Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
Abstract
Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term "kinetic Thomas-Fermi" (KTF) solutions. We point out that a large class of light-shift potentials gives rise to KTF-solutions. As elementary examples, we consider one-dimensional and two-dimensional optical lattice scenarios, obtained by means of the superposition of two, three and four laser beams, and discuss the stability properties of the corresponding KTF-solutions. A general method is proposed to excite two-dimensional KTF-solutions in experiments by means of time-modulated light-shift potentials.
Keywords
Cite
@article{arxiv.1005.5488,
title = {Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation},
author = {M. Ölschläger and G. Wirth and C. Morais Smith and A. Hemmerich},
journal= {arXiv preprint arXiv:1005.5488},
year = {2015}
}