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The control of atomic motion using periodic standing waves of light (optical lattices) is a very powerful and versatile technique. For example a one-dimension optical lattice is a convenient tool to prepare a quasi-2D cold atomic sample. When the zero-point vibration energy at the lattice nodes is larger than the chemical potential and the temperature of the gas, the motion along the lattice direction is frozen and the gases in the various nodal planes of the lattice are effectively 2D.
Thermodynamics of a Bose gas in 2D is quite different from the usual 3D situation. In a 2D homogeneous system, phase fluctuations induced by long wavelength phonons destroy long range order at any finite temperature, and the phase correlation function is expected to decay algebraically. In addition, 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 transition from a superfluid state at low temperature, to a normal state at high temperature. Atomic gases constitute convenient systems to investigate the various aspects of quantum 2D physics. By preparing two planes of atoms with similar temperatures and chemical potentials, and by letting them overlap and interfere, one realizes a matter wave heterodyning experiment, which gives a direct access to several features of the phase distributions of the planes. Free vortices appear as sharp dislocations of the interference patterns, and long wavelength phonons create a smooth and random variation of the interference fringes. The talk will first give a short review on various aspects of 2D physics for quantum gases, and it will then present some recent experimental results obtained with rubidium quasi-2D condensates, using this matter wave heterodyning technique [1]. [1] S. Stock, Z. Hadzibabic, B. Battelier, M. Cheneau, and J. Dalibard, Phys. Rev. Lett. 95, 190403 (2005). |
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