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Bose condensation in a model microcavity

EASTHAM, PAUL

Published Jan 1, 2000• 20 citations
OpenAlex

Abstract

We study the equilibrium properties of a system of dipole-active excitons coupled to a single photon mode at fixed total excitation. Treating the presence or absence of a trapped exciton as a two-level system produces a model, the Dicke model, that is exactly soluble. It gives a simple description of polariton condensation in optical cavities, beyond the low-density bosonic regime.

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arXiv:1705.00469•May 1, 2017•0 citations
We study the equilibrium properties of a system of dipole-active excitons coupled to a single photon mode at fixed total excitation. Treating the presence or absence of a trapped exciton as a two-level system produces a model, the Dicke model, that is exactly soluble. It gives a simple description of polariton condensation in optical cavities, beyond the low-density bosonic regime.
We explore the behavior of a system that consists of a photon mode dipole coupled to a medium of two-level oscillators in a microcavity in the presence of decoherence. We consider two types of decoherence processes, which are analogous to magnetic and nonmagnetic impurities in superconductors. We study different phases of this system as the decoherence strength and the excitation density are changed. For a low decoherence we obtain a polariton condensate with comparable excitonic and photonic parts at low densities and a BCS-like state with a bigger photon component due to the fermionic phase-space filling effect at high densities. In both cases there is a large gap in the density of states. As the decoherence is increased, the gap is broadened and suppressed, resulting in a gapless condensate and finally a suppression of the coherence in a low-density regime and a laser at the high-density limit. A crossover between these regimes is studied in a self-consistent way analogous to the Abrikosov and Gor'kov theory of gapless superconductivity [A. A. Abrikosov and L. P. Gor'kov, Sov. Phys. JETP 12, 1243 (1960)].
In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal-equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.
The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.
The properties of traps for exciton polaritons in a semiconductor optical microcavity with an embedded quantum well were considered. The two-component Bose condensate of photons and excitons was described by a coupled system of equations similar to the Gross-Pitaevskii equations, and analytical solutions in the Thomas-Fermi approximation were obtained for traps with weak exciton confinement. For strong confinement, condensate behavior was investigated numerically, and spatial profiles of coupled condensates of excitons and photons (which appear to be different in general case) were determined.
Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.