Bose condensate in a double-well trap: Ground state and elementary excitations

We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground-state density profile of ${}^{23}$Na atoms and the Bogoliubov spectrum of the elementary excitations as a function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.