Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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



M Edwards, L M. DeBeer, M Demenikov, J Galbreath, B Nelson, Charles W. Clark


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.
Journal of Physics


Bose-Einstein condensate, gaussian, GP equation, Lagrangian variational, optical lattice


Edwards, M. , DeBeer, L. , Demenikov, M. , Galbreath, J. , Nelson, B. and Clark, C. (2005), A Hybrid Lagrangian Variational Method for Bose-Einstein Condensates in Optical Lattices, Journal of Physics, [online], (Accessed April 23, 2024)
Created February 6, 2005, Updated October 12, 2021