New approach for solving the Wigner function from the Husimi function in the two-mode entangled state representation

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate.     

广义压缩粒子数态的非经典性质及其退相干

研究了三参数的压缩算符产生的广义压缩粒子数态的非经典性质及其在光子损失通道中的退相干问题.利用有序算符内的积分技术和Weyl编序算符在相似变换下的不变性,简洁地导出了广义压缩粒子数态的Wigner函数(Laguerre-Gaussian函数).基于Wigner函数的演化积分公式,解析地推导出了在耗散通道中的Wigner函数表达式.特别地,根据Wigner函数负部体积讨论了其非经典性.     

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.     

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.     

光子增减叠加相干态在热环境中的退相干

研究了由光子增减叠加操作作用于相干态而得量子态的非经典性及其在热环境中的退相干问题.通过解析导出了Mandel's Q参数、光子数分布、Wigner函数等,讨论其非经典性.研究表明一阶光子增减相干叠加相干态在相空间总是取负值,只要满足条件∣2z* +α-α*∣2＜1.基于Wigner函数的演化积分公式,解析地推导出了在热环境中Wigner函数的简洁表达式.研究首次表明:如果κt＜1/2ln[(2(η)+2)/(2(η)+1)]得以满足,一阶光子增减相干叠加相干态在相空间最小值点处Wigner函数分布总存在负部.此外,根据Wigner函数负部体积讨论了其非经典特性.     

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.     

On the Wigner distribution function for an oscillator

We present two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian. Both methods are facilitated using a formula which expresses the Wigner function as a simple trace. The first method of derivation then utilizes a modification of a theorem due to Messiah. An alternative procedure makes use of the coherent state representation of an oscillator. The Wigner distribution function gives a semiclassical joint probability for finding the system with given coordinates and momenta, and the joint probability is factorable for the special case of an oscillator. An important application of this result occurs in the theory of nuclear fission for calculating the probability distributions for the masses, kinetic energies, and vibrational energies of the fission fragments at infinite separation.     

Simple Approach for Deriving the Weyl Correspondence Product Formula

By making use of the coherent state representation of the Wigner operator we present a simple approach for deriving the Weyl correspondence product formula in complex phase space. The formula tells us how to express the Weyl classical function corresponding to an operator F = AB in terms of the Weyl functions corresponding to A and B.     

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

Using the 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 calculation of the WF to an overlap between two pure states in an enlarged Fock space. It is found that this formula brings us much convenience to investigate 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 the diffusive AHO.     

远场几何光路追踪唯象模型

在激光靶耦合流体模拟程序中,相对于传统几何光路追踪方法,Wigner分布函数光路追踪方法可以描述激光衍射效应;但Wigner分布函数方法需要大量的激光光线来刻画激光能量在相空间的分布,降低了流体计算效率。基于Wigner分布函数方法提出了一个唯象模型,可以用较少的光线刻画宏观特征。该模型将Wigner分布函数分解成坐标空间与相空间两部分函数的乘积,并假定相空间分布函数具有特定的形式。该模型适用于空间相干度较低的实际光束,成功描述了OMEGA激光器光束,并且可以描述经过连续相位板匀滑后的实际光束。     

激光光路追踪Wigner分布函数方法

提出了一种考虑衍射效应的激光几何光路追踪方法。引入由激光标量场定义的Wigner激光能量相空间分布函数,并给出该函数满足的刘维尔运动方程。Wigner分布函数用来描述经过空间任一点沿任一方向传输的激光光线上的能量分配。激光能量沿由波包色散关系定义的光线轨迹保持不变（真空中）或者衰减（等离子体中）。与传统几何光路追踪方法相比,该方法从理论上给出了激光光线初始携带能量份额的计算方法,并且将激光标量场的相位信息自然地包含在Wigner分布函数的定义里。算例表明,该方法与解析模型及广泛使用的菲涅耳衍射积分方法结果一致。     

