Dynamics of Bose-Einstein condensates under the influence of periodic and harmonic potentials

A variational method is developed to describe the dynamics of a Bose-Einstein condensate (BEC) trapped in an applied external potential consisting of both a harmonic and periodic component. Using this variational method, the BEC dynamics is shown to be well approximated by four coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude (width), chirp, center position, and center frequency. The simplified analytic theory allows for an efficient and convenient method for characterizing the experimental BEC behavior when localized condensates are generated. It further gives the critical strength ratio of harmonic to periodic potential necessary to support multiple stable lattice sites for the condensate and demonstrates that there can be an underlying chaotic behavior in the condensate system.