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A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices

Mark Edwards·Lisa M. DeBeer·Mads Demenikov·Jacob Galbreath·T. Joseph Mahaney·Bryan Nelsen·Charles W. Clark
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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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Mark Edwards, Lisa M. DeBeer, Mads Demenikov, Jacob Galbreath, T. Joseph Mahaney, Bryan Nelsen, Charles W. Clark. 2005-01-13. A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices. https://doi.org/10.1088/0953-4075%2F38%2F4%2F004

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