Theory of Nonlinear Matter Waves in Optical Lattices

Details Theory of Nonlinear Matter Waves in Optical Lattices Theory of Nonlinear Matter Waves in Optical Lattices

2004-05-17

arxiv.org/abs/cond-mat/0405334v1

Modern Physics Letters B, 18, 627-551 (2004)

Physics

Condensed Matter

Soft Condensed Matter

Modern Physics Letters B (invited brief review), 25 pages, 9 figures

Scientific paper

10.1142/S0217984904007190

We consider several effects of the matter wave dynamics which can be observed in Bose-Einstein condensates embedded into optical lattices. For low-density condensates we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross-Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force, and lattice defects affect the nonlinear matter waves.

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