  We consider the precise quantum state of two trapped, coupled Bose Einstein
condensates in the two-mode approximation. We seek a representation of the
state in terms of a Wigner-like distribution on the two-mode Bloch sphere. The
problem is solved using a self-consistent rotation of the unknown state to the
south pole of the sphere. The two-mode Hamiltonian is projected onto the
harmonic 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 the
number difference depend on the physical parameters. Considering negative
scattering lengths, we show that there is a regime of squeezing in the relative
phase of the condensates which occurs for weaker interactions than the
superposition states found by Cirac et al% (quant-ph/9706034, 13 June 1997).
The phase squeezing is also apparent in mildly asymmetric trap configurations.
