  The two-mode relative phase associated with Gaussian states plays an
important role in quantum information processes in optical, atomic and
electronic systems. In this work, the origin and structure of the two-mode
relative phase in pure Gaussian states is studied in terms of its dependences
on the quadratures of the modes. This is done by constructing local canonical
transformations to an associated two-mode squeezed state. The results are
illustrated by studying the time dependence of the phase under a nonlocal
unitary model evolution containing correlations between the modes. In a more
general context, this approach may allow the two-mode phase to be studied in
situations sensitive to different physical parameters within experimental
configurations relevant to quantum information processing tasks.
