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Physical Review A

Polariton condensation with nonlinear photons

Xiaoyong Guo, Zhongzhou Ren, Zimeng Chi

Published Feb 7, 2012• 16 citations
Publisher

Abstract

In this paper we propose a model of polariton condensation with Kerr-type nonlinear photons. We introduce a generalized Dicke Hamiltonian to describe our system. By constructing the partition function as a path integral, the analytical and numerical solutions are presented. On the mean-field level, it is shown that the polariton condensation can occur and the Kerr nonlinearity affects the character of the polariton condensate. As the nonlinear coefficient increases, the condensate evolves from more photon-like to more exciton-like. Although the photon nonlinearity gives rise to a chemical potential greater than the photon energy, the quasiparticle excitation spectrum is still fully gapped. For the condensate collective excitations, the nonlinearity destroys the Goldstone modes and mixes the phase modes with the amplitude modes, resulting four non-zero-frequency collective modes. In addition, the influence of the photon-exciton detuning on the polariton condensate is also discussed.

DOI
10.1103/physreva.85.023608

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In this paper we propose a model of polariton condensation with Kerr-type nonlinear photons. We introduce a generalized Dicke Hamiltonian to describe our system. By constructing the partition function as a path integral, the analytical and numerical solutions are presented. On the mean-field level, it is shown that the polariton condensation can occur and the Kerr nonlinearity affects the character of the polariton condensate. As the nonlinear coefficient increases, the condensate evolves from more photon-like to more exciton-like. Although the photon nonlinearity gives rise to a chemical potential greater than the photon energy, the quasiparticle excitation spectrum is still fully gapped. For the condensate collective excitations, the nonlinearity destroys the Goldstone modes and mixes the phase modes with the amplitude modes, resulting four non-zero-frequency collective modes. In addition, the influence of the photon-exciton detuning on the polariton condensate is also discussed.
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.
In this paper, we investigate the nonlinear optical properties and photon correlations in a cavity containing quantum wells and interacting with a third-order nonlinear medium. More precisely, we study the interaction of the photonic Kerr nonlinearity with polariton and dipolariton quasiparticles in thermal environments. The optical bistability, the intensity spectrum, and the squeezing spectrum of the transmitted radiation are analyzed. It is shown that the regime of the bistability is reached in the dipolariton cavity faster than attained by the polariton system. Furthermore, the increase of the coupling with the wells reduces the squeezing. More interestingly, it turns out that the additional interactions arising in the dipolariton cavity, between direct and indirect excitons, slow down the variation of the squeezing. As a consequence, dipolaritons offer a greater margin of squeezed light than polaritons, and also than the ${\ensuremath{\chi}}^{(3)}$ medium in the absence of quantum wells. Moreover, the dipolariton system is found to be much more robust against the bath temperature in the weak-coupling regime.
A full quantum theory beyond the mean-field regime is developed for an exciton polariton condensate, to gain a complete understanding of quantum fluctuations. We find analytical solution for the polariton density matrix, showing the polariton nonlinearity causing fast relaxation correlated with the pump so as to yield the condensation at threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian and to a nonclassical distribution beyond the understanding at the level of off-diagonal long-range order. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning and temperature.
Within the framework of quantum field theory, we show that the photon system in a blackbody whose interior is filled by a Kerr nonlinear crystal is in a condensation state. In the condensation state, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired bare photons are transformed into a new kind of quasiparticle, the nonpolariton. The photon-pair system is a condensate and the nonpolariton system is a boson gas. At zero temperature the condensate possesses a largest persistent energy density. The persistent energy density of the condensate is a monotonically decreasing function of temperature and Kerr nonlinear coefficient. The QQQ function of a Kerr nonlinear blackbody at any temperature is derived analytically. In the transition from the normal to the condensation state, the phase symmetry of the photon system is spontaneously broken.