Generalized Two-Mode Squeezed States and Some Nonclassical Characteristics

A class of generalized two-mode squeezed states |φ〉 is presented, which are generated from the generalized two-mode squeezing operator U(γ,λ) acting on the two-mode coherent state |α ₁,α ₂〉. We first investigate some mathematical properties of U(γ,λ) including the squeezing transformation under U(γ,λ), ket-bra integral form in the coordinate representation, normally ordered form. Then we evaluate some nonclassical characteristics of the state |φ〉 such as higher-order squeezing behavior, entanglement analysis and analytical expression of the Wigner function.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

Non-Gaussianity of photon-added-then-subtracted squeezed vacuum state

In this paper, the photon-added-then-subtracted squeezed vacuum state (PASSVS), a non-Gaussian state, is presented by adding then subtracting photon to a squeezed vacuum state. It is found that PASSVS is just a superposition state between S(r) | 0〉 and S(r) | 2〉, where S(r) is the single-mode squeezing operator with the squeezing parameter r. Its non-Gaussianity is exhibited via its Wigner function and the Hilbert–Schmidt distance. In addition, a possible scheme is presented to produce the PASSVS by virtue of the cavity QED.     

New Parameterized Coherent-Entangled State Representation and Its Applications

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 _μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 _μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 _μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.     

Photon-Subtracted Two-Mode Squeezed Thermal State and Its Photon-Number Distribution

We construct the photon-subtracted two-mode squeezed thermal state (PSTMSTS) by subtracting any number of photons from two-mode squeezed thermal state (TMSTS). It is found that the normalization factor of the density operator of PSTMSTS is a Jacobi polynomial of squeezing parameter λ and average photon number [`(n)]\bar{n} of the thermal state. We investigate the photon-number distribution (PND) of PSTMSTS and find a remarkable result that it is a quotient of two Jacobi polynomials, as well as derive a corresponding character of Jacobi polynomial.     

Fröhlich 极化子的非经典基态

本文计及波矢 q,q' 声子间动力学关联效应,采用双模-压缩(声子)相干态作为再一次正则变换方案,基于Huybrechts变分近似,求解 Fröhlich 大极化子的非经典基态.由于双模-压缩(声子)相干态导致声子相干态-压缩声子态关联效应,相干参量 f_q 与双模压缩角 φqq' 关键词： 双模-压缩(声子)相干态 位移-声子压缩态 Frö hlich 极化子 非经典基态     

Laguerre-Polynomial-Weighted Two-Mode Squeezed State

We propose a new optical field named Laguerre-polynomial-weighted two-mode squeezed state. We find that such a state can be generated by passing the l-photon excited two-mode squeezed vacuum state C_la^?lS₂|00〉 through an single-mode amplitude damping channel. Physically, this paper actually is concerned what happens when both excitation and damping of photons co-exist for a two-mode squeezed state, e.g., dessipation of photon-added two-mode squeezed vacuum state. We employ the summation method within ordered product of operators and a new generating function formula about two-variable Hermite polynomials to proceed our discussion.     

基于双模相干-纠缠态表象的算符恒等式构造法

利用最近引进的相干-纠缠态|x,α〉表象和有序算符内的积分技术,给出了关于双模光场正交分量（X₁+X₂）/2^1/2和参数化的正交分量（μX₁+νX₂）/λ的函数的若干正规乘积展开式,这对于研究场的高阶压缩行为和构建广义压缩态是有用的. 关键词： 双模相干-纠缠态 算符恒等式 有序算符内的积分技术     

Detaching two single-mode squeezing operators from the two-mode squeezing operator

It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within Ω-ordering and β-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a β-ordered two-mode squeezing operator （with a new squeezing parameter） and two single-mode squeezing operators （with another squeezing parameter）. This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

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.     

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.     

Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula

We propose a new two-mode squeezed coherent state representation |z₁, z₂〉_g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from (z₁, z₂) to in |z₁, z₂〉_g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens-Fresnel integration transformation describing optical diffraction) in entangled form.     

Evolution of a two-mode squeezed vacuum in the amplitude dissipative channel

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.     

Evolution of a two-mode squeezed vacuum in the amplitude dissipative channel

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.     

The Unitary Operator Corresponding to the General Two-Mode Coordinate-Momentum Mixed Transformation

We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation(q2,p2)→(Aq1 Bq2,Cq1 Dp2),where A,B,C and Dare arbitrary real numbers,Suitably selecting the parameters A,B,Cand D,we obtain a new two-mode bosonic realization of the SU(1,1) Lie algebra.We also study the squeezing effects of the squeezed vacuum associated with the new two-mode bosonic realization of the SU(1,1) Lie algebra.The results show that the new squeezed vacuum does not possess second-order squeezing,but exhibits higher-order squeezing.     

The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite S_n(λ) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of a_j and \(a_{j}^{\dagger }\) under the operation of S_n(λ) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state |λ〉 is obtained. Based on this, the variances of the n-mode quadratures in |λ〉 are evaluated and the violation of the Bell inequality for |λ〉 is examined by using the formalism of Wigner representation.     

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.     

Kerr介质中双模纠缠相干光与Bell态原子相互作用系统的原子偶极压缩

运用全量子理论并结合数值计算方法，研究了Kerr介质腔中处于Bell态的两个全同二能级纠缠原子与双模纠缠相干光场相互作用系统的原子偶极压缩特性.讨论了双原子体系的初态、光场的平均光子数、双模纠缠相干光场的纠缠程度以及Kerr介质与双模光场的耦合强度对原子偶极压缩特性的影响.结果表明：双原子体系的初态为|β₁₁>时，不会出现偶极压缩效应；初态为|β₀₀>，|β₀₁>或|β₁₀>时在一定条件下可能出现原子压缩效应，且此时原子压缩的特性与Kerr介质与双模光场的耦合强度、初始光场的平均光子数、双模纠缠相干光场的纠缠程度有关. 关键词： 量子光学 Bell态 双模纠缠相干光场 Kerr介质     

Entanglement swapping of continuous variable using squeezed vacuum states

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.