Observation of spatial first-order coherence in an optical quantum gas in a box

The emergence of long-range phase correlations is a key signature for phase transitions to ordered states of matter. Exploring the first-order spatial coherence in large samples with uniform density provides direct insight into such correlations insensitive to the local density. Here we report measurements of the spatial phase correlations in a two-dimensional photon gas inside a box potential trap realized in a nanostructured dye-filled microcavity. The correlations of the uniform optical quantum gas are determined both from the momentum space distribution and by interferometry of the microcavity emission. While in the normal gas the coherence length is governed by short-range thermal correlations, the quantum degenerate gas is observed to build up quasi-long-range correlations that decay exponentially. As the coherence length exceeds the finite size of the box trap, the optical quantum gas condenses, as verified for different system sizes.