  The collective behavior of a many-body system near a continuous phase
transition is insensitive to the details of its microscopic physics[1].
Characteristic features near the phase transition are that the thermodynamic
observables follow generalized scaling laws[1]. The
Berezinskii-Kosterlitz-Thouless (BKT) phase transition[2,3] in two-dimensional
(2D) Bose gases presents a particularly interesting case because the marginal
dimensionality and intrinsic scaling symmetry[4] result in a broad fluctuation
regime which manifests itself in an extended range of universal scaling
behavior. Studies on BKT transition in cold atoms have stimulated great
interest in recent years[5-10], clear demonstration of a critical behavior near
the phase transition, however, has remained an elusive goal. Here we report the
observation of a scale-invariant, universal behavior of 2D gases through
in-situ density and density fluctuation measurements at different temperatures
and interaction strengths. The extracted thermodynamic functions confirm a wide
universal region near the BKT phase transition, provide a sensitive test to the
universality prediction by classical-field theory[11,12] and quantum Monte
Carlo (MC) calculations[13], and point toward growing density-density
correlations in the fluctuation region. Our assay raises new perspectives to
explore further universal phenomena in the realm of classical and quantum
critical physics.
