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Journal of Modern Optics

Decoherence of the two-mode squeezed vacuum state in a diffusion process

LU Dao-ming

Published May 7, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2019.1613577

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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.
The quantum properties of weak cohetent state in terms of squeezing effect and antibunching effect were investigated in the diffusion.Master equation of density operator in the diffusion process can be concisely solved by virtue of thermo-entangled state representation and the technique of integration within an ordered product of operators,which contains normal ordering,antinormal ordering and Weyl ordering.The solution of master equation of density operator in diffusion process was given by Kraus operator.The evolution formula of the field density operator which is in weak coherent state initially was get.Its squeezing effect and antibunching are investigated by the numerical method.The effect of decoherence on its nonclassical property is discussed.Numerical results show that compression depth is weakened and the compression range decreases with diffusion time increasing.On the other hand,the light field displays antibunching effect in the early diffusion.When the diffusion time is greater than a certain value,its antibunching effect disappears.
The diffusion master equations of density operators under action of linear resonance force were concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The evolution formula of the field density operator was given,and the Wigner function evolution formula which is in superposition of vacuum state and single-photon state initially was obtained.By numerically calculating the Wigner function was plotted,and the evolution of negative volume of Wigner function with dissipation time was calculated.Through the analysis of the Wigner function,the effect of decoherence on nonclassical property of the state was discussed.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease until vanish with dissipation time.In addition,on the other hand,Wigner function can be slipped under the action of linear resonance force.
Master equations of density operators can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The solution of master equations of density operators is given.We get the Wigner function evolution formula in phase space and photon number distribution formula of the state,which is a superposition of vacuum state and single-photon state initially in laser process.By numerical calculation we plot its Wigner function and photon number distribution evolution curves,when cavity gain constant and cavity loss constant are both equal to certain values.The effect of decoherence on nonclassical property of the state is discussed by comparing negative area size and the depth of negativity of Wigner function.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease and then vanish with dissipation.In addition,we calculate the variation of negative volume of Wigner function with dissipation time.We find that it decreases with dissipation time increasing.These results show that the nonclassical properties of the state are weakened and then disappear with dissipation time increasing.
We explore the time evolution law of a two-mode squeezed light field (pure state) passing through twin diffusion channels, and we find that the final state is a squeezed chaotic light field (mixed state) with entanglement, which shows that even though the two channels are independent of each other, since the two modes of the initial state are entangled with each other, the final state remains entangled. Nevertheless, although the squeezing (entanglement) between the two modes is weakened after the diffusion, it is not completely removed. We also highlight the law of photon number evolution. In the calculation process used in this paper, we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.
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 two-mode thermo- and squeezing-mixed optical field, described by the new density operator ρ = ( 1 − e f − | g | 2 ) e g a † b † e f a † a | 0 ⟩ b b ⟨ 0 | e g ∗ a b , where | 0 ⟩ b b ⟨ 0 | is the b -mode vacuum, e f a † a represents the thermo-field, and e g a † b † indicates squeezing. The photon statistics for ρ is studied by virtue of the method of integration within ordered product (IWOP) of operators. Such a field can be generated when a two-mode squeezed state passes through a one-mode dissipation channel.