Physics – Quantum Physics
Scientific paper
1995-04-11
Quant.Semiclass.Opt.7:803-834,1995
Physics
Quantum Physics
32 pages, no figures, REVTeX with amssymb, to be published in Quantum and Semiclassical Optics
Scientific paper
10.1088/1355-5111/7/5/004
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.
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