Structure of the Phase in Pure Two-Mode Gaussian States

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.