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Chinese Physics B

A new two-mode thermo- and squeezing-mixed optical field

Jun Zhou, Hong-Yi Fan, Jun Song

Published Jun 1, 2017• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/26/7/070301

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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.
The development of quantum optics theory based on the method of integration within an ordered product of operators (IWOP) has greatly stimulated the study of quantum states in the light field, especially non-Gaussian states with various non-classical properties. In this paper, the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field. The density operator of the new light field, its entanglement property and photon number distribution are analyzed. We also note that tracing a three-mode pure state can yield this new light field. These methods represent a theoretical approach to investigating new density operators of light fields.
In a 3-wave mixing process occurring in some nonlinear optical medium when }a1†a_{1}^{\dagger}a1†​{\small mode interacts with both }$a_{2}^{\dagger}% modeand{\small mode and }modeanda_{3}^{\dagger}mode,wetheoreticallystudythesqueezingeffectgeneratedbytheoperator{\small mode, we theoretically study the squeezing effect generated by the operator }mode,wetheoreticallystudythesqueezingeffectgeneratedbytheoperatorS_{3}\equiv \exp[μ(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+ν(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})].Thenew3−modesqueezedvacuumstateinFockspaceisderived,andtheuncertaintyrelationforitisdemonstrated,Itturnsoutthat{\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }.Thenew3−modesqueezedvacuumstateinFockspaceisderived,andtheuncertaintyrelationforitisdemonstrated,ItturnsoutthatS_{3}mayexhibitenhancedsqueezing.Byvirtueofthetechniqueofintegrationwithinanorderedproduct(IWOP)ofoperators,wealsoderive{\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }mayexhibitenhancedsqueezing.Byvirtueofthetechniqueofintegrationwithinanorderedproduct(IWOP)ofoperators,wealsoderiveS_{3}${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.
For the first time we derive the dissipating result of an initial two-mode squeezed pure vacuum state passing through a two-mode amplitude dissipative channel described by the direct product of two independent single-mode master equations. Although these two master equations do not mix the two modes (there is no coupling between them), since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from passing this channel is a two-mode mixed density operator. The compact expression of the outcoming state is obtained, which manifestly shows that as time evolves, the squeezing effect decreases.
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.
For the density operator(mixed state) describing squeezed chaotic light(SCL) we search for its thermal vacuum state(a pure state) in the real-fictitious space. Using the method of integration within ordered product(IWOP) of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals: the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.