New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ1,ξ2 C,D C,D ξ1,ξ2| is a Radon transform of Wigner operator.     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP），建立了一种称之为相干纠缠态的两粒子体系的新表象，研究了这种新表象的性质，从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉，既具有相干态的特性，又体现了纠缠态的特征，具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product,which exhibits both the properties of a coherent state and an entangled state,and spans a complete and orthonormal representation.The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation.Moreover,a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters.As applications of this four-mode continuous variable coherent-entangled state,a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.     

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.     

利用|x〉导出λ■+μ■的本征矢

利用坐标本征矢|x〉在Fock空间的展开式,导出了算符λ■+μ■在Fock空间的本征矢|ψ〉,并证明了其正交完备性.结果表明,得到的|ψ〉既是完备的,又是正交的,完全可以作为一个表象使用.当λ和μ分别取1和0时,|ψ〉约化为坐标本征态|x〉,而当λ和μ分别取0和1时,|ψ〉约化为动量本征态|p〉.因此,|ψ〉所构成的表象是介于坐标表象和动量表象之间的中介表象.     

New Representation of Rotation Operator and Its Application

By employing the technique of integration within an ordered product of operators, we derive natural representations of the rotation operator, the two-mode Fourier transform operator and the two-mode parity operator in entangled state representations. As an application, it is proved that the rotation operator constructed by the entangled state representation is a useful tool to solve the exact energy spectra of the two-mode harmonic oscillators with coordinat-momentum interaction.     

双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符，利用有序算符内的积分（IWOP）技术分析了其变换特性，并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量，从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

介观耗散LC并联电路的量子效应

对介观耗散LC并联电路作阻尼谐振子处理，将其量子化。在此基础上，研究了Fock态及压缩真空态下，介观耗散LC并联电路中各支路电流和电压的量子涨落。结果表明，各支路电流电压的量子涨落均与电路器件的固有参数及所选量子态有关。     

介观压电石英晶体等效电路的量子化

借鉴阻尼谐振子作量子力学处理的研究思想,将介观压电石英晶体等效电路量子化,在此基础上研究了真空态和压缩真空态下,各支路电流和电压的量子涨落. 关键词： 介观压电石英晶体 等效电路 阻尼谐振子 量子涨落     

The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique

The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.