Squeezed States as Representations of Symplectic Groups

Details Squeezed States as Representations of Symplectic Groups Squeezed States as Representations of Symplectic Groups

1998-03-11

arxiv.org/abs/physics/9803017v1

Physics

Optics

RevTex 6 pages,no figures,presented at the 5th International Conference on Squeezed States and Uncertainty Relations (Lake Bal

Scientific paper

It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon states. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.

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