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Bose-Einstein Condensates in Superlattices

Porter, Mason A. and Kevrekidis, P. G. (2005) Bose-Einstein Condensates in Superlattices. SIAM Journal on Applied Dynamical Systems, 4 (4). pp. 783-807. ISSN 1536-0040. http://resolver.caltech.edu/CaltechAUTHORS:PORsiamjads05

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Abstract

We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices 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 coherent 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, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns.


Item Type:Article
Additional Information:© 2005 Society for Industrial and Applied Mathematics Received by the editors June 26, 2004; accepted for publication (in revised form) by T. Kaper June 14, 2005; published electronically October 7, 2005. The work of this author [MAP] was supported by a VIGRE grant awarded to the School of Mathematics at Georgia Tech, where much of this research was conducted. The work of this author [PGK] was supported by NSF-DMS-0204585 and NSF-DMS0505063, the Eppley Foundation for Research, and an NSF-CAREER award. We wish to acknowledge Todd Kapitula for numerous useful interactions and discussions during the early stages of this work, and the three anonymous referees and the SIADS editors for several helpful comments and suggestions. We also thank Jit Kee Chin, Peter Engels, and Li You for useful interactions.
Subject Keywords:Bose-Einstein condensates, multiple scale perturbation theory, Hamiltonian systems
Record Number:CaltechAUTHORS:PORsiamjads05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:PORsiamjads05
Alternative URL:http://epubs.siam.org/SIADS/volume-04/art_61061.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2136
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:10 Mar 2006
Last Modified:26 Dec 2012 08:47

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