I will give a short introduction to the physics of trapped 2D gases, and present some recent experimental results obtained with rubidium quasi-2D condensates.
In a homogeneous 2D system, long wavelength phase fluctuations destroy the long range order at any finite temperature. Further, when the temperature increases, bound vortex-antivortex pairs are expected to break, and a proliferation of free vortices is expected. This is the Kosterlitz-Thouless (KT) phase transition from a superfluid state with algebraic order at low temperature, to a normal state at high temperature. In a trapped gas, the harmonic confinement can make the superfluid phase more robust, and the nature of the low temperature state is a topic of some theoretical debate.
In an optical lattice, we can create two parallel, independent 2D atomic clouds with similar temperatures and chemical potentials. Interference of such clouds realizes a matter wave heterodyning experiment which gives direct access to several features of the phase distributions in the two planes. Free vortices appear as sharp dislocations in the interference pattern, and long wavelength phase fluctuations create a smooth and random variation of the interference fringes. Temperature study of these effects could give new insights into the KT physics.