N00N态的Wigner函数及N00N态作为输入的量子干涉

根据量子力学相干态表象下的Wigner函数公式, 推导了N00N态在相空间的Wigner分布函数的解析表达式. 基于相空间方法, 研究N00N态作为输入的量子干涉. 推导了与输入光场参数和干涉仪参数相关的输出端探测光子概率的解析表达式, 并进行了数值分析. 从分析结果发现, 当相移参数φ取0和π时, 输出量子态仍为N00N态. 当输入2002态时, 输出结果总是2002态, 与相移参数无关. 随着N的增加, 条件概率随相位的分布峰数一般只有一个, 两个, 三个或四个, 且峰变得更窄. 这些结果可以为实验提供理论指导. 关键词： N00N态 Wigner函数 相空间 量子干涉     

非Lamb-Dicke近似下制备囚禁冷离子的振动相干态

根据非Lamb-Dicke近似下激光-离子相互作用动力学规律,讨论了如何利用一系列的激光脉冲来驱动冷离子,从而从运动基态出发获得一系列振动数态的宏观叠加态.具体研究了这些叠加态的Q函数、Wigner函数和它们的非经典特性,如压缩和反群聚效应等.结果表明,合适地调节各个所用激光的脉冲长度,所产生的叠加态能很好地逼近熟知的振动相干态. 关键词： Lamb-Dicke近似 叠加态 相干态 非经典特性     

双模压缩数态光场的Wigner函数及其特性

借助纠缠态表象及Wigner算符在该表象下的表示,得到双模压缩数态的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,发现双模压缩数态两模之间相互关联、相互纠缠,对相空间中Wigner函数分布产生影响. 关键词： 双模压缩数态 Wigner函数 纠缠态表象     

一类特殊单模压缩态的Wigner函数

本文运用IWOP技术推导出Wigner算符的相干态显式,计算出一类特殊单模压缩态 |z〉_f,g=exp[－(|z|²)/2 +(fz+gz^*)a⁺－fga⁺²]|0〉的Wigner函数解析式,通过数值计算可以看到,参数f和g的任一个取值固定时,另一个参数的旋转取值会使得特殊 关键词： IWOP技术 Wigner算符 Wigner函数     

相干态表象在量子相空间分布函数中的应用

利用相干态表象和IWOP技术导出了自由热态密度矩阵的正规乘积形式,进而根据相干态表象下的Wigner函数定义重构了自由热态和热相干态的Wigner函数.结果表明利用相干态表象下的Wigner函数定义和算符的正规乘积形式可以方便简捷重构一些量子态的Wigner函数.     

增光子奇偶相干态的Wigner函数

利用相干态表象下的Wigner算符, 重构了增光子奇偶相干态的Wigner函数.根据此Wigner函数在相空间中随复变量α的变化关系, 讨论了增光子奇偶相干态的非经典性质. 结果表明, 增光子奇偶相干态总可呈现非经典性质, 且在m取奇(或偶)数时, 增光子偶(或奇)相干态更容易出现非经典性质. 根据增光子奇偶相干态的Wigner函数的边缘分布, 阐明了此Wigner函数的物理意义. 同时, 利用中介表象理论获得了增光子奇偶相干态的量子tomogram函数. 关键词： 增光子奇偶相干态 Wigner函数 中介表象 tomogram函数     

利用微脉塞重构腔场的Wigner函数

提出了重构腔场Wigner函数的一种新方案.该方案可以用微脉塞来实现.发现在腔场的Wigner函数与原子的布居数之间存在一个简单的关系.在实验上测得原子的布居数后，进行一个简单的数值积分，就可得到腔场的Wigner函数.以单光子Fock态和Schr?dinger猫态为例进行了数值模拟，发现与用精确公式计算的结果很好地相符. 关键词： 量子态重构 Wigner函数 微脉塞     

Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer

Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the interferometer, the Heisenberg limit can be approached with parity detection. At the same time, the negativity volume of Wigner function of detection mode comes entirely from the input state and varies periodically with the encoding phase. In addition, the negativity volume of Wigner function is positively correlated with the phase sensitivity of the SU(1,1) interferometer. The positive correlation may mean that the non-classicality indicated by negative Wigner function is a kind of resource that can verify some related research results of phase estimation.