The s-parameterized Weyl-Wigner correspondence in the entangled form and its applications

Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form.Some of its applications in quantum optics theory are presented as well.

一种基于Weyl-Wigner对应规则显解压缩态的方法

理论上,压缩态是通过压缩算符作用于某态而得到的。由于算符之间不对易,一般不能直接得到相应压缩态的具体形式。文章提出一种显解压缩态的方法,即采用Weyl-Wigner对应规则导出单模、双模压缩态的具体形式。该方法避免了繁冗的算符排序和分解,也可推广到求解广义的多模情况。

Preserving Coherence of Coherent State Studied via Weyl-Wigner Correspondence

By means of the Weyl correspondence and the explicit normally ordered expression of the Wigner operatorwe convert the time evolution equation of coherent states,governed by some Hamiltonian operators,into seeking forconsistent solution of a set of evolution equtions of classical variables which can meet the requirment that an initialcoherent state remains coherent all the time.

用Weyl-Wigner理论研究有限温度下介观电路的量子特性

利用相干热态表象理论,研究有限温度下RLC电路的Wigner函数及量子涨落。借助于Weyl-Wigner理论讨论了介观RLC电路Wigner函数的边缘分布。结果表明:Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量。

介观RLC电路的量子化及其在有限温度下的量子效应

利用正则化变换,给出了介观RLC电路体系的量子化方案．借助数值计算的方法,研究了体系热真空态的Wigner函数随温度变化的规律,同时借助量子算符及其Weyl-Wigner对应研究了体系中电荷及自感磁通量在热真空态下的量子效应．结果表明,低温下热真空态的Wigner函数为一稳定的波包,随温度升高,波包逐渐扩散;体系中电荷及自感磁通量在热真空态下的的量子涨落除与电路参数相关外,还与温度及时间密切相关．

带电粒子在均匀磁场中运动的Wigner函数

研究Wigner函数具有十分重要的物理意义,因为它是密度矩阵的特殊表示形式,并且是相空间中的一个准概率分布函数。本文首先回顾了Wigner函数的计算方法及其性质;然后通过求解星本征方程(Moyal方程)得到了均匀磁场中二维带电粒子的Wigner函数。

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。

非对易相空间中带电谐振子的Wigner函数

从Moyal—Weyl乘法与Bopp变换出发，考虑了坐标-坐标、动量-动量的非对易性；利用非对易相空间量子力学的代数关系，讨论了非对易相空间中带电谐振子的Wigner函数，在所给出的非对易相空间带电谐振子的Wigner函数中出现了依赖于非对易参数的附加项。

用Weyl-Winger对应求证相干态的一个重要性质

一般而言,一个量子算符只有其在某个表象中所有的矩阵元都知道了才能被确定。可是当一个量子算符的相干态平均值(对角表示)知道了,这个算符本身就确定了,这是一个值得注记的性质。本文用W eyl-W inger对应的唯一性证明这一性质。

New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

By virtue of the completeness of Wigner operator and Weyl correspondence we construct a general equation for deriving pure state density operators. Several important examples are considered as the applications of this equation, which shows that our approach is effective and convenient for deducing these entangled state representations.

New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering

Using the Weyl ordering of operators expansion formula(Hong-Yi Fan,J.Phys.A 25(1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △(q',p')(q-number transform) in phase space quantum mechanics,and its inverse where Q,P are the coordinate and momentum operators,respectively.We apply it to study mutual converting formulae among Q-P ordering,P-Q ordering and Weyl ordering of operators.In this way,the contents of phase space quantum mechanics can be enriched.The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.

Optical complex integration-transform for deriving complex fractional squeezing operator

We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.

有结构中性粒子在外电磁场中运动的魏格纳函数

魏格纳函数在量子力学、量子光学、热力学和量子统计力学中有着重要的地位和非凡的作用,所以在量子力学中研究处于外电磁场中有结构的中性粒子的魏格纳函数具有很高的价值.本文首先介绍了的魏格纳函数的性质和应用,然后在对称规范下给出了极性原子的哈密顿量,最后通过Bopp变换求解了具有Moyal-Weyl星乘的能量本征方程,得到了处于电磁场中的中性极性粒子的能级和魏格纳函数.

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 Properties of Two-mode Displaced Excited Squeezed Vacuum States

In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.

Applications of Weyl Ordered Two-Mode Wigner Operator for Quantum MechanicalEntangled System

Based on the technique of integral within a Weyl ordered product of operators, wc present applicationsof the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.

Recapitulating Quantum Phase Space Representation by Virtue of Normally Ordered Gaussian Form of Wigner Operator

用 Wigner 操作符的通常订的 Gaussian 形式，我们概括量阶段空格表示，我们为寻找量的古典通讯导出一个新公式机械操作符；我们也看那是否在那里存在特徵向量 | q 坐标和动量操作员的线性联合，(Q + P ) ，实数，和 | q 是完全的，然后投影机 | qq |一定是 Wigner 操作员的氡变换。这条途径似乎简明、物理呼吁。

Mutual transformations between the P–Q, Q–P, and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator ?k(p,q) with a real k parameter and can unify the P–Q, Q–P, and Weyl ordering of operators in k = 1,-1, 0, respectively, we find the mutual transformations between δ(p- P)δ(q- Q), δ(q- Q)δ(p- P), and Ωk(p,q), which are, respectively, the integration kernels of the P–Q, Q–P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The P- and Q- ordered forms of Ωk(p,q) are also derived,which helps us to put the operators into their P- and Q- ordering, respectively.

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin.Phys.B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator (μ,ν) (in its entangled form) in phase space quantum mechanics,and its inverse transformation.In this way,some operator ordering problems regarding to ((a_1～■)-a_2)(a_1+(a_1～■))can be solved and the contents of phase space quantum mechanics can be enriched,where a_i,a_i～■ are bosonic creation and annihilation operators,respectively.