Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

摘要: A general anaylsis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4,openR). Within framework unitary (metaplectic) representation this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving made. We exploit U(2) invariant criterion to divide set all into two-parameter family distinct equivalence classes with representative elements chosen each class. Familiar in literature are recognized our seen form measure zero. Examples squeezed coherent thermal states worked out. The need extend heterodyne detection scheme encompass emphasized, known experimental situations where can be reproduced briefly described.