Due to their photonic components, exciton-polariton systems provide a convenient platform to study the coherence properties of weakly-interacting Bose gases. In particular, optical interferometry enables the measurement of the first-order coherence function which provides information about the intrinsic correlations of the system. In this paper, we derive a universal curve for the coherent fraction of a noninteracting, equilibrium, homogeneous, two-dimensional Bose gas, with density expressed in units of the observation area, and compare to recent experimental results. Although there is a sharp transition from normal to superfluid phases in the thermodynamic limit, the coherent fraction of the gas varies continuously across this transition due to the finite system size. We find that the theory agrees nearly perfectly with the experimental data in the low-density limit with no free parameters other than the effective temperature, highly constrained by the measurements. At higher density, the experiments are consistent with standard weakly-interacting Bose gas theory. By having a theory that treats both the optical diffraction and Bose coherence, we can clearly see the effect of the quantum statistics on the coherence.
Jachinowski et al. (Tue,) studied this question.