Coherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications

Details Coherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications Coherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications

1996-04-23

arxiv.org/abs/quant-ph/9604025v1

Invited talk published in "Proc. of the fourth int. conf. on Squeezed States and Uncertainty Relations", NASA Conf. Pub.3322.(

Physics

Quantum Physics

7 pages, 2 figures (can be obtained from author by snail mail)

Scientific paper

We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the `Barut Girardello' coherent states to the Kronecker Product of two non-compact groups.The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of `pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting `bi-pair coherent states' in the context of four-mode interactions in quantum optics.

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