2-MODE QUANTUM-SYSTEMS - INVARIANT CLASSIFICATION OF SQUEEZING TRANSFORMATIONS AND SQUEEZED STATES

A general analysis of squeezing transformations for two-mode systems i s given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of th is group, a distinction between compact photon-number-conserving and n oncompact photon-number-nonconserving squeezing transformations is mad e. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of disti nct equivalence classes with representative elements chosen for each c lass. Familiar two-mode squeezing transformations in the literature ar e recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The n eed to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) eleme nts can be reproduced are briefly described.