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arXiv:cond-mat/0211628 · Journal of Physics B Atomic Molecular and Optical Physics

Interference patterns of Bose-condensed gases in a two-dimensional optical lattice

Shujuan Liu, Hongwei Xiong, Xu Zhi-Jun, Guoxiang Huang

Published May 7, 2003• 26 citations
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Abstract

For the Bose-condensed gas confined in a magnetic trap and in a two-dimensional optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i)only the optical lattice is swithed off, and (ii)both the optical lattice and the magnetic trap are swithed off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space.

DOI
10.1088/0953-4075/36/10/316

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For the Bose-condensed gas confined in a magnetic trap and in a two-dimensional optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i)only the optical lattice is swithed off, and (ii)both the optical lattice and the magnetic trap are swithed off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space.
We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross–Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bose-condensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas, we discuss the evolution process of the central and side peaks of the interference pattern.
Based on the Gross-Pitaevskii equation and by using the effective chemical poten tial,we study the distribution of the Bose-condensed gas in the combined potenti als (magnetic trap and three-dimensional optical lattices).The normalized ground-state wave function is given from the distribution of the Bose-condensed gas.The analytical expression of the density distribution of the Bose-condensed gas is given by using the propagator method when the combined potentials and only the optical lattices are switched off,respectively.When the combined potentials are switched off,the theoretical results of this work agree well with the experiment by Greiner et al.When only the optical lattices are switched off,it is show n that the interference pattern will oscillate in the magnetic trap.In addition,the evolution of the interference pattern is also investigated in the case of an isotropic magnetic trap.
For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross–Pitaevskii (G-P) equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase Δϕ between successive subcondensates trapped on an optical lattices is also studied. For Δϕ = π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.
For the Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross-Pitaevskii (G-P) equation and the propagator method, we study the formation of matter-wave interference upon releasing the condensate from the combined potential. The analytical result of the wave function for matter wave interference at any time t is given, and the relation between the interference fringe period and the optical lattice period is obtained. The interference pattern of Bose-condensed gas in the optical lattices is analogous to the multiple slit interference pattern in optics, and coincides with the results of experiment performed by Andrews et al. and Peil et al. and the numerical solution of the G-P equation by Sadhan K. Adhikari.