Studies of Bose-Einstein condensation in dilute atomic gases have attracted a lot of attention from the Physics community, as testified by the 2001 Nobel Prize. This active and competitive research is the meeting point of several disciplines, from high precision measurements to condensed matter physics. Two prominent research topics have been vortices in rotating Bose-Einstein condensates, and condensates confined in optical lattices. The present project combines these two subfields of research. We plan t o study experimentally the physical properties of an ensemble of coupled disk-shaped condensates, set in rotation using a moving laser beam. The disk structure is produced by an optical standing wave which strongly confines the atoms in one direction, while keeping the confinement in the other two dimensions much weaker. The number of layers and the coupling between them is controlled by changing the period and the strength of the standing wave. The physical problems to be studied with this system are connected to important questions in condensed matter and statistical physics. First, a stack of coupled rotating planar condensates is reminiscent of a system of weakly coupled layered superconductors; we shall investigate whether the phase transition of vorte x lattice melting known to occur in the latter system can be explored in the layered gas. We also intend to address the regime of fast rotation, leading to strongly correlated ground states of the gas; this includes regimes analogous to the fractional Quantum Hall effect, which are expected to occur if the number of vortices is increased to the number of atoms in a given disk. Finally, the reduced dimensionality will also increase the importance of quantum fluctuations, and the resulting absence of true lo ng-range order can lead to spontaneous creation of vortices. This should allow us to observe the Kosterlitz-Thouless transition, i.e. the binding of the vortices into pairs at sufficiently low temperature.
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