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Chinese Physics B

Decoherence of photon-subtracted squeezed vacuum state in dissipative channel

Xue-xiang Xu, Hong‐Chun Yuan, Hong-Yi Fan

Published Feb 1, 2011• 11 citations
Publisher

Abstract

This paper investigates the decoherence of photo-subtracted squeezed vacuum state (PSSVS) in dissipative channel by describing its statistical properties with time evolution such as Wigner function, Husimi function, and tomogram. It first calculates the normalization factor of PSSVS related to Legendre polynomial. After deriving the normally ordered density operator of PSSVS in dissipative channel, one obtains the explicit analytical expressions of time evolution of PSSVS's statistical distribution function. It finds that these statistical distributions loss their non-Gaussian nature and become Gaussian at last in the dissipative environment as expected.

DOI
10.1088/1674-1056/20/2/024203

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This paper investigates the decoherence of photo-subtracted squeezed vacuum state (PSSVS) in dissipative channel by describing its statistical properties with time evolution such as Wigner function, Husimi function, and tomogram. It first calculates the normalization factor of PSSVS related to Legendre polynomial. After deriving the normally ordered density operator of PSSVS in dissipative channel, one obtains the explicit analytical expressions of time evolution of PSSVS's statistical distribution function. It finds that these statistical distributions loss their non-Gaussian nature and become Gaussian at last in the dissipative environment as expected.
We investigate statistical properties of photon-subtracted squeezed vacuum (PSSV) in a thermal environment with average thermal photon number n¯ and dissipative coefficient κ by deriving the analytical expressions of the density operator and the Wigner function (WF). The normalization of m-PSSV is proved to be the m-order Lagendre polynomials. Time evolution of the photocount distribution is also related to Lagendre polynomials. The tomogram of PSSV is calculated by using the intermediate coordinate-momentum representation. Especially, the nonclassicality is discussed by virtue of the negativity of WF. It is found that the WF is always negative for all squeezing parameters λ if κt<½ ln(2n¯+2)/(2n¯+1) for the single-PSSV.
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}).
The statistical properties of m -coherent superposition operation (μ a + va † ) m on the single-mode squeezed vacuum state (M-SSVS) and its decoherence in a thermal environment are studied. Converting the M-SSVS to a squeezed Hermite polynomial excitation state, we obtain a compact expression for the normalization factor of M-SSVS, which is the Legendre polynomial of the squeezing parameter. We also derive the explicit expression of the Wigner function (WF) of the M-SSVS, and find the negative region of the WF in phase space. The decoherence effect on this state is then discussed by deriving the time evolution of the WF. Using the negativity of the WF, the loss of nonclassicality is then discussed.
We investigate the statistical properties of photon subtractions from a 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. A compact expression for the Wigner function (WF) is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the WF. The decoherence effect on this state is then discussed by deriving the time evolution of the WF. It is shown that the WF is always positive for any squeezing parameter and any photon-subtraction number if the decay time exceeds an upper bound (κt>½ ln 2n¯+2/2n¯+1).
We studied the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of the Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.
The statistical properties of m-coherent superposition operation(μa + νa■)m on the single-mode squeezed vacuum state(M-SSVS) and its decoherence in a thermal environment are studied.Converting the M-SSVS to a squeezed Hermite polynomial excitation state,we obtain a compact expression for the normalization factor of M-SSVS,which is the Legendre polynomial of the squeezing parameter.We also derive the explicit expression of the Wigner function(WF) of the M-SSVS,and find the negative region of the WF in phase space.The decoherence effect on this state is then discussed by deriving the time evolution of the WF.Using the negativity of the WF,the loss of nonclassicality is then discussed.