双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符,利用有序算符内的积分（IWOP）技术分析了其变换特性,并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

基于双模相干-纠缠态表象的算符恒等式构造法

利用最近引进的相干-纠缠态|x,α〉表象和有序算符内的积分技术,给出了关于双模光场正交分量（X₁+X₂）/2^1/2和参数化的正交分量（μX₁+νX₂）/λ的函数的若干正规乘积展开式,这对于研究场的高阶压缩行为和构建广义压缩态是有用的. 关键词： 双模相干-纠缠态 算符恒等式 有序算符内的积分技术     

量子光学态的Ridgelet变换

利用有序算符内积分技术推导出一个有用的双模算符正规乘积公式. 然后在量子力学框架下, 计算出相干态、特殊压缩相干态、中介纠缠态表象的Radon变换. 在此基础上, 通过选取“墨西哥帽”母小波函数, 分别分析了以上三种量子光学态的Ridgelet变换. 关键词： 有序算符内积分技术 Radon变换 Ridgelet变换     

高斯积分在量子表象理论中的应用

首先证明了真空投影算符的正规乘积形式,然后结合有序算符内积分技术,把数学上的高斯积分推广到量子算符的积分形式.通过表象的完备性与对称性,进一步给出了坐标表象、动量表象、中介表象和相干态表象的具体形式.     

单双模连续压缩真空态及其量子统计性质

利用有序算符内的积分技术研究了通过双模压缩算符作用于两个单模压缩 态上得到的单双模 连续压缩态. 导出了单双模连续压缩算 符的正规乘积形式, 并在此基础上研究了单双模连续压缩真空态的量子统计性质. 特别是利用Weyl编 序算符在相似变换 下的不变性, 简洁地导出了单双模连续 压缩真空态的Wigner函数. 最后, 还简单地提出 了单双模连续压缩 真空态的实验产生方案.     

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     

新纠缠态表象的构建及其性质

运用有序算符内积分(IWOP)技术,构建了(x)2—p1和.(x)1—P2的共同本征态｜η〉,并分析了该新纠缠表象的Schmidt分解形式.另外,我们还得到纠缠态｜η>的共轭态｜ξ〉,同时计算了它们的内积.最后我们给出了新双模压缩算符S2=μ∫d2η/π｜μη〉〈η｜的显式,并分析了其压缩特性.     

双模积分型投影算符及其应用

引进了幺正的双模积分型投影算符,利用有序算符内的积分(IWOP)技术分析了其变换特性;然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数;最后讨论了特例情形.     

n模耦合谐振子量子系统的精确波函数

利用不变本征算符法研究了n模耦合谐振子量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出坐标表象中系统的精确波函数的解析解.并对不同情形的耦合系数进行了讨论,认识到n模动量耦合谐振子体系和n模坐标耦合谐振子体系是本文所研究的体系的特例.     

利用IWOP技术构建量子力学新表象

基于对坐标表象、动量表象及相干态表象完备性关系式的正规乘积内纯高斯积分形式的分析,阐述了利用有序算符内的积分技术构建量子力学新表象的思路和方法,并具体以单模坐标-动量中介表象、双模纠缠态表象和双模相干纠缠态表象的构建为例进行了论述.     

Irreversible quantum graphs

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a single harmonic oscillator is coupled to it. This mechanism is shown to imply that the quantum dynamics is irreversible. Moreover, it demonstrates the surprising result that irreversibility can be introduced by a ‘bath’ which consists of a single harmonic oscillator.     

双模耦合谐振子哈密顿量的一般解法

双模耦合谐振子哈密顿量是广义坐标■和广义动量■的一般二次型,通过一个坐标变换可以将其表示为新基底下的标准二次型,经计算得知,新基底之间满足准正则对易关系,从而引入准粒子的产生和湮没算符,这样就消除了耦合项,哈密顿量化简成为双模独立谐振子情形,使问题得到解决.这样的解决方法可以推广到各向异性n模谐振子的耦合体系.     

Oscillator Laser Model

A laser model is formulated in terms of quantum harmonic oscillators. Emitters in the low lasing states are usual harmonic oscillators, and emitters in the upper states are inverted harmonic oscillators. Diffusion coefficients, consistent with the model and necessary for solving quantum nonlinear laser equations analytically, are found. Photon number fluctuations of the lasing mode and fluctuations of the population of the lasing states are calculated. Collective Rabi splitting peaks are predicted in the intensity fluctuation spectra of the superradiant lasers. Population fluctuation mechanisms in superradiant lasers and lasers without superradiance are discussed and compared with each other.     

Some Unitary Operators Derived Using the Quantum State and Its Application

Some unitary operators are derived using quantum state by depending on the technique of integration within an ordered product of operators, for example parity operator, displacement operator, squeezed operator, etc. The characteristics of these operators are analyzed. Their unitary transformations play an essential role in some transformations. As applications, the dynamic problems of the double momentum coupling harmonic oscillators are solved exactly.     

利用二次型求解n模耦合谐振子能量本征值精确解

利用二次型理论构造一个幺正矩阵进行坐标和动量变换,把n模动量耦合谐振子体系的哈密顿量化为标准的二次型,进而得到n模动量耦合谐振子体系的能量本征值.对n模坐标耦合的情况也进行了类似求解,并提供了解决该类问题的一般数学方法.     

Non perturbative effective potentials of quantum oscillators

Non perturbative analogues of the Gaussian effective potential (GEP) are defined for quantum oscillators obeyingq—or (q,p)—deformed commutation relations. These are called the non perturbativeq-effective potential (NP _q EP) and the non perturbativeqp effective potential (NP _qp EP), in the respective cases. A system-specific effective potential (SSEP) is also introduced by means of an additional minimization with respect to theq orq andp parameters. The method is applied toq and (q,p) oscillators of the quartic and sextic types. The SSEP in the case of ground states of theq-oscillators corresponds toq=1, which is the ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is seen to exist in the case of quantum oscillators sitting in a double well potential.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Irreversible quantum graphs

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a single harmonic oscillator is coupled to it. This mechanism is shown to imply that the quantum dynamics is irreversible. Moreover, it demonstrates the surprising result that irreversibility can be introduced by a 'bath' which consists of a single harmonic oscillator.     

各向异性n模耦合谐振子的精确求解

利用量子变换理论,极其简洁地给出了种向异性耦合谐振子的能谱,从而提出了一种普遍的方法。     

An algebraic description of anharmonic diatom–diatom inelastic collisions in the semiclassical approximation

An algebraic model to describe inelastic collisions between two anharmonic diatomic molecules in the semiclassical approximation is presented. The interactions for the diatomic systems are modelled in terms of Morse potentials, while an exponential repulsive potential is taken for the interactions between the nearest atoms of the diatomic systems. This problem is treated in the interaction potential framework, where an approximation in terms of the generators of three SU(2) groups is proposed, two corresponding to the Morse oscillators and the other to the interaction. The transition probabilities are given in terms of a sum of the products of three Wigner's d(β) functions corresponding to the three SU(2) groups. As an example the systems N₂?+?N₂ and H₂?+?H₂ are described and compared with exact quantum mechanical calculations.