Barrier effects on the collective excitations of split Bose-Einstein condensates

TL;DR

This paper studies how barriers in split Bose-Einstein condensates affect their collective excitations, revealing merging of excitation levels with increasing barrier height through hydrodynamic and exact methods.

Contribution

It provides a detailed analysis of barrier effects on collective excitations in split BECs using hydrodynamic and Gross-Pitaevskii equation solutions, highlighting level merging phenomena.

Findings

Pairs of excitation levels merge as barrier height increases.

Hydrodynamic and Gross-Pitaevskii results agree on excitation spectrum behavior.

Spatial excitation patterns depend on the degree of condensate splitting.

Abstract

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.