We discuss the dynamics of classical Dicke-type models, aiming to\nclarify the mechanisms by which coherent states could develop in potentially\nnon-equilibrium systems such as semiconductor microcavities. We present\nsimulations of an undamped model which show spontaneous coherent states\nwith persistent oscillations in the magnitude of the order parameter. These\nstates are generalisations of superradiant ringing to the case of inhomogeneous\nbroadening. They correspond to the persistent gap oscillations proposed in\nfermionic atomic condensates, and arise from a variety of initial conditions. We\nshow that introducing randomness into the couplings can suppress the oscillations,\nleading to a limiting dynamics with a time-independent order parameter. This\ndemonstrates that non-equilibrium generalisations of polariton condensates can\nbe created even without dissipation. We explain the dynamical origins of the\ncoherence in terms of instabilities of the normal state, and consider how it can\nadditionally develop through scattering and dissipation.
We discuss the dynamics of classical Dicke-type models, aiming to\nclarify the mechanisms by which coherent states could develop in potentially\nnon-equilibrium systems such as semiconductor microcavities. We present\nsimulations of an undamped model which show spontaneous coherent states\nwith persistent oscillations in the magnitude of the order parameter. These\nstates are generalisations of superradiant ringing to the case of inhomogeneous\nbroadening. They correspond to the persistent gap oscillations proposed in\nfermionic atomic condensates, and arise from a variety of initial conditions. We\nshow that introducing randomness into the couplings can suppress the oscillations,\nleading to a limiting dynamics with a time-independent order parameter. This\ndemonstrates that non-equilibrium generalisations of polariton condensates can\nbe created even without dissipation. We explain the dynamical origins of the\ncoherence in terms of instabilities of the normal state, and consider how it can\nadditionally develop through scattering and dissipation.
We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an undamped model which show spontaneous coherent states with persistent oscillations in the magnitude of the order parameter. These states are generalizations of superradiant ringing to the case of inhomogeneous broadening. They correspond to the persistent gap oscillations proposed in fermionic atomic condensates, and arise from a variety of initial conditions. We show that introducing randomness into the couplings can suppress the oscillations, leading to a limiting dynamics with a time-independent order parameter. This demonstrates that non-equilibrium generalizations of polariton condensates can be created even without dissipation. We explain the dynamical origins of the coherence in terms of instabilities of the normal state, and consider how it can additionally develop through scattering and dissipation.
Non-equilibrium polariton condensates entangle properties of lasers, atomic Bose- Einstein condensates (BEC) and semiconductor physics. They provide a great variety of physical phenomena while maintaining a simple theoretical description. Among those phenomena are nonlinear excitations such as solitons or spontaneous spin bifurcations. In this paper I first present a short overview on the theoretical basis of polaritons. Then starting from a scenario of excitation generation in equilibrium BEC I turn to corresponding phenomenona in polariton condensates such as dark soliton formation. Later the spin sensitive phenomena such as nonequilibrium bright solitons and half-bright solitons in semiconductor microcavities are discussed. Theoretically all the considered scenarios are described by partial differential equations (PDEs) and coupled systems thereof. The system of PDEs defines a so called condensate wave function, which completely describes the experimental relevant aspects of the physical system in a certain parameter regime where condensation occurs. The developed theories enables us particularly to make a variety of statements about excitations such as solitons and half-solitons in spinor systems forming within a non-equilibrium condensate. It turns out that by those means we can elucidate in particular the experimental implementation of a coherent superposition analog in a spin sensitive setting forming a macroscopic QUBIT within the semiconductor microcavity at temperatures in the Kelvin range.
Development of spontaneous coherence is one of the hallmarks of bosonic condensation in a variety of physical systems, such as cold atoms, confined photons, and hybrid light-matter quasiparticles like exciton polaritons in semiconductors. While spatial coherence is well understood once a steady-state condensate has been established, its temporal evolution as the condensate forms is largely unexplored. Here, we explore the dynamical formation of a non-equilibrium, driven-dissipative exciton-polariton condensate through both time-resolved experiments and numerical modeling. Our study reveals that the spatial coherence is established through two distinct stages. The early-time stage is interaction-driven and features transient oscillations in spatial coherence. This stage is followed by a steady-state regime characterized by a spatially-uniform high degree of coherence that extends over the entire size of the system and persists over time. These stages of spatial coherence development occur in both free flowing and confined exciton-polariton systems that undergo a quench - rapid growth of the condensate starting from two different initial settings. Our study offers a deep insight into the process by which long-range spatial coherence is established in a non-equilibrium bosonic condensate.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
The demonstration of coherent polariton emission from a CdTe microcavity structure [1] has provided a new system for the study of condensate physics. Unlike atomic condensates, the microcavity system is not in equilibrium; the polariton life-time in the cavity is only ∼ 2ps, so the population has to be maintained by pumping. This raises interesting questions about how the properties of such a non-equilibrium condensate differ from those of an equilibrium system. Recent experimental measurements of the first (g(1)) and second (g(2)) order correlation functions of the emitted light have shown that the decay times of both are ∼ 100−200ps, much longer than the cavity life-time. In this work, we present a theroetical treatment which provides a quantitative explanation of these results, and shows that the ultimate cause of the coherence decay is interactions between polaritons in the condensate. The microcavity polariton condensate is a mesoscopic quantum system, consisting of N ∼ 102 po-laritons within the finite size excitation spot. As a result, number fluctuations of ∼ N 1 2 are expected. For a finite equilibrium condensate of interacting particles, it is straight forward to show that the decay
Motivated by recent experiments on light-matter interacting systems, we investigate a dilute Bose gas and self-bound quantum droplets in a one-dimensional optical lattice coupled to a lossy cavity mode. Using a classical-field approach, we determine the stationary states and collective excitations of this non-equilibrium system. Apart from the usual Bogoliubov modes, we identify a polariton-like gapped excitation, the frequency of which softens as a precursor of the density ordering transition. Moreover, its relaxation time diverges as the critical point is approached, signaling the non-equilibrium nature of this transition. Dynamically, this polariton-like mode can be probed by inducing cavity field fluctuations, which in turn generates spatio-temporal oscillations of both the condensate and droplet states. In the droplet regime, we also analyze the bound modes which bear the characteristics of such non-equilibrium self-bound state. In addition, we uncover solitonic non-equilibrium states, including condensate with kink-like configuration and double-droplet state, and investigate their robustness following a sudden quench. Remarkably, although these states become unstable beyond a critical coupling, they continue to manifest in the dynamics, akin to the scarring phenomena. Our results demonstrate that dissipative cavity coupling provides a versatile route for exploring rich non-equilibrium dynamics of condensates and quantum droplets within experimentally accessible settings.