A Closed Class of Hydrodynamical Solutions for the Collective Excitations of a Bose-Einstein Condensate

TL;DR

This paper presents a class of exact hydrodynamical solutions for collective excitations in a Bose-Einstein condensate, including a specific mode with an amplitude-dependent frequency shift matching experimental data.

Contribution

It introduces a closed-form solution for certain collective modes of a BEC using a trajectory approach, advancing analytical understanding of condensate dynamics.

Findings

Derived an exact solution for the {n=0, m=2} mode in a cylindrically symmetric trap.

Calculated amplitude-dependent frequency shifts that agree with experimental results.

Identified a broad class of solutions for trap-induced excitations in BECs.

Abstract

A trajectory approach is taken to the hydrodynamical treatment of collective excitations of a Bose-Einstein condensate in a harmonic trap. The excitations induced by linear deformations of the trap are shown to constitute a broad class of solutions that can be fully described by a simple nonlinear matrix equation. An exact closed-form expression is obtained for the solution describing the mode {n=0, m=2} in a cylindrically symmetric trap, and the calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.