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Physical Review B

Quantum kinetic equations for interacting bosons and their application for polariton parametric oscillators

Ivan Andreevich Shelykh, R. Johne, Dmitry D. Solnyshkov, Alexey Vitalievich Kavokin, Николай Алексеевич Гиппиус, G. Malpuech

Published Oct 10, 2007• 19 citations
Publisher

Abstract

We derive quantum kinetic equations describing a system of interacting polaritons relaxing the Markovian approximation. We demonstrate the crucial role played by the nonclassical four-particle correlators in the dynamics. The decoherence process is shown to be responsible for the transition from the quantum limit to the classical limit. The general formalism is applied to the description of the dynamics of the polariton parametric oscillator. It allows accounting self-consistently for both signal-idler correlations and pump depletion.

DOI
10.1103/physrevb.76.155308

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Abstract We present an extension of the previous descriptions based on the Dynamics Controlled Truncation Scheme of light‐matter interaction beyond mean‐field, including the microscopic description of the exciton‐photon interaction. This enables the microscopic analysis of the influence of decoherence and noise on the polariton quantum correlations originating from nonlinear optical processes. We expand the operators involved in the dynamics in terms of exact eigenstates of the electron system, the photon and phonon operators and treat phonon‐assisted transitions within the Markov approximation. In particular, we present quantum Heisenberg‐Langevin equations describing light‐induced excitations in semiconductor systems interacting with the phonon bath. This theoretical framework is applied to study the influence of dephasing and noise due to photoluminescence on polariton quantum correlations generated by parametric emission in microcavities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.