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Journal of Optics B Quantum and Semiclassical Optics

Nonlinear coherent state representation and related generalized Wigner function

Hong-Yi Fan, Hailing Cheng

Published Nov 23, 2001• 12 citations
Publisher

Abstract

The generalized Wigner operator and Wigner distribution function in phase space corresponding to the field-intensity-dependent operators is constructed in the nonlinear coherent state representation. The generalized Wigner theorem is also derived. The whole discussion is based on the technique of integration within an ordered product of the field-intensity-dependent operators.

DOI
10.1088/1464-4266/3/6/307

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Acta Sinica Quantum Optica•Jan 1, 2009•0 citations
The generalized Wigner operator and Wigner distribution function in phase space corresponding to the field-intensity-dependent operators is constructed in the nonlinear coherent state representation. The generalized Wigner theorem is also derived. The whole discussion is based on the technique of integration within an ordered product of the field-intensity-dependent operators.
Abstract Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the |n〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.