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Acta Sinica Quantum Optica

Evolution of Husimi Function of Excitation on Coherent State in a Dissipative Channel

Liyun Hu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

On the basis of the technique of integration within an ordered product of operators and the coherent state representation,we investigate the evolution of Husimi function of excitation on coherent state in a dissipative channel.For the first time we derive the analytical expression for Husimi function and then discuss the effect of some parameters on this Husimi function.

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On the basis of the technique of integration within an ordered product of operators and the coherent state representation,we investigate the evolution of Husimi function of excitation on coherent state in a dissipative channel.For the first time we derive the analytical expression for Husimi function and then discuss the effect of some parameters on this Husimi function.
A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.
We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.
Abstract This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.
In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 Phys. Rev. B 1 4584) and recent (Kowalski and Rembieliński 2005 J. Phys. A: Math. Gen. 38 8247 ) formulations of coherent states for this problem. We introduce a general application, the Husimi function, which takes into account collective and environmental effects, and which can be derived in a variety of ways. However, we calculate this function as the expected value of the density operator in a basis of coherent states.