Physics – Condensed Matter
Scientific paper
2003-05-13
Eur. Phys. J. D 27, 247 (2003)
Physics
Condensed Matter
version published in EPJ D
Scientific paper
10.1140/epjd/e2003-00284-4
We discuss the Bloch-state solutions of the stationary Gross-Pitaevskii equation and of the Bogoliubov equations for a Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The results for the compressibility, effective mass and velocity of sound are analysed as a function of the lattice depth and of the strength of the two-body interaction. The band structure of the spectrum of elementary excitations is compared with the one exhibited by the stationary solutions (``Bloch bands''). Moreover, the numerical calculations are compared with the analytic predictions of the tight binding approximation. We also discuss the role of quantum fluctuations and show that the condensate exhibits 3D, 2D or 1D features depending on the lattice depth and on the number of particles occupying each potential well. We finally show how, using a local density approximation, our results can be applied to study the behaviour of the gas in the presence of harmonic trapping.
Kraemer Meret
Menotti Chiara
Pitaevskii Lev
Stringari Sandro
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