Optical probes of coherence in two dimensional Bose gases of polaritons

Abstract: Due to their photonic components, exciton-polariton systems provide a convenient platform to study the coherence properties of weakly-interacting Bose gases and the Bose-Einstein condensate transition. In particular, optical interferometry enables the measurement of the first-order coherence function which provides insight into the phase of the system. In this paper, we analyze the buildup of coherence in finite-sized, noninteracting, equilibrium Bose gases through the condensate fraction and the related coherent fraction, defined via the first-order coherence function. Our results provide a baseline to compare against experimental data. Discrepancies may indicate where interacting or nonequilibrium models are necessary to describe the system. In the normal phase, before the Bose-Einstein condensate transition, Bose gases exhibit partial spatial and temporal coherence. This significantly alters the paraxial propagation and interference of optical signals from exciton-polariton systems. Therefore, we also analyze diffraction related to the introduction of apertures and time-delay between interferometry arms, given the partial coherence of the source. Comparison to experiment shows remarkable agreement with the noninteracting Bose gas theory, even approaching the quasi-condensate regime.