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.     

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states:Non-classical and non-Gaussian properties

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation(AC) and creation-then-annihilation operation(CA) to the thermal state(TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number,Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.     

铷原子D1线真空压缩光场的产生及态重构

碱金属原子是光量子存储的良好介质,与碱金属原子共振的非经典光场是量子信息处理的重要资源.本文采用周期极化磷酸氧钛晶体作为非线性介质,利用参量振荡过程产生了795 nm(铷原子D1线)的真空压缩光场.通过对平衡零拍探测系统的时域信号进行采集,得到压缩光场不同相位角下的噪声分布;利用极大似然估计法对压缩光场进行了态重构,得到了密度矩阵及相空间的Wigner函数.理论计算了真空压缩场的光子数分布和Wigner函数,并对理论计算结果和极大似然重构结果进行了分析和比较.     

增光子圆态及其性质

利用光场产生算符的逆算符作用于圆态来构造增光子圆态.讨论了此态的非经典性质,同时计算并模拟出它的维格纳(Wigner)函数.结果表明,在不同光强下,随着激发数的增大增光子圆态光场的平均光子数增加与减少交替地出现;光子激发后,光场的亚泊松统计特性得到增强,压缩效应却受到抑制.维格纳函数图像显示了增光子圆态显著的非经典性质,发现了光子激发与圆态光强的增大都能使量子态由叠加引起的干涉效应明显增强.另外,在不同叠加数的情况下,通过适当选择参量可使维格纳函数具有相同的变化规律.     

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.     

复合函数算符的微商法则及其在量子物理中的应用

给出了在量子物理学、量子统计学、算符排序理论、矩阵论以及控制理论中有着重要用途的复合函数算符的一般微分法则,利用这一法则研究了Wigner算符和Weyl对应规则中的积分问题,证明了两类典型的算符恒等公式.给出了Wigner算符的有序算符内的微分形式,并得到了一些重要函数的新的微分式.最后,引入了一个参数型的Wigner算符来统一正规序、Weyl编序以及反正规序三种算符排序.     

拉盖尔多项式算符激发相干态的非经典性质

将拉盖尔多项式算符作用在相干态上,构造了拉盖尔多项式算符激发相干态.利用有序算符积分技术,导出了它的归一化系数以及〈a^la^+m〉的计算表达式.采用数值计算方法,讨论了相干态相位角和平均光子数对它的非经典性质的影响.研究结果表明:一阶拉盖尔多项式算符激发相干态呈现出压缩效应、反聚束效应、亚泊松分布和Wigner函数负性等量子特性,并且相干态的相位角对它的量子特性有重要影响;另一方面,随相干态平均光子数增大,它的反聚束效应和亚泊松分布性质逐渐减弱,压缩效应和Wigner函数的负性却先增强,而后又逐渐减弱.     

Wigner Function of Density Operator for Negative Binomial Distribution

By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.     

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.     

Quantum mechanical photoncount formula derived by entangled state representation

By introducing the thermo entangled state representation,we derive four new photocount distribution formulas for a given light field density operator.It is shown that these new formulas,which are convenient to calculate the photocount,can be expressed as integrations over a Laguerre-Gaussian function with a characteristic function,Wigner function,Q-function and P-function,respectively.     

Optical Parametric Amplification of Single Photon: Statistical Properties and Quantum Interference

By using phase space method, we theoretically investigate the quantum statistical properties and quantum interference of optical parametric amplification of single photon. The statistical properties, such as the Wigner function (WF), average photon number, photon number distribution and parity, are derived analytically for the fields of the two output ports. The results indicate that the fields in the output ports are multiphoton states rather than single photon state due to the amplification of the optical parametric amplifiers (OPA). In addition, the phase sensitivity is also examined by using the detection scheme of parity measurement.     

Wigner functions for two arbitrary operators and spectrum perturbation

We have concentrated on the Wigner function for the photon number and a quadrature operator, which we find to differ from zero outside the spectrum of the photon number operator. We have provided an illustration with a coherent state.     

Thermal vacuum state corresponding to squeezed chaotic light and its application

For the density operator(mixed state) describing squeezed chaotic light(SCL) we search for its thermal vacuum state(a pure state) in the real-fictitious space. Using the method of integration within ordered product(IWOP) of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals: the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.     

Statistical Properties of Photon-Added Two-Mode Squeezed Coherent States

The nonclassical and non-Gaussian quantum states—photon-added two-mode squeezed coherent states have been theoretically introduced by adding multiple photons to each mode of the two-mode squeezed coherent states. Starting from the new expression of two-mode squeezing operator in entangled states representation, the normalization factor is obtained, which is directly related to bivariate Hermite polynomials. The sub-Poissonian photon statistics, cross-correlation between two modes, partial negative Wigner function are observed, which fully reflect the nonclassicality of the target states. The negative Wigner function often display non-Gaussian distribution meanwhile. The investigations may provide experimentalists with some better references in quantum engineering.     

On the quantum-mechanical Fokker-Planck and Kramers-Chandrasekhar equation

In the classical theory of Brownian motion we can consider the Langevin equation as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, we can reinterpret the Langevin equation as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta we can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. We may associate, according to Weyl functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions we can express the streaming as a continuity equation of the Wigner function. We find that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation.     

Thermo Vacuum State for Describing the Density Operator of Photon-subtracted Squeezed Chaotic Light

For the density operator describing s?photon-subtracted squeezed chaotic light (PSSCL) we search for its thermo vacuum state (a pure state) in the real-fictitious space. We find that it reduces to a thermo vacuum state of squeezed chaotic light when s = 0, and to a thermo vacuum state of the optical negative binomial field when no squeezing. The new thermo vacuum state simplifies calculating photon number average, quantum fluctuation and Mandel’s Q parameter of PSSCL. Using the method of integration within ordered product (IWOP) of operators we also derive the normalization coefficient and explicitly analytical expressions of Wigner function for PSSCL.     

SOME APPLICATIONS OF COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

In this paper both the normal product form and the coherent state form of the Wigner operator are derived. Furthermore, the applications of the new forms of the Wigner operator are also presented, which are involved in deriving some new quantum operator formulas, in the coherent state generalization of the Moyal theorem, and in evaluating some quantum operators which corresponds to the given classical functions in the Weyl manner and vice versa.     

相位型三头薛定谔猫态的量子统计属性

本文详细研究了一种相位型三头薛定谔猫态的一些量子统计属性,包括光子数分布、平均光子数、亚泊松分布、压缩效应以及Wigner函数等.我们发现,三头猫态的Wigner函数都可以出现负值,与二、四头猫态一样,说明它们都可以体现出非经典特性.与二头猫态不同,三头猫态在一定参数范围内可以呈现亚泊松分布,这点与四头猫态相类似,但弱于四头猫态.另外,三头猫态和四头猫态都没有压缩属性,但二头猫态具有压缩属性.     

多输入多输出量子密钥分发信道容量研究

量子安全通信是一个量子密钥分发过程,目前采用的通信技术严重制约了量子密钥分发的比特率.将多输入多输出（MIMO）技术应用于量子密钥分发系统,可提高量子密钥分发的比特率,促进量子安全通信向高速大容量发展.文中首先构造出MIMO量子密钥分发信道中多光子纠缠态Wigner算符矩阵.并在此基础上,推导出多光子双模压缩纠缠态Wigner算符矩阵和MIMO量子密钥分发信道容量.为开发稳健的MIMO量子安全通信空时处理算法和优化设计高性能MIMO量子密钥分发系统提供理论支撑和技术基础. 关键词： 多输入多输出 双模压缩态 多光子纠缠态 信道容量