A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices
Abstract
Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid varation along one spatial direction. Examples of such systems include a BEC subjected to a one--dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian Variational Method for the GP equation in which a hybrid trial wavefunction assumes a gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi--one--dimensional GP equation coupled to ordinary differential equations for the widths of the transverse gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non--adiabatically.
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Cite
@article{arxiv.cond-mat/0501323,
title = {A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices},
author = {Mark Edwards and Lisa M. DeBeer and Mads Demenikov and Jacob Galbreath and T. Joseph Mahaney and Bryan Nelsen and Charles W. Clark},
journal= {arXiv preprint arXiv:cond-mat/0501323},
year = {2009}
}
Comments
16 pages and 1 figure