Excitations of a Bose-condensed gas in anisotropic traps

TL;DR

This paper studies the collective excitations of a Bose-condensed gas in anisotropic traps at zero temperature, analyzing how mode frequencies evolve with trap anisotropy using the Gross-Pitaevskii and Bogoliubov equations.

Contribution

It provides a detailed analysis of collective mode frequencies and their evolution in anisotropic traps, extending understanding beyond isotropic cases.

Findings

Mode frequencies depend on trap anisotropy.

Evolution of modes from isotropic to anisotropic traps is characterized.

Mode classification includes parity and angular momentum quantum number m.

Abstract

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.