Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation

TL;DR

This paper introduces exact kinetic Thomas-Fermi solutions to the Gross-Pitaevskii equation, exploring their properties, stability, and methods for experimental excitation in optical lattice setups.

Contribution

It presents the concept of kinetic Thomas-Fermi solutions, extending the traditional Thomas-Fermi approximation to include kinetic energy, and discusses their realization in optical lattice experiments.

Findings

KTF solutions exist for a large class of light-shift potentials.

Stability analysis of KTF solutions in optical lattices.

Proposed method for experimental excitation of KTF solutions.

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.