Squeezed states and quadratic Hamiltonians: a Wigner distribution approach

This analysis addresses the unitary evolution of general Gaussian states (squeezed and displaced in phase space) under the action of quadratic Hamiltonians. The technique used was developed in the context of problems involving a class of partially coherent light beams known as the Gaussian Schell-model beams acted on by first order optical systems. The basic idea is to focus attention on the Wigner distribution of the state rather than on the state function itself. This shift of focus reduces this problem to one of 2 x 2 real matrices and their transformations and also leads to an elegant geometric picture where the Gaussian states are represented by vectors and the unitary evolution by Lorentz transformation in a (2+1)-dimensional Minkowski space. 22 references