非对易相空间三模坐标动量耦合谐振子的能谱

本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的.     

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.     

Q形变的非简谐振子广义相干态

利用变换算符导出了Q形变的非简谐振子代数,由此得到Q形变的非简谐振子广义相干态.这些状态具有过完备性,是Q形变的自然算符的极小测不准状态.在主压缩区间中偶相干态的相对压缩率随形变程度的增大而增大.     

Q形变的非简谐振子广义相干态

利用变换算符导出了Q形变的非简谐振子代数,由此得到Q形变的非简谐振子广义相干态．这些状态具有过完备性,是Q形变的自然算符的极小测不准状态．在主压缩区间中偶相干态的相对压缩率随形变程度的增大而增大．     

二维耦合量子谐振子的本征值和本征函数

运用广义线性量子变换理论,给出一类二维耦合量子谐振子的能量本征值、本征函数、坐标和动量算符在能量表象中的矩阵元及演化算符.     

经典菲涅耳变换的量子力学对应

介绍经典菲涅耳变换的量子力学对应,它是相干态在相空间中的代表点做辛运动所对应的量子菲涅耳算符.     

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.     

量子光学中的一种新变换

我们发现量子光学理论中一个新的积分变换,它不但能够反映量子光学中的Baker-Hausdorff公式的功效,而且可以实现相空间多项式和纠缠态的函数空间之间的变换.此变换可逆,且满足类Parseval定理.在相空间中结合Wigner变换和此新积分变换,可以得到相空间函数h(p,q)和其Weyl-Wigner对应算符之间的一个新的积分变换公式.     

第一类PschlTeller势的非线性代数结构

在形变李代数理论的基础上 ,利用哈密顿算符和自然算符 ,构造出第一类P schl Teller势的非线性谱生成代数 .该非线性代数能够完全确定势场的能量本征态集合和本征值谱 ,在适当的非线性算符变换下可以化为谐振子代数 ,显示了该系统具有新的对称性     

非对易空间的三模谐振子能谱

在非对易空间中,用不变本征算符方法(IEO),对非耦合、坐标耦合、动量耦合三种三模谐振子系统能谱进行求解,并将求解结果与一般对易空间的能谱进行比较分析.通过比较发现,当非对易参数为零时,所求能级差还原到了与普通空间相对应的一般量子系统哈密顿量能级差,验证了推导结果的正确性;同时讨论了耦合系数对非对易空间能谱的影响. 关键词： 不变本征算符 非对易空间 三模谐振子能谱 能级差     

An SU(1,1) Boson Realization Involved in Solving the Three Coupled Harmonic Oscillators' Problem

We find that a three-mode boson realization of the SU(1,1) Lie algebra is involved in solving the three coupled harmonic oscillators' problem. Tire unitary operator U, which is found to be able to transform the Fock space of a three-dimcrrsional isotropic Irarmonic oscillator into the space in which the Hamiltonian of three coupled oscillators is diagonized, is further decomposed as a quantum-mechanical rotation in three-mode Hilbert space followed by an SU(1,1) squeezing transformation. The coordinate representation of this SU(1,1) unitary operator is obtained.     

New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the multimode coordinate--momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the multimode phase shifting operator.     

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.     

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.     

A Kind of New Three-Mode Coherent-Entangled State and Its Application

A kind of new continuous variable three-mode coherent-entangled state (CV-CES) is proposed in Fock space by the technique of integration within an ordered product (IWOP), which exhibits both the properties of coherent state and entangled state, and spans a complete and orthonormal representation. The conjugate state of CV-CES is derived by Fourier transformation. Moreover, the simple experimental protocol of generating a CV-CES is proposed by beam-splitters. As applications of this CV-CES, a three-mode entangled state and a three-mode squeezing-Fresnel operator are constructed.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco-Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Mapping of Householder Transformation in Euclidean Space to Rotation-Reflection Operator

By virtue of the technique of integration within an ordered product (IWOP) of operators we maoifestly show that Householder transformation in 3-dimensional Euclidean space directly maps to the normally-ordered rotation-reflection operator. A new "dyad" form of it in three-mode Fock space is also deduced.     

可控三模纠缠相干态的产生

采用量子理论,考虑边界振动的微腔与腔内的三模辐射场构成的系统,给出了系统的时间演化算符及其变换,得到了系统的态函数随时间的演化关系.结果表明,当振动边界回到初态时,三模腔场处于纠缠相干态,并且可以调控不同纠缠相干态的产生.给出了九个不同的三模纠缠相干态,这些态中含有不同的相位因子,这些相位因子充分体现了场和振动边界的相互作用和相互影响.这些结果为可控纠缠相干态的实验制备提供了重要的理论依据.     

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