Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

在 Bose 操作员身份和纠缠的州的表示的帮助下并且基于我们的以前的工作[Phys。Lett。一 325 (2004 ) 188 ] 我们导出也让 Bessel 作为他们的答案工作的一些新概括 Besselequations。它为这些 intricatehigher 顺序意味着那微分方程，没有使用详述的力量系列扩大方法，我们能得到 Bessel 函数解决方案。

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.

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.

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operatorand the three-mode number combination operator.It is shown that these operators are on the same footing in theentangled state representation as the one of Turski in the coherent state representation.

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.

Complex-Variable Fokker-Planck Equation Solved in Entangled State Representation

We find that the Fokker-Planck equation in complex variables can be conveniently solved in the context of bipartite entangled state representation and its relationship with SU(2) Lie algebraic generators' new realization {(1/4)[(Q_1-Q_2)~2+(P_1+P_2)~2], (1/4)[(Q_1+Q_2)~2+(P_1-P_2)~2], and-(i/2)(Q_1P_2+Q_2P^1)}, the quadratic combination of canonical operators.

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p, x2, x3, x4〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p → eλ1p, x2 → eλ2x2, xs → eλ3x3, and x4 → eλ4x4 in the state | p, x2, x3, x4〉 is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.

A new approach to the time evolution of characteristic function of the density operator obtained by virtue of thermal entangled state representation

Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.

Atomic Coherent State,Entangled State and Phase Operator for Studying Interference Between Two Bose-Einstein Condensates

For studying the interference between two Bose-Einstein condensates we introduce the atomic coherentstate(ACS)in the Schwinger bosonic realization along with the phase operator to directly calculate the interferencepattern with steady relative phase cos φ.Eigenstates of the density operator of condensates are classified as A CS is alsodemonstrated.The entangled state representation is used in some calculations.

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagationin GRIN media or some lens-setup.

Kraus operator solutions to a fermionic master equation describing a thermal bath and their matrix representation

We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quan- tum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature.

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.

Evolution law of a negative binomial state in an amplitude dissipative channel

For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.

New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator（AHO） to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function（WF） for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF＇s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.

Optical field's quadrature excitation studied by new Hermite-polynomial operator identity

We study the optical field＇s quadrature excitation state Xm 10）, where X = （a ＋ at）/x/2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state＇s normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators （IWOP）. The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.

Wigner function of the thermo number states

Based on thermo field dynamics （TFD） and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature （named thermo number states）. The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.

New approach for deriving density operator for describing continuum photodetection process

By introducing the two-mode entangled state representation 〈η｜ whose one mode is a fictitious one accompanying the system mode, this paper presents a new approach for deriving density operator for describing continuum photodetection process.

Phase State as a Limiting Case of SU(1,1) Coherent State

我们出现 Susskind—Glogower 阶段状态是一种苏(1,1 ) 的一个限制盒子协调状态。由类比，基于由两部组成的纠缠的州的表示(ESR ) ，我们证明协调状态二模式的单一的阶段操作员使镇定下来的适当的苏(1,1 ) 也在二模式的 Fock 空间导致一个新阶段状态。是在 ESR 的 diagonalized。

Husimi Functions of Excited Squeezed Vacuum States

Based on the Husimi operator in pure state form introduced by Fan et al,which is a squeezed coherentstate projector,and the technique of integration within an ordered product (IWOP) of operators,as well as the entangledstate representations,we obtain the Husimi functions of the excited squeezed vacuum states (ESVS) and two marginaldistributions of the Husimi functions of the ESVS.

On Bosonic Magnetic Flux Operator and Bosonic Faraday Operator Formula

<正> In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator,thefundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usuallypreengaged.In this paper we show that such a relation can be deduced from the basic Bose operators' commutativerelation through the entangled state representation.The Faraday formula in bosonic form is then equivalent to thesecond Josephson equation.The current operator equation for LC mesoscopic circuit is also derived.