Superfluid Dynamics of a Bose-Einstein Condensate in a Periodic Potential

Details Superfluid Dynamics of a Bose-Einstein Condensate in a Periodic Potential Superfluid Dynamics of a Bose-Einstein Condensate in a Periodic Potential

2003-10-31

arxiv.org/abs/cond-mat/0310780v1

New J. Phys. 5 (2003) 112

Physics

Condensed Matter

Soft Condensed Matter

13 pages, 7 figures, movies and published paper available at http://www.iop.org/EJ/abstract/1367-2630/5/1/112

Scientific paper

10.1088/1367-2630/5/1/112

We investigate the superfluid properties of a Bose-Einstein condensate (BEC) trapped in a one dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce {\it two} different, density dependent, effective masses and group velocities. The Bogoliubov spectrum predicts the existence of sound waves, and the arising of energetic and dynamical instabilities at critical values of the BEC quasi-momentum which dramatically affect its coherence properties. We investigate the dependence of the dipole and Bloch oscillation frequencies in terms of an effective mass averaged over the density of the condensate. We illustrate our results with several animations obtained solving numerically the time-dependent Gross-Pitaevskii equation.

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