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arXiv:1303.4802 · Chinese Physics Letters

Damping Law of Photocount Distribution in a Dissipative Channel

Hong-Yi Fan, Sen‐Yue Lou, Liyun Hu

Published Sep 1, 2013• 5 citations
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Abstract

For a dissipative channel governed by the master equation of the density operator describing the photon loss, we find that the photocount distribution formula at time t can be related to the initial photocount distribution by replacing the efficiency of the detector ξ with ξe −2κt , as if the quantum efficiency ξ of the detector becomes ξe −2κt . This law greatly simplifies the theoretical study of the photocount distribution for quantum optical fields.

DOI
10.1088/0256-307x/30/9/090304

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For a dissipative channel governed by the master equation of the density operator describing the photon loss, we find that the photocount distribution formula at time t can be related to the initial photocount distribution by replacing the efficiency of the detector ξ with ξe −2κt , as if the quantum efficiency ξ of the detector becomes ξe −2κt . This law greatly simplifies the theoretical study of the photocount distribution for quantum optical fields.
We find that in optical fields' diffusion process, the l-photocounting probability formula [Formula: see text] at time t = 0 should be generalized to a new formula [Formula: see text] at time t, where ρ(0) is the initial density operator of the field, Ll is the Laguerre polynomial, : : denotes normal ordering, and ξ is the quantum efficiency of the photocounting detector. This new formula brings much convenience for different ρ0, because for deriving [Formula: see text] there is no need to derive the corresponding ρ(t) in the diffusion channel.
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.
We consider a single-mode radiation field initially in a displaced squeezed thermal state. The weak interaction of such a field with a heat bath of arbitrary temperature is shown to preserve the Gaussian form of the characteristic function. Accordingly, the study of the time development of the density operator reduces to our previous description [P. Marian and T. A. Marian, preceding paper, Phys. Rev. A 47, 4474 (1993)] of the initial quantum state. As examples, photon statistics and squeezing properties of the damped field are analyzed. Based on the close relation between field dissipation and photon detection, we derive simple analytic formulas for the counting distribution and its factorial moments. Nonclassical features of a displaced squeezed thermal state, such as oscillations of the photon-number distribution, survive in the counting process, provided that the quantum efficiency of the detector is high enough.
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.