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Journal of Physics A Mathematical and General

SU(1,1) intelligent states: analytic representation in the unit disk

Constantin Brif, Y. Ben-Aryeh

Published Dec 21, 1994• 18 citations
Publisher

Abstract

Intelligent states of the SU(1,1) Lie group are investigated using the analytic representation in the unit disk of the SU(1,1) coherent-state basis. By developing this representation, we study a special class of states, which are both intelligent and coherent. These states can be created using Hamiltonians, for which SU(1,1) is the dynamical symmetry group.

DOI
10.1088/0305-4470/27/24/025

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Intelligent states of the SU(1,1) Lie group are investigated using the analytic representation in the unit disk of the SU(1,1) coherent-state basis. By developing this representation, we study a special class of states, which are both intelligent and coherent. These states can be created using Hamiltonians, for which SU(1,1) is the dynamical symmetry group.
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Robertson intelligent states which minimize the Schr\" odinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the su(3)su(3)su(3) algebra. The construction is based on the analytic representations of su(3)su(3)su(3) coherent states. New classes of coherent and squeezed states are explicitly derived.
A contour representation in the unit disk based on SU(1,1) coherent states is introduced. The scalar product is given by a contour integral. The regions of convergence of the functions representing ket and bra states are studied. An analytic representation in the unit disk is also considered, where the scalar product is represented by an integral over the unit disk, with the Lobachevsky measure. Various relations which connect these analytic functions with other phase-space quantities are derived.