Spectral Properties of Coupled Bose-Einstein Condensates

Abstract

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture which is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form which suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows to recover, in the classical limit, the symmetry breaking effect that characterizes the system classically.

8 pages, 3 figures; submitted to Phys. Rev. A. The present extended form replaces the first version in the letter format

References in corpus (2)

• Theory of Bose-Einstein condensation in trapped gases
• Time dependent mean field theory of the superfluid-insulator phase transition

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