Abstract
Bernard Deconinck
Bose-Einstein condensates trapped in standing light waves.
The cubic nonlinear Schrodinger equation with trigonometric potential
models a quasi-one-dimensional dilute gas Bose--Einstein condensate
trapped in a standing light wave. Families of stationary solutions are
presented for single and coupled condensates. Their stability is examined
using analytical and numerical methods. For condensates with repulsive
atomic interaction, stable solutions are off-set from zero; they are
deformations of the ground state of the linear Schrodinger equation. Our
results show that a large number of condensed atoms is sufficient to form
a stable, periodic condensate. For condensates with attractive atomic
interaction, stable solutions have nodes and are localized in the troughs
of the potential. Finally, exact solutions which are valid beyond
mean-field theory are discussed.
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