偏振光的χ矢量表示及应用

从Jones矢量的定义中引入了χ矢量,利用该矢量的定义给出了偏振光的χ矢量复平面表示,在该二维复平面上,确定了各个点与偏振光的态势相对应的关系.同时证明了与Jones矢阵的本征态有关的几个重要的结论:任何光学系统的Jones矩阵都有两个本征态;旋光介质的两个本征态是左旋和右旋圆偏振光;偏振器的本征态是两个正交的线偏振光;双折射介质的两个本征态是分别沿快、慢轴方向的线偏振光.     

混合纠缠态的几何描述

给出了Hilbert-Schmidt(H-S)空间中密度矩阵的向量表示,建立了完整的H-S空间中的度规 ,由此将混合纠缠态的判据纳入到直观的几何图像中,讨论了最大混合态附近可分离态的紧 致邻域,得到了关于该邻域体积测度的更强的结果. 关键词： 纠缠 混合态 Hilbert-Schmidt空间     

非马尔可夫环境下原子的几何相位演化

从微观哈密顿量出发,研究了原子在非马尔可夫环境影响下的几何相位演化. 结果表明,在强耦合条件下原子的几何相位比弱耦合时获得的几何相位大, 而且这一差别随环境损耗的增加而增大. 在环境损耗较小时,原子的几何相位随时间变化出现连续和不连续两种演化行为,且不连续的范围随环境的损耗增加而增大. 总之,在非马尔可夫环境下,原子的几何相位演化将出现丰富而复杂的演化特征. 关键词： 几何相位 原子 腔场 非幺正     

三环非均匀混合偏振同轴矢量光束的聚焦特性

基于Richards-Wolf矢量衍射积分公式,数值分析了同轴三环非均匀混合偏振矢量光束经过高数值孔径透镜的聚焦特性。该矢量光束由同轴三环局域线偏振矢量光束通过一个相位延迟角为δ的液晶相位延迟器产生,光束偏振变为包含线偏振、圆偏振和椭圆偏振的混合态。同轴三环局域线偏振矢量光束的偏振分布是由径向向内偏振的外环光束、径向向外偏振的内环光束和线偏振方向与径向方向夹角为φ2的中环光束构成。数值模拟结果显示该混合偏振矢量光束的聚焦强度分布与参数φ2和相位延迟角δ密切相关,当选取适当的φ2和δ时,在焦平面附近产生沿光轴方向的三维多点光俘获结构——暗光链,这在光学微操纵领域具有潜在的应用价值。     

超球坐标下氢分子体系势能矩阵元的解析表达式

给出了在非正则超球坐标系下对氢分子薛定谔方程进行直接求解时所涉及的所有势能矩阵元的解析表达式,以及主要的推导。在推导过程中,引入了付立叶变换及９维矢量将势能各项用超球谐函数来展开,并且利用了合流超几何函数,拉卡系数和维格纳系数的一些性质。     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

旋转磁场中朗道系统的非绝热非周期性量子几何相位和Hannay角

基于代数动力学，精确求解了旋转磁场中的朗道系统，讨论了它的一般几何相位，给出了一般量子几何相位中对应于规范势的那部分相位的经典对应. 数值计算结果显示出非绝热演化和绝热演化的重大区别：非绝热演化诱导的非绝热量子激发引起系统物理量的非周期性和复杂性，体现了环境对系统的影响.     

时间演化矩阵乘积算符方法及其在量子开放系统中的应用

量子开放系统在量子科学的发展中占据着举足轻重的地位,因此对其数值计算方法进行研究具有重要的意义.对于量子开放系统,在20世纪90年代发明的准绝热传播子路径积分方法是为数不多的精确的数值计算方法,但其计算复杂度随着系统的大小和关联时间长度呈指数增长,因此在实际计算中它所能计算的物理模型比较受限.近年来,张量网络的研究和应用有了长足的进展.使用张量网络来表达该方法可以使其计算复杂度变成多项式增长,极大地提高了计算效率.由此发展出的新方法则被称为时间演化矩阵乘积算符方法,是一种高效的、数值精确的、并且非马尔可夫的计算方法,在量子开放系统的研究中有着广泛的应用前景.本文首先综述了准绝热传播子路径积分方法,接着介绍了矩阵乘积态的基本思路,然后利用矩阵乘积态来表述准绝热传播子路径积分方法,从而对时间演化矩阵乘积算符方法进行介绍;最后综述了该方法在量子开放系统中的应用,并以自旋-玻色子系统中的关联函数和热流计算为例对该方法进行了展示.     

光学多通投影相关矩阵—矢量乘法器

基于几何光学的投影相关原理,本文提出了用非相干多通投影相关器作矩阵-失量乘法运算的新方论;讨论了这种矩阵矢量乘法器的一般结构形式和物理极限;并给出了实验结果,实验表明该方法简单易行.     

实验检验双光子的几何相位

Pancharatnam在研究两束光干涉时提出的几何相位的概念;紧接