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The low energy properties of a trapped bose gas split by a potential barrierare determined over the whole range of barrier heights. We derive aself-consistent two-mode model which reduces, for large $N$, to a Bogoliubovmodel for low barriers and to a Josephson model for any (asymmetric) doublewell potential, with explicitly calculated tunneling and pair interactionparameters. We compare the numerical results to analytical results thatprecisely specify the role of number squeezing and finite temperatures in theloss of coherence.

Coherence of an Interacting Bose Gas: from a Single to a Double Well