Imaging Phase Fluctuation in a Coherently Coupled Bose Mixture

We experimentally study fluctuations in a quantum simulator of (2+1)D massive relativistic fields, constructed by coherent coupling of two spin states in a homogeneous 2D 39K gas. Using RF manipulation, we convert relative phase fluctuations in the coupled mixture into relative spin population fluctuations, which we directly image and analyze on different length scales. By quenching the ratio of the spin chemical potential to the coherent coupling strength, we demonstrate the growth (and reduction) of relative phase fluctuations as interaction becomes more (or less) dominant.