Analytic representations based on SU(1,1) coherent states and their applications

Details Analytic representations based on SU(1,1) coherent states and their applications Analytic representations based on SU(1,1) coherent states and their applications

1996-07-26

arxiv.org/abs/quant-ph/9607022v1

J.Phys.A29:5873-5886,1996

Physics

Quantum Physics

LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.html

Scientific paper

10.1088/0305-4470/29/18/017

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.

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