10 research outputs found
A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices
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.Comment: 16 pages and 1 figur
A Hybrid Lagrangian Variational Method for Bose–Einstein Condensates in Optical Lattices
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 variation 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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