Detecting Phase Coherence of 2D Bose Gases via Noise Correlations

We measure the noise correlations of two-dimensional (2D) Bose gases after free expansion, which allows us to characterize the in-situ phase coherence across the Berezinskii-Kosterlitz-Thouless (BKT) transition. The noise correlation function features a characteristic spatial oscillatory behavior in the superfluid phase, which gives direct access to the superfluid exponent. This oscillatory behavior vanishes above the BKT critical point, as we demonstrate for both single-layer and decoupled bilayer 2D Bose gases. Our work establishes noise interferometry as a general tool to probe and identify many-body states of bilayer quantum gases.