K J H Law et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 195303 doi:10.1088/0953-4075/41/19/195303
K J H Law1, P G Kevrekidis1, B P Anderson2, R Carretero-González3 and D J Frantzeskakis4
Show affiliationsIn this work, we study two-dimensional Bose–Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found that the ground state as well as some of the excited states may be stable or weakly unstable for both attractive and repulsive interatomic interactions. Higher excited states are typically found to be increasingly more unstable.
03.75.Hh Static properties of condensates; thermodynamical, statistical and structural properties
03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow
Issue 19 (14 October 2008)
Received 5 May 2008, in final form 26 August 2008
Published 22 September 2008
K J H Law et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 195303
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