任意两个相干态的叠加态的相位分布和Wigner函数

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉 and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

任意两个相干态的叠加及其量子统计性质

研究了由两个任意相干态构成的叠加态｜ψ〉=a｜β〉+be^iφ｜mβe^iδ 〉的量子统计性质，结果表明此种叠加态普遍存在着压缩效应或光子反群聚效应.叠 加态的量子效应依赖于β²和振幅系数m，同时改变相干态间的位相差δ和叠加 系数间的位相差φ也将对叠加态的压缩效应或反群聚效应起着重要的作用. 关键词： 相干态 叠加态 压缩效应 反群聚效应     

一种新的非线性叠加相干态的相位特性

根据Pegg-Barnett 相位定义,计算了一种新的非线性叠加相干态的相位概率分布函数和光子数-相位压缩效应,并进行了数值模拟.     

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     

多光子激发相干态的Wigner函数

Wigner函数的负性是非经典量子态的重要判据之一.利用Fock态表象下Wigner函数的一般表达式,重构了相干态｜z〉的k光子激发态｜+k,z〉～a^－k｜z〉（k≥1）的Wigner函数,并根据其数值结果讨论了该量子态的非经典特性（这里a^－1为Bose湮没算符的逆算符,其作用相当于Bose产生算符）.结果表明,不论k取奇数还是偶数,相干态的这些k光子激发态都具有非经典特性;而且k的取值越大,这些量子态的非经典特性越明显. 关键词： 非经典量子态 激发相干态 Wigner函数 非经典特性     

叠加对相干态的相位概率分布特性

讨论了叠加对相干态的完备性关系,并根据Pegg和Barnett的相位算符和相位态的定义,计算了叠加对相干态的相位概率分布函数,并应用数值计算讨论了其特性.结果表明,叠加对相干态的相位概率分布受到相位参数和叠加参数的调制.     

增、减光子奇偶相干态的Wigner函数

利用Fock态表象下的Wigner函数定义，重构了增、减光子奇偶相干态的Wigner函数，并据此 讨论了它们的非经典性质.结果表明：增光子奇偶相干态总呈现出非经典特征，而减光子奇 偶相干态分别仅在k为偶数和奇数时呈现出非经典特征. 关键词： 奇偶相干态 玻色算符的逆算符 Wigner函数     

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。     

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。     

双模场真空态与相干态的叠加态的准几率分布函数

辐射场的非经典态在量子光学中占有十分重要的位置,在实践中有着非常广泛的应用背景,因此如何构造出各种各样的非经典态引起了越来越多的人的极大兴趣和重视。本文中,我们构造了辐射场的一类新的非经典态,称之为双模真空态与相干态的叠加态。我们对该态做了详细的数值计算以及量子统计性质的讨论。我们构造了双模真空态与相干态的叠加态的数学结构,讨论了它的准几率分布函数。数值计算结果表明,双模真空态与相干态的叠加态具有非常显著的非经典性质,因此双模真空态与相干态的叠加态是一类新的非经典光场态。     

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.     

激发压缩真空态的相位概率分布

应用Pegg和Barnett提出的相位算符和相位态理论,研究了激发压缩真空态的相位概率分布特性.数值计算结果表明,激发压缩真空态的相位概率分布主要受到相位参量和压缩参量的调节,相位参量使相位概率分布呈峰值结构,压缩参量的变化将影响相位概率分布的峰值强度,此外激发光子数对相位概率分布也有较大的影响.     

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ is the Gauss/an form exp（-κ（q＇ - q）2}, and exp{（p＇ - p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.     

Entanglement Involved in Pair Coherent State Studied via Wigner Function Formalism

We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.     

Entanglement Involved in Pair Coherent State Studied via Wigner Function Formalism

We calculate Wigner function, tomogram of the pair coherent state byusing its Schmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement (QE) between two two-variable Hermite polynomials (TVHP) and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

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.     

Wigner Functions and Tomograms of the Even and Odd Negative Binomial States

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics. Project 10574060 supported by the National Natural Science Foundation of China and project Q2007A01 supported by the Natural Science Foundation of Shandong Province.