Projector-based renormalization approach to electron-hole-photon systems in nonequlibrium steady-state

TL;DR

This paper extends the projector-based renormalization method to non-equilibrium electron-hole-photon systems, enabling analysis of exciton and polariton condensation, spectral properties, and steady-state behaviors in semiconductor microcavities.

Contribution

It introduces a non-equilibrium extension of the renormalization approach for coupled fermion-boson systems, capturing correlation effects beyond mean-field theory.

Findings

Demonstrates Bose-Einstein condensation of excitons and polaritons.

Shows a smooth transition in condensation with increasing excitation density.

Provides detailed spectral and steady-state properties of the system.

Abstract

We present an extended version of the projector-based renormalization method that can be used to address not only equilibrium but also non-equilibrium situations in coupled fermion-boson systems. The theory is applied to interacting electrons, holes and photons in a semiconductor microcavity, where the loss of cavity photons into vacuum is of particular importance. The method incorporates correlation and fluctuation processes beyond mean-field theory in a wide parameter range of detuning, Coulomb interaction, light-matter coupling and damping, even in the case when the number of quasiparticle excitations is large. This enables the description of exciton and polariton formation, and their possible condensation through spontaneous phase symmetry breaking by analyzing the ground-state, steady-state and spectral properties of a rather generic electron-hole-photon Hamiltonian, which also includes the coupling to two fermionic baths and a free-space photon reservoir. Thereby, the steady-state behavior of the system is obtained by evaluating expectation values in the long-time limit by means of the Mori-Zwanzig projection technique. Tracking and tracing different order parameters, the fully renormalized single-particle spectra and the steady-state luminescence, we demonstrate the Bose-Einstein condensation of excitons and polaritons and its smooth transition when the excitation density is increased.