We describe a recent experiment performed with rubidium atoms ($^{87}$Rb), aiming at studying the coherence properties of a two-dimensional gas of bosonic particles at low temperature. We have observed in particular a Berezinskii--Kosterlitz--Thouless (BKT) type crossover in the system, using a matter wave heterodyning technique. At low temperatures, the gas is quasi-coherent on the length scale set by the system size. As the temperature is increased, the loss of long-range coherence coincides with the onset of the proliferation of free vortices, in agreement with the microscopic BKT theory.

To appear in "ATOMIC PHYSICS 20" Proceedings of the XX International Conference on Atomic Physics (ICAP)