Quantum fluctuations and collective oscillations of a Bose-Einstein condensate in a 2D optical lattice.
We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.
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BEC-INFM and Dipartimento di Fisica, Universitá di Trento, 1-38050 Povo, Italy.
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