Bose-Einstein condensation in an optical lattice: A perturbation approach

Abstract

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function.

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Cited by in corpus (6)

• One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential
• Bose-Einstein condensates in optical lattices: mathematical analysis and analytical approximate formulae
• Excited states of exciton-polariton condensates in 2D and 1D harmonic traps
• Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice
• Superfluidity and collective oscillations of trapped Bose-Einstein condensates in a periodical potential
• Collective modes of trapped spinor Bose condensates