  The observation of non-classical correlations arising in interacting two to
size weakly coupled Bose-Einstein condensates was recently reported by Esteve
et al. [Nature 455, 1216 (2008)]. In order to observe fluctuations below the
standard quantum limit, they utilized adiabatic passage to reduce the thermal
noise to below that of thermal equilibrium at the minimum realizable
temperature. We present a theoretical analysis that takes into account the
spatial degrees of freedom of the system, allowing us to calculate the expected
correlations at finite temperature in the system, and to verify the hypothesis
of adiabatic passage by comparing the dynamics to the idealized model.
