Analytic representations based on SU(1,1) coherent states and their applications
Quantum Physics
2008-11-26 v1
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 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.
Cite
@article{arxiv.quant-ph/9607022,
title = {Analytic representations based on SU(1,1) coherent states and their applications},
author = {C. Brif and A. Vourdas and A. Mann},
journal= {arXiv preprint arXiv:quant-ph/9607022},
year = {2008}
}
Comments
LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.html