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We consider the precise quantum state of two trapped, coupled Bose Einsteincondensates in the two-mode approximation. We seek a representation of thestate in terms of a Wigner-like distribution on the two-mode Bloch sphere. Theproblem is solved using a self-consistent rotation of the unknown state to thesouth pole of the sphere. The two-mode Hamiltonian is projected onto theharmonic oscillator phase plane, where it can be solved by standard techniques.Our results show how the number of atoms in each trap and the squeezing in thenumber difference depend on the physical parameters. Considering negativescattering lengths, we show that there is a regime of squeezing in the relativephase of the condensates which occurs for weaker interactions than thesuperposition states found by Cirac et al% (quant-ph/9706034, 13 June 1997).The phase squeezing is also apparent in mildly asymmetric trap configurations.Comment: 26 pages, 11 figure

Quantum state of two trapped Bose-Einstein condensates with a Josephson coupling