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Canadian Journal of Physics

Photon-added chaotic field and its damping in a thermo enviroment

Hong-Yi Fan, Rui He

Published Sep 15, 2014• 4 citations
Publisher

Abstract

We propose a new photon field in quantum field theory, named Laguerre-polynomial-weighted chaotic field. This field will emerge when an initial photon-added chaotic field, which is represented by its density operator [Formula: see text], dissipates in an amplitude damping channel described by time evolution equation [Formula: see text], where κ is a damping coefficient, that is, the initial field will evolve into [Formula: see text] with [Formula: see text], where Ls is the s-order Laguerre-polynomial, and : : denotes normal ordering. We employ the method of summation within an ordered product of operators to obtain our result.

DOI
10.1139/cjp-2014-0405

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We propose a new photon field in quantum field theory, named Laguerre-polynomial-weighted chaotic field. This field will emerge when an initial photon-added chaotic field, which is represented by its density operator [Formula: see text], dissipates in an amplitude damping channel described by time evolution equation [Formula: see text], where κ is a damping coefficient, that is, the initial field will evolve into [Formula: see text] with [Formula: see text], where Ls is the s-order Laguerre-polynomial, and : : denotes normal ordering. We employ the method of summation within an ordered product of operators to obtain our result.
We examine how a Laguerre-polynomial-weighted chaotic photon field (LPWCPF), whose density operator is [Formula: see text], evolves in an amplitude-damping channel. By using a newly derived generating function of two-variable Hermite polynomials we obtain the evolution law of LPWCPF, which turns out to be a new LPWCPF with a new parameter, depending on 1 − e−2κt, where κ represents decay rate. The technique of integration (summation) within an ordered product of operators is used in our discussions.
In this paper, we investigate how a kind of non-Gaussian states (l-photon excited thermo vacuum state [Formula: see text]) evolves in a single-mode damping channel. We find that it evolves into a Laguerre-polynomial-weighted real–fictitious squeezed thermo vacuum state, which exhibits strong decoherence and its original nonclassicality fades. In particular, when l = 0, in this damping process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic. In overcoming the difficulty of calculation, we employ the summation method within ordered product of operators, a new generating function formula about two-variable Hermite polynomials is derived.
Photon-added chaotic field is constructed by creation operator roling in chaotic field.Nonclassical property and decoherence of photon-added chaotic field are analysed.Master equations of density operators can be concisely solved by the technique of integration with in an ordered product of operators and virtue of thermo-entangled state representation.We get the evolution formula of the field density operator which is in photon-added chaotic field initially.The evolutions of its Wigner function and the evolutions of Prepresentation are given.The nonclassical property is discussed by calculating its Wigner function in phase space.Numerical results show that the photon-added chaotic field displays nonclassical property initially,and its nonclassical property is weakened with dissipation time increasing.On the other hand,its nonclassical property is also weakened with added photon number increasing.
Based on the Kraus operator of laser theory which we derived in [2] and by virtue of the technique of integration within ordered product of operators we exactly calculate the evolving result of a chaotic field, governed by the master equation describing the laser process, we find that the initial density operator evolves into a new chaotic field, with where g and κ represent the cavity gain and loss of the laser, respectively. When g = 0, the system reduces to an amplitude dissipative channel, and f' becomes −ln [(e−f − 1) e2κt + 1]. The law of photon number decay in this process is evaluated, and the corresponding Wigner function's evolution is also demonstrated.