Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential

Abstract

The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case.

37 pages, 27 figures, with an appendix by J. C. Bronski

References in corpus (7)

• Cold bosonic atoms in optical lattices
• Bose-Einstein Condensation of Atomic Hydrogen
• Regimes of quantum degeneracy in trapped 1D gases
• Quantum Logic Gates in Optical Lattices
• Bose-Einstein condensation in quasi2D trapped gases
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• Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential