Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

New light fields based on integration theory within the Weyl ordering product of operators

The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.

Squeezing in Representation by Quadratic Combinations of Canonical Operators

The technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P2, Q2, PQ + QP) to those of the basis operators (a2, a?2, a?a). The coherent state representation of unitary squeezing operators in the factorized form and their normal product form are thus derived. The squeezing engendered by operators of the general form is also obtained.

Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

A new kind of special function and its application

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.

New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

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 of quantum states via Weyl expansion in dissipative channel

Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation,we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator.It is shown that they can be related by a transformation matrix corresponding to the unitary evolution.In addition,for any density operator going through a dissipative channel,the evolution formula of the Wigner function is also derived.As applications,we considered further the two-mode squeezed vacuum as inputs,and obtained the resulted Wigner function and density operator within normal ordering form.Our method is clear and concise,and can be easily extended to deal with other problems involved in quantum metrology,steering,and quantum information with continuous variable.

Some applications of a new coherent-entangled state in two-mode Fock space

Using the technique of integration within an ordered product of operators, we find a new kind of coherent-entangled state （CES）, which exhibits both coherent and entangled state properties. The set of CESs makes up a complete and partly nonorthogonal representation. Using a beam splitter, we propose a simple experimental scheme to produce the CES. Finally~ we present some applications of CESs in quantum optics.

Time evolution of negative binomial optical field in a diffusion channel

We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.

基于矩阵特殊运算的高阶流形单元分析

在数值流形法的单元分析中广泛采用单纯形积分进行精确积分,然而在高阶数值流形法中采用单纯形积分并不容易,因为要求被积函数为显式多项式函数。采用Kronecker积、Hadamard积和拉直等矩阵特殊运算进行高阶流形单元分析,使得单元矩阵的推导过程简单且被积函数易表示为多项式形式。在此基础上,开发了三维弹性连续体静力分析的高阶数值流形法程序。通过实例验证了公式和程序的正确性。

相干态在算符正规排序中的应用

利用相干态的超完备性与有序算符内的积分技术,给出若干量子玻色算符的正规排序形式.与其他方法相比,此方法在理论应用中具有简捷明了的特点.

在介观RLC电路中通过量子菲涅耳变换获得压缩机制和压缩态(英文)

按照有序算符内积分技术,时间演化算符可以表示为坐标-动量相位空间中经典变换的量子映射。依据已经提出的LC电路量子化方案所得到的哈密顿量,推广应用到RLC(电阻、电容和电感)电路量子化方案并得到相应哈密顿量。借助相应的理论计算,可以发现在量子化的RLC电路中存在压缩机制。利用有序算符内积分技术和量子菲涅耳变换关系,可以进一步推导出量子介观RLC电路中相应压缩态的简明形式。

引入Wigner函数,Weyl对应和Wigner算符相干态表象的新途径

用坐标、动量完备性的正规乘积内积分形式直接地引入了Wigner函数和Wigner算符的相干态表象,简洁地阐述了它与Weyl对应的关系。

n阶常系数线性微分方程求解新探

要讨论了ｎ阶常系数线性微分方程的算子方法，给出了齐次方程特解的一种求法以及非齐次方程解的积分公式，还给出了一种非常简便的求非齐次方程特解的积分－比较系数法。

对应负二项式光场的热真空态及其应用

有限温度下的光场理论的核心是引入热真空态,它也是利用量子统计手段全面研究电磁场的基础.本文在Takahashi和Umezawa的热场动力学理论基础上,首次采用有序算符内的积分方法对负二项式光场ρs=∞∑n=0(n+s n)γs+1(1-γ)n|n><n|,寻找相应的热真空态.发现该热真空态是基于在混沌光场所对应的热真空态上的虚模激发,或取负二项式纯态的形式∞∑n=0(n+s n)γs+1(1-γ)n|n,s+>,其中"s"代表虚模自由度.对此热真空态求纯态平均可方便地得到负二项式光场的Wigner函数和光子数涨落.

涉及双变量Hermite多项式的新二项式定理及应用

利用量子光学方法,将普通的二项式定理推广到涉及双变量Hermite多项式情况,解析推导出几个新的广义二项式定理及其推论.作为应用,解析证明多光子扣除压缩态a^mb^ne^(sa+b++ra++tb+)|00〉等价于实验上易于调控的非高斯纠缠信息源,即以双变量Hermite多项式为权重的非高斯量子态;而且发现自旋相干态的Wigner函数恰好正比于Laguerre多项式.

压缩真空态的另一表示

本文用正规乘积内积分法证明态矢exp(λQ^2)|0>(|0>是真空谐振子态,Q=1/2^(1/2)(a+a^+))在适当地选择λ后构成压缩真空态。