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Canadian Journal of Physics

Time evolution law of the Laguerre-polynomial-weighted chaotic photon field in an amplitude-damping channel

Cheng Da, Qian-Fan Chen, Pengfei Zhang, Hong-Yi Fan

Published Aug 11, 2014• 2 citations
Publisher

Abstract

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.

DOI
10.1139/cjp-2014-0278

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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.
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.
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.
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.