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Physica B Condensed Matter

General behavior for the condensation of an interacting Bose gas in an 1D optical lattice

Ahmed S. Hassan

Published Jun 3, 2010• 2 citations
Publisher
DOI
10.1016/j.physb.2010.05.083

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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.
Based on the Gross-Pitaevskii theory, for a Bose-condensed gas confined in a harmonic trap and in a one-dimensional (1D) optical lattice, the relationship of the Gaussian width of the sub-condenses and the intensity of 1D-optical lattices potential is studied by using the G-P energy functional and the variational method. For the ideal non-interacting model, the Gaussian width of the sub-condenses is analyzed. Concerning interacting Bose-condensed atoms, the Gaussian approximate model is advanced and the analytic expression of the Gaussian width with the intensity of optical lattices potential is obtained. And then, those analytical results are compared with the straightforward numerical calculation. It indicates that the Gaussian approximate model is closer to the results of the numerical solution, and both are reaching unanimity with the intensity of ID-optical lattices potential increasing.
The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.