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

We study the optical field's quadrature excitation state X m |0 , where X = (a+a+)/ √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.     

Time evolution law of a two-mode squeezed light field passing through twin diffusion channels

We explore the time evolution law of a two-mode squeezed light field(pure state)passing through twin diffusion channels,and we find that the final state is a squeezed chaotic light field(mixed state)with entanglement,which shows that even though the two channels are independent of each other,since the two modes of the initial state are entangled with each other,the final state remains entangled.Nevertheless,although the squeezing(entanglement)between the two modes is weakened after the diffusion,it is not completely removed.We also highlight the law of photon number evolution.In the calculation process used in this paper,we make full use of the summation method within the ordered product of operators and the generating function formula for two-variable Hermite polynomials.     

A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators

Based on the two mutually conjugate entangled state representations ｜ξ〉 and ｜η〉, we propose an integration transformation in ξ - η phase space ∫∫ d^2ξd^2η/π^2e^（ξ-η）（η^＊ -v^＊）-（η-v）（ξ^＊-μ^＊）F（ξ^＊,μ^＊） F（ξ, η）≡D（μ,v）, and its inverse trans- formation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to （Q1 -Q2） （P1 - P2） ordered and simultaneously （P1 ＋ P2） （Q1＋ Q2） ordered operators.     

Normal coordinate in harmonic crystal obtained virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.     

激光光场经历扩散通道后的温度演变

本文研究激光光场经历扩散通道后的温度变化效应,用有序算符内积分的方法以及经典扩散方程来求解量子相干态经历扩散后的演变.发现扩散后的激光光场变为平移混沌光场.并推导出温度的解析表达式,此公式反映了当有光子扩散到激光光场中温度的升高规律.     

Schwinger Bose实现下自旋相干态Wigner函数的特性分析

在Schwinger Bose实现下,引入纠缠态表象及Wigner算符在该表象下的表示,得到自旋相干态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现在SchwingerBose实现下自旋相干态确实体现出纠缠特性。     

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 properties of 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.     

A generalized Weyl—Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.     

The Fresnel—Weyl complementary transformation

Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation(for(a 1 a 2)/√ 2) and the Weyl transformation(for(a 1 + a 2)/√ 2).Physically,(a 1 a 2)/√ 2 and(a 1 + a 2)/√ 2 could be a symmetric beamsplitter’s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.     

Schwinger玻色子表示中转动算符的对易性质

本文发展Schwinger玻色子表示中的角动量理论, 其中包括用正规乘积内积分法导出转动算符对易子[e^iaJx,e^iβJy]的正规乘积表达式及不同次序的转动对相干态波函数的影响. 还给出了e^σJ-e^λJ+等算符的正规乘积表达式及其对原子相干态的应用.