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

Abstract

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.

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

References in corpus (2)

• Improvement of measurement accuracy in SU(1,1) interferometers
• Parity-dependent squeezing of light

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