Bose-Einstein Condensates in Superlattices

Mason Alexander Porter, P. G. Kevrekidis

Published Jan 1, 2005• 18 citations

Abstract

Abstract. We consider the Gross–Pitaevskii (GP) equation in the presence of periodic and quasi-periodic su-perlattices to study cigar-shaped Bose–Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coher-ent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system’s equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identify-ing them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns. Key words. Bose–Einstein condensates, multiple scale perturbation theory, Hamiltonian systems

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