title: Observation of scale invariance and universality in two-dimensional Bose gases.
abstract: The collective behaviour of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics; for example, thermodynamic observables follow generalized scaling laws near the phase transition. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry result in a broad fluctuation regime and an extended range of universal scaling behaviour. Studies of the BKT transition in cold atoms have stimulated great interest in recent years, but a clear demonstration of critical behaviour near the phase transition has remained elusive. Here we report in situ density and density-fluctuation measurements of two-dimensional Bose gases of caesium at different temperatures and interaction strengths, observing scale-invariant, universal behaviours. The extracted thermodynamic functions confirm the existence of a wide universal region near the BKT phase transition, and provide a sensitive test of the universality predicted by classical-field theory and quantum Monte Carlo calculations. Our experimental results provide evidence for growing density-density correlations in the fluctuation region, and call for further explorations of universal phenomena in classical and quantum critical physics.
authors.affiliation: The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA. clhung@uchicago.edu
authors.forename: Chen-Lung
authors.initials: CL
authors.lastname: Hung
authors.forename: Xibo
authors.initials: X
authors.lastname: Zhang
authors.forename: Nathan
authors.initials: N
authors.lastname: Gemelke
authors.forename: Cheng
authors.initials: C
authors.lastname: Chin