Photon states associated with Holstein-Primakoff realization of SU(1,1) Lie algebra
Abstract
Statistical and phase properties and number-phase uncertainty relations are systematically investigated for photon states associated with the Holstein-Primakoff realization of the SU(1,1) Lie algebra. Perelomov's SU(1,1) coherent states and the eigenstates of the SU(1,1) lowering generator (the Barut-Girardello states) are discussed. A recently developed formalism, based on the antinormal ordering of exponential phase operators, is used for studying phase properties and number-phase uncertainty relations. This study shows essential differences between properties of the Barut-Girardello states and the SU(1,1) coherent states. The philophase states, defined as states with simple phase-state representations, relate the quantum description of the optical phase to the properties of the SU(1,1) Lie group. A modified Holstein-Primakoff realization is derived, and eigenstates of the corresponding lowering generator are discussed. These states are shown to contract, in a proper limit, to the familiar Glauber coherent states.
Keywords
Cite
@article{arxiv.quant-ph/9504008,
title = {Photon states associated with Holstein-Primakoff realization of SU(1,1) Lie algebra},
author = {C. Brif},
journal= {arXiv preprint arXiv:quant-ph/9504008},
year = {2008}
}
Comments
32 pages, no figures, REVTeX with amssymb, to be published in Quantum and Semiclassical Optics