems, we find non-Hermitian phenomena such as the coalescence of crossing precursor modes and the emergence of exceptional points (EPs). The general formulation of our model allows us to explain the role of an angle between transverse pump and the cavity deviating from 90∘. This offers us a unified perspective on the plethora of different implementations of such systems.
Abstract As a crucial role in various aspects of quantum transport, quantum pumping usually refers to the controlled movement of particles through external manipulation. This work reports a unique occurrence of self-organized quantum pumping for photons without any external driving in a spin–cavity system, where an assemble of quantum emitters interact with photonic modes confined in two tunneling-coupled cavities. Specifically, undermirror-symmetry breaking of cavity dissipations and spin–cavity coupling strengths, a steady photon current spontaneously emerges between the two cavities when the system reaches its superradiant phase. Investigation shows that cavity dissipation, which acts as a pump, assists the system to sustainably extract photons from the surroundings and generate a superradiant photon current with photon loss via dissipation channels. Generating with Z 2 spontaneous symmetry breaking, this kind of counter-intuitive photon current provides a spontaneous regime for the occurrence of current in real space.
Experiments on Bose-Einstein condensates in optical cavities have observed a coherent state of the matter-light system-superradiance. The nature of these experiments demands consideration of collective dynamics. Including cavity leakage and the backreaction of the cavity field on the condensate, we find a rich phase diagram including multiphase coexistence regions, and persistent optomechanical oscillations. The proximity of the phase boundaries results in a critical slowing down of the decay of many-body oscillations, which can be enhanced by large cavity loss.
In this paper we investigate the finite-temperature properties of a Bose-Einstein condensate (BEC)-cavity system with a strong nonlinear atom-photon interaction by means of a functional path-integral approach. It is shown that the experimentally observed phase diagram [Baumann, Guerlin, Brennecke, and Esslinger, Nature (London) 464, 1301 (2010)] can be better explained in our finite-temperature theory. More importantly, we identify a new dynamical unstable phase in this experiment. By tuning various experimental parameters, we reveal some rich temperature-driven phase diagrams and, in particular, predict a four-phase coexistence point. Finally, we find analytically that the specific heat in the superradiant phase increases exponentially at lower temperatures. Moreover, it has a large jump at the temperature-driven critical point where the superradiant-normal phase transition occurs. As a result, we argue that the specific heat can serve as a powerful tool to probe the thermodynamic properties of the BEC-cavity system.