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

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 2z 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.