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International Journal of Modern Physics B

Evolution of l-photon excited thermo vacuum state in a single-mode damping channel

Rui He, Hong-Yi Fan

Published Jan 19, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979216500090

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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.
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.
Extending the recent work completed by Biswas and Agarwal [Phys. Rev. A75, 032104 (2007)] to the case of m-photon-subtracted squeezed vacuum states (m-PSSVSs), we focus our study on nonclassicality and decoherence of the m-PSSVSs. The nonclassical properties are investigated in terms of the squeezing character, the oscillation of photon-number distribution, and the partial negativity of Wigner function (WF).We then study the effect of decoherence on the m-PSSVSs in two different channels, viz., thermal process and phase damping. In each case, the time-evolution of density operators and WFs of such states is derived analytically. After undergoing the thermal channel, the initial pure m-PSSVSs evolve into a mixed state that turns out to be a Laguerre polynomial of combination of creation and annihilation operators within normal ordering; however, they become another mixed state with the exponential decay due to phase damping. At long times, these fields decay to a highly classical thermal field as a result of thermal noise, but they still keep nonclassicality in the phase-damping channel.
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 have studied the case in which one mode of the light field in the two-mode squeezed vacuum state evolves in a diffusion channel. By virtue of thermo-entangled state representation and the technique of integration within an ordered product, the evolution formula of the field density operator is given. Its non-classical properties, such as squeezing effect, antibunching effect, the violation of Cauchy–Schwartze inequality and the entanglement property between two modes, are studied. The influences of the squeezing parameter and the dissipation time on the non-classical properties are discussed. The results obtained by the numerical method show that its non-classical properties are all weakened with the dissipation. On the other hand, its squeezing effect and the entanglement property between two modes are strengthened, but its antibunching effect and the violation of Cauchy–Schwartze inequality are weakened with the increase of the squeezing parameter.
We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$κt>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).