Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis

We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed.     

New decomposition of the Fresnel operator corresponding to the optical transformation in AB CD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.     

Three-Mode Cyclic Squeezed States Constructed via EPR Entangled State

We construct the three-mode cyclic squeezed states and analyze its squeezing property by using the technique of integration within an ordered product of operators and the natural representation of the two-mode squeezing operator in the Einstein-Podolsky-Rosen entangled state basis.     

Nonclassicality and Entanglement of Photon-Subtracted Two-Mode Squeezed Coherent States Studied via Entangled-States Representation

We theoretically introduce a kind of non-Gaussian entangled states, i.e., photon-subtracted two-mode squeezed coherent states (PSTMSCS), by successively subtracting photons from each mode of the two-mode squeezed coherent states. The normalization factor which is related to bivariate Hermite polynomials is obtained by virtue of the two-mode squeezing operator in entangled-states representation. The sub-Poissonian photon statistics, antibunching effects, and partial negative Wigner function, respectively, are observed numerically, which fully reflect the nonclassicality of the resultant states. Finally, employing the SV criteria and the EPR correlation, respectively, the entangled property of PSTMSCS is analyzed. It is shown that the photon subtraction operation can effectively enhance the inseparability between the two modes.     

Newton-Leibniz integration for ket-bra operators (III)—Application in fermionic quantum statistics

The Newton-Leibniz integration over Dirac’s ket-bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] is generalized to Newton-Leibniz-Berezin integration over fermionic ket-bra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac’s symbolic method for Fermi system can also be developed, which exhibits Bose-Fermi supersymmetry in this aspect.     

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles’ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.     

Squeezing entangled state of two particles with unequal masses

For two unequal-mass particles, we construct the entangled state representation and then derive the corresponding squeezing operator. This squeezing operator has a natural realization in the entangled state representation, which exhibits the intrinsic relation between squeezing and quantum entanglement. This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings. The maximum squeezing occurs when the two particles possess equal mass. When two particles' mass difference becomes large, the component of the two single-mode squeezings becomes dominant.     

Optical complex integration-transform for deriving complex fractional squeezing operator

We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.     

三能级原子与奇偶纠缠相干光作用的光场压缩

采用求解薛定谔方程和数值计算方法,研究了V型三能级原子与双模奇偶纠缠相干光场相互作用过程中的光场压缩效应,讨论了压缩效应与双模奇偶纠缠相干光场的纠缠程度、系统失谐量、双模光场的平均光子数和原子基态概率幅的依赖关系。结果表明：光场压缩效应与双模奇偶纠缠相干光场的纠缠程度、失谐量、平均光子数和原子初态相关联：双模纠缠相干光场处于非纠缠状态时的光场压缩量比光场处于纠缠状态时要大;原子处在单纯的基态或激发态时光场都有明显的压缩现象出现;而原子初态中基态和激发态的概率幅较接近时无光场压缩现象;无论光场是否处于纠缠态,只有两模平均光子数接近时,光场才会出现压缩效应。     

单-双模组合压缩热态的纠缠性质及在量子隐形传态中的应用

基于单-双模组合压缩真空态一定范围内能够获得压缩增强的效果,引入单-双模组合压缩热态(DSMST),讨论其纠缠性质.利用Weyl编序算符在相似变换下的不变性,简洁方便地导出了DSMST的纠缠度-负对数值,并给出了当热效应存在时保持纠缠的条件.研究表明:与通常的双模压缩态相比,随着参数的增加,DSMST的纠缠度增加.作为DSMST的应用,利用其实现相干态的量子隐形传输.结果表明:不同于纠缠度随压缩参数增加,保真度获得改善是有条件的,该条件恰好就是一正交分量涨落出现压缩增强的参数区域.此外,解析推导了有效隐形传输保真度(1/2)的条件.     

Collins diffraction formula studied in quantum optics

We find that the Collins diffraction formula in cylindrical coordinates is just the transformation matrix element of a three-parameter two-mode squeezing operator in the deduced entangled state representation. This is a new tie connecting the unitary transform in quantum optics to the generalized Hankel transform in Fourier optics. The group multiplication rule of the squeezing operators maps to the Collins formula related to two successive Hankel transforms.     

Statistical Properties of Photon-Added Two-Mode Squeezed Coherent States

The nonclassical and non-Gaussian quantum states—photon-added two-mode squeezed coherent states have been theoretically introduced by adding multiple photons to each mode of the two-mode squeezed coherent states. Starting from the new expression of two-mode squeezing operator in entangled states representation, the normalization factor is obtained, which is directly related to bivariate Hermite polynomials. The sub-Poissonian photon statistics, cross-correlation between two modes, partial negative Wigner function are observed, which fully reflect the nonclassicality of the target states. The negative Wigner function often display non-Gaussian distribution meanwhile. The investigations may provide experimentalists with some better references in quantum engineering.     

Entanglement Swapping for Displaced Two-Mode Squeezed States

We discuss the entanglement swapping of two pairs of displaced two-mode squeezed states and find that the squeezing parameter of the outcoming squeezed state is less than that of the originM squeezed states. The calculation is greatly simplified by virtue of the natural expression of the two-mode squeezing operator in EPR eigenstate representation. A protocol for such entanglement swapping is proposed.``     

Conditionally Teleported States Using Optical Squeezers and Photon Counting

By virtue of the neat expression of the two-mode squeezing operator in the Einstein,Podolsky and Rosen entangled state representation,we provide a new approach for discussing the teleportation scheme using optical squeezers and photon counting devices.We derive the explicit form of the teleported states,so that the conditional property of teleportation and teleportation fidelity of this protocol can be seen more clearly.The derivation is concise.     

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived.     

Fresnel Operator for Deriving the Propagator of 2D Harmonic Oscillator with Cross Coupling

Using the identity of operator decomposition we obtain a normal ordered form of the time-evolution operator for cross coupling quantum harmonic oscillator Hamiltonian system in two dimensions, which is just a special two-mode Fresnel operator. The Feynman propagator for the Hamiltonian system is found by a direct calculation by means of the method deriving the matrix element of two-mode Fresnel operator in the entangled state representation. The technique of integration within an ordered product (IWOP) of operators is employed to derive the matrix elements of the operator in the coherent state and the entangled state representations.     

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutesa loyal group representation of symplectic group. The result of successively applying squeezing operators on numberstate can be easily derived.     

V型三能级原子双模光场系统中光场压缩性质

本文利用格子液体方法对文献中给出的V型三能级原子玻色-爱因斯坦凝聚体与双模压缩相干态光场相互作用系统的哈密顿量进行分析,发现文献中对原子间相互作用部分的处理有不合理之处,从而对该哈密顿量作出了改进并研究了V型三能级原子双模光场系统中光场压缩性质.结果表明:光场两正交分量交替呈现周期性压缩现象,其压缩深度与光场初始压缩因子密切相关,而压缩时间与双模光场的频率有关. 关键词： 玻色-爱因斯坦凝聚 V型三能级原子 压缩相干态 双模压缩态光场     

Phase Properties of Two-Mode Squeezing-Rotating Entangled Representation

By virtue of the squeezing-rotating entangled representation, we mainly establish thc new two-mode phase operator and phase angle operator, which is a general form including the foregoing formalist in two-mode Fock space.In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotating coherent state,squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.     

Wigner Function of the Two-Mode Squeezing-Enhanced Vacuum State

We find the two-mode generalized squeezing operator with two parameters can be separated into the product of a ordinary squeezing operator S ₂(ξ) and a rotating operator R ₂(θ). Acting it on the two-mode vacuum state, one can get two-mode squeezing-enhanced vacuum state (TSEVS). Compared with the usual two-mode squeezed vacuum state, TSEVS exhibits stronger squeezing properties. With the help of the operator’s Weyl-ordering invariance under the similarity transformation, we derive the Wigner function of the TSEVS.