Ja n 20 05 Superfluid to Mott insulator transition in one , two , and three dimensions

We have created one-, two-, and three-dimensional quantum gases and study the superfluid to Mott insulator transition. Measurements of the transition using Bragg spectroscopy show that the excitation spectra of the low-dimensional superfluids differ significantly from the three-dimensional case. A low dimensional gas can be created in a trap when the confining potential restricts the motion of the particles to one or two dimensions with the other motional degrees of freedom being frozen out. Quantum mechanically this implies that the particles occupy only the ground state in the restricted directions, i.e. both, the thermal energy k B T and the interaction energy µ have to be much smaller than the energy level spacing. In general, low-dimensional systems exhibit increased quantum fluctuations of the phase. For a homogeneous 2D gas these phase fluctuations allow Bose-Einstein condensation only at zero temperature and for a homogeneous 1D gas no Bose condensation is possible at all. For trapped low-dimensional gases the Bose-Einstein phase transition takes place at finite temperatures for both, 1D 1 and 2D 2 , but the fluctuating phase alters the properties of the gas. Low-dimensional quantum systems exhibit a wealth of fascinating phenomena whose explanations go beyond the mean-field description 3. For example, in one dimension bosons acquire fermionic properties at low densities and strong interactions, forming the so-called Tonks-Girardeau gas 4. For two dimensions a Berezinskii-Kosterlitz-Thouless transition is predicted resulting in the spontaneous formation of vortices from thermal excitations 5 .