Keldysh field theory for nonequilibrium condensation in a parametrically pumped polariton system

TL;DR

This paper develops a Keldysh quantum field theory for parametrically pumped polaritons, revealing that the non-equilibrium phase transition to an optical parametric oscillator resembles equilibrium condensation, with observable spectral signatures.

Contribution

It introduces a theoretical framework using Keldysh Green's functions to analyze non-equilibrium polariton condensation, highlighting the analogy to equilibrium phase transitions.

Findings

The phase transition is characterized by an effective chemical potential.

The system exhibits an effective temperature at the transition.

Spectral properties like luminescence reflect the transition dynamics.

Abstract

We develop a quantum field theory for parametrically pumped polaritons using Keldysh Green's function techniques. By considering the mean-field and Gaussian fluctuations, we find that the low energy physics of the highly non-equilibrium phase transition to the optical parametric oscillator regime is in many ways similar to equilibrium condensation. In particular, we show that this phase transition can be associated with an effective chemical potential, at which the system's bosonic distribution function diverges, and an effective temperature. As in equilibrium systems, the transition is achieved by tuning this effective chemical potential to the energy of the lowest normal mode. Since the occupations of the modes are available, we determine experimentally observable properties, such as the luminescence and absorption spectra.