Time-dependent Solution of the Nonlinear Schrödinger Equation for Bose-condensed Trapped Neutral Atoms

Document Type

Article

Publication Date

6-1-1995

Publication Title

Physical Review A

DOI

10.1103/PhysRevA.51.4704

ISSN

2469-9926

Abstract

We present numerical results from solving the time-dependent nonlinear Schrödinger equation (NLSE) that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature. With this method we are able to find solutions for the NLSE for ground state condensate wave functions in one dimension or in three dimensions with spherical symmetry. These solutions corroborate previous ground state results obtained from the solution of the time-independent NLSE. Furthrmore, we can examine the time evolution of the macroscopic wave function even when the trap potential is changed on a time scale comparable to that of the condensate dynamics, a situation that can be easily achieved in magneto-optical traps. We show that there are stable solutions for atomic species with both positive and negative s-wave scattering lengths in one-dimensional (1D) and 3D systems for a fixed number of atoms. In both the 1D and 3D cases, these negative scattering length solutions have solitonlike properties. In 3D, however, these solutions are only stable for a modest range of nonlinearities. We analyze the prospects for diagnosing Bose-Einstein condensation in a trap using several experiments that exploit the time-dependent behavior of the condensate.

Comments

Authors have the right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website. (source: http://journals.aps.org/authors/transfer-of-copyright-agreement) Article obtained from Physical Review A.

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