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 one-dimensional potentials consisting of two harmonic wells separated by a distance ${2z}_{0}$, since they essentially contain all the barrier effects that one may visualize in the three-dimensional situation. We find, within a hydrodynamic approximation, that regardless of the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighboring 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 obtained from exactly solving the time-dependent Gross-Pitaevskii equation. We also analyze the characteristics of the spatial pattern of excitations of three-dimensional boson systems according to the amount of splitting of the condensate.
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