Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

Abstract

We develop a fully quantum-mechanical approach, based on stochastic trajectories, for an incoherently pumped system of interacting bosons in contact with a thermal reservoir. It enables a complete characterization of coherence in such a multimode system. We apply our model to microcavity exciton polaritons interacting with acoustic phonons and observe the formation of a macroscopic occupation in the lowest-energy mode accompanied by the simultaneous establishment of temporal and spatial coherence. We describe the transition from thermal to coherent statistics together with the expected emergence of an off-diagonal long-range order.

Kinetic Monte Carlo approach to nonequilibrium bosonic systems

“…This is consistent with earlier works 15,27 . In addition to describing the behaviour of polaritons below and above threshold, the kinetic Monte Carlo theory is able to access the cross-over between the incoherent and condensed regimes.…”

“…However, these methods do not account for quantum fluctuations, which are needed for the unified treatment of nonequilibrium condensation below and above threshold. In principle, density matrix approaches 25 (possibly supplemented with Monte Carlo techniques 26 ) are applicable to this task, however, in practice they are only feasible for systems with small numbers of particles and modes 27 . Bosonic cascade lasers 28,29 , which may operate with millions of particles have been treated with stochastic sampling of the positive-P distribution 30,31 , however, such a method is only accurate in the presence of an initial coherent state.…”

Evolution of Temporal Coherence in Confined Exciton-Polariton Condensates

“…[30], where stochastic quantum jumps are applied to randomly collapse the system wavefunction. This allows to account for the following: (i) Inelastic polariton interactions with a thermal phonon bath of mean populationn th (T ) following a Bose-Einstein distribution, and in particular the emission or absorbtion of phonons to relax or gain energy with scattering rate γ…”

Effects of the non-parabolic kinetic energy on non-equilibrium polariton condensates

“…The interaction of photons with electrons and holes makes use of the dipole and the rotating wave approximation. The Hamiltonian of the polariton modes [4,15,16] has an effective k dependent interaction strength due to the variation of the Hopfield coefficients [17] in k along the lower/upper polariton branch (see e.g. [2]), the Coulomb interaction becomes stronger as the polariton becomes more excitonic, and the saturation interaction is strongest when the polariton consists equally of photon and exciton components.…”

“…The interaction of photons with electrons and holes makes use of the dipole and the rotating wave approximation. The Hamiltonian of the polariton modes 4 , 15 , 16 has an effective k dependent interaction strength due to the variation of the Hopfield coefficients 17 in k along the lower/upper polariton branch (see e.g. ref.…”