Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

由介绍一个虚构模式是在评论下面的系统模式的一个对应物模式，我们介绍纠缠的州的表示 η| ，它能由于 η| 的漂亮性质作为州向量的进化方程在量统计安排密度操作符 ρ (t) 的主人方程。这样，许多掌握方程(分别地描述抑制振荡器，激光，阶段敏感，并且有不同起始的密度操作员的阶段散开过程) 能简明地被解决。特殊，为腐烂常数 κ 的一个抑制过程特征，我们发现在在 η 的时间 t 的 ρ (t) 的矩阵元素|表示与在腐烂的纠缠的州的 ηe −κt 的起始的 ρ 0 的成正比|表示，与抑制因素的 Gaussian 伴随。因此，我们关于消散的过程的性质有新卓见。我们也建立了密度操作员的所谓的纠缠 thermo 的州的表示， ρ =∫ ( 与所有以前的已知的代表不同的 d 2η/π)η|ρD(η), 。

Quantum mechanical photoncount formula derived by entangled state representation

By introducing the thermo entangled state representation, we derive four new photocount distribution formulas for a given light field density operator. It is shown that these new formulas, which are convenient to calculate the photocount, can be expressed as integrations over a Laguree Gaussian function with a characteristic function, Wigner function, Q-function and P-function, respectively.

Relationship Between Wave Function and Corresponding Wigner Function Studied in Entangled State Representation

由使用纠缠的 Wigner 操作符和纠缠的州的表示的明确的形式，我们为由两部组成的纠缠的系统导出在波浪功能和相应 Wigner 功能之间的关系。在操作员的一个订的产品(IWOP ) 以内的集成的技术在我们的讨论被采用。

Four-mode continuous-variables entangled state:generation from beam splitter,a parametric down-conversion and a polarizer

We introduce a new kind of four-mode continuous variable entangled state in Fock space. The completeness relation and the partly nonorthonormal property of such a state are proven. The scheme to generate this state is presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. After making a single-mode quadrature amplitude measurement, the remaining three modes are kept in entanglement. And its applications are also discussed.

Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications

Our primary purpose of this work is to explicitly construct the general multipartite Einstein Podolsky-Rosen (EPR) entangled state in muIti-mode Fock space for a system with different masses of particles,which makes up anew quantum mechanical representation owing to completeness relation and orthogonal property.Its entanglement canbe seen more clearly by analyzing its standard Schmidt decomposition.In addition,some applications of the multipartiteentanglement are proposed including deriving the generalized Wigner operator and squeezing operator.

Application of Bipartite and Tripartite Entangled State Representations in Quantum Teleportation of Continuous Variables

We mostly investigate two schemes. One is to teleport a multi-mode W-type entangled coherent state using a peculiar bipartite entangled state as the quantum channel different from other proposals. Based on our formalism,teleporting multi-mode coherent state or squeezed state is also possible. Another is that the tripartite entangled state is used as the quantum channel of controlled teleportation of an arbitrary and unknown continuous variable in the case of three participators.

Multi-mode Coherent-Entangled State Representation and Its Applications

We introduce the so-called coherent-entangled state (CES) in the four-mode Fock space,which makesup a new quantum mechanical representation owing to completeness relation and orthogonal property.Its standardSchmidt decomposition and experimental generation using beam-splitter (BS) are proposed.In addition,its applicationsin quantum optics are presented.Finally,we extend it to multi-mode case and discuss some applications,too.

Wave function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.

Establishing path integral in the entangled state representation for Hamiltonians in quantum optics

Based on two mutually conjugate entangled state representations, we establish the path integral formalism for some Hamiltonians of quantum optics in entangled state representations. The Wigner operator in the entangled state representation is presented. Its advantages are explained.

Photon-number distribution of two-mode squeezed thermal states by entangled state representation

Using the entangled state representation, we convert a two-mode squeezed number state to a Hermite polynomial excited squeezed vacuum state. We first analytically derive the photon number distribution of the two-mode squeezed thermal states. It is found that it is a Jacobi polynomial; a remarkable result. This result can be directly applied to obtaining the photon number distribution of non-Gaussian states generated by subtracting from （adding to） two-mode squeezed thermal states.

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining fleld-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.

Squeeze-swapping by Bell measurement studied in terms of the entangled state representation

By virtue of the entangled state representation （Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704） and the two-mode squeezing operator＇s natural representation （Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958） we propose the squeeze-swapping mechanism which can generate quantum entanglement and new squeezed states of continuum variables.

New approach for analysing master equations of generalized phase diffusion models in the entangled state representation

By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Energy level formula for two moving charged particles with Coulomb coupling derived via the entangled state representations

This paper derives energy level formula for two moving charged particles with Coulomb coupling by making full use of two mutually conjugate entangled state representations. These newly introduced entangled state representations seem to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.

Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation

By analysing the properties of two-mode quadratures in an entangled state representation （ESR） we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.

Fractional squeezing-Hankel transform based on the induced entangled state representations

Based on the fact that the quantum mechanical version of Hankel transform kernel（the Bessel function） is just the transform between ｜q, r〉 and（s, r′｜, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform（FrSHT） caused by the operator e（-iα）（a1-a-2-＋a-1a-2）e-（-iπa2-a2）, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner functions,etc.These discussions demonstrate the beauty and elegance of the entangled state representation.