基于坐标表象的脊波变换研究

在小波变换量子力学机制的启发下, 通过采用Fock空间里双模坐标本征态改写经典Ridgelet变换, 定义了量子光学态的Ridgelet变换. 然后利用IWOP技术给出不对称积分算符的显式, 并推导出了两个有用的双模算符正规乘积公式. 在此基础上, 通过选取双模“墨西哥帽”母小波函数, 分析了相干态、特殊压缩相干态、中介纠缠态表象的Ridgelet变换. 关键词： IWOP技术 Ridgelet变换 相干态     

基于纠缠态表象的复脊波变换理论

本文基于连续变量量子态构造小波变换的研究结果, 从经典信息的连续脊波变换出发, 利用有序算符内ket-bra型积分, 构造连续复脊波变换对应的量子算符和表象表示, 采用表象的内积运算与态矢投影展开, 研究量子光学态的复脊波变换理论. 关键词： 有序算符内积分技术 复脊波变换 纠缠态表象 相干态     

单光分束器的量子变换算符研究

针对理想情况下单光分束器,得到了其对应的变换矩阵.用相干态表象和有序算符内积分技术,给出其对应的幺正变换算符.纠缠态的实验制备方案,说明单光分束器在量子信息源研究中具有十分重要的作用.     

量子光学的混合态表象及其演化

量子光学中的相干态是一个纯态表象,用有序算符内的积分方法可以方便地引入一个混合态表象,其Radon变换是坐标——动量中介表象。进一步为了改善其不正定性,我们引入参数,使之纯态化。新的正定的纯态是一个平移压缩态,其特点是平移参数与压缩参数相关。     

求解三模耦合谐振子精确能谱的一种方法

基于相空间中的幺正转动变换,利用有序算符内的积分技术,得到了相空间中转动算符、傅里叶变换算符和宇称算符的相干态表示.进而引入并利用相空间中的三模转动算符,简捷地实现了三模坐标-动量耦合谐振子哈密顿量的退耦合,给出了该耦合形式谐振子的精确能谱及其能量本征态.     

奇偶二项式光场态的小波变换

利用有序算符内积分方法,小波变换可以表示为被转换态矢|f〉在压缩平移算符U(μ,s)作用下向母小波态矢〈ψ|转换的矩阵元〈ψ|U(μ,s)|f〉. 在此基础上,计算了奇、偶二项式态的小波变换,得到小波变换谱. 结果表明,小波变换谱可以起到识别这些量子力学态的作用,具有直观易辨的优点. 关键词： 小波变换 奇偶二项式态 有序算符内积分     

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.     

光束分离器算符的分解特性与纠缠功能

光束分离器是量子光学中的基本线性器件之一, 它在量子纠缠态的制备与测量上起着重要作用. 基于光束分离器(BS)对算符的矩阵变换关系, 本文导出了BS算符在若干表象中的自然表示. 利用这个自然表示(而非SU(2)李代数关系)及有序算符内的积分技术, 可直接导出BS算符的正规乘积、紧指数表示及多种分解形式. 此外, 可直接导出一种纠缠态表象及其Schmidt分解. 这对于讨论连续变量量子隐形传输是十分方便的. 关键词： 光束分离器算符 纠缠态表象 有序算符内的积分技术 Schmidt分解     

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.     

从二维正态分布密度函数的角度研究量子力学基本表象

利用二维正态分布密度函数和有序算符内的积分技术,简捷地得到了坐标本征态、动量本征态、坐标-动量中介表象和相干态在Fock表象中的表达式.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Quantum Mechanics Version of Wavelet Transform Studied by Virtue of IWOP Technique

Using the technique of integral within an ordered product (IWOP) of operators we show that the wavelet transform can be recasted to a matrix element of squeezing-displacing operator between the mother wavelet state vector and the state vector to be transformed in the context of quantum mechanics. In this way many quantum optical states' wavelet transform can be easily derived.     

Optical wavelet-fractional squeezing combinatorial transform

By virtue of the method of integration within ordered product(IWOP)of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform(WFrST)operator.The way we successfully combine them to realize the integration transform kernel of WFr ST is making full use of the completeness relation of Dirac’s ket–bra representation.The WFr ST can play role in analyzing and recognizing quantum states,for instance,we apply this new transform to identify the vacuum state,the single-particle state,and their superposition state.     

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.     

相干态的小波变换

根据小波变换的量子力学机理, 通过选取不同的系数, 构造出两组新的母小波函数. 在此基础上, 利用正规乘积内积分技术, 推导出相干态和粒子数态的小波变换, 并数值模拟出它们的小波变换图谱.     

Wigner function and tomogram of the Hermite polynomial state

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner function for the Hermite polynomial state (HPS). The tomogram of the HPS is calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.     

Newton-Leibniz integration for ket-bra operators (III)—Application in fermionic quantum statistics

The Newton-Leibniz integration over Dirac’s ket-bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] is generalized to Newton-Leibniz-Berezin integration over fermionic ket-bra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac’s symbolic method for Fermi system can also be developed, which exhibits Bose-Fermi supersymmetry in this aspect.     

Dynamical behavior of a mesoscopic circuit in phonons bath derived by virtue of the IWOP technique

Taking into account the interactions between electrons and phonons, we study the dynamic behavior of a dissipative mesoscopic circuit for pure initial coherent state of phonon bath modes by virtue of the IWOP technique. It shows that if the bath modes are initially in coherent states, some phenomena like Brownian behavior will appear in mean charge and current of the mesoscopic circuit. The quantum fluctuations of charge and current are constant and irrelevant to the coupled coefficients between electrons and phonons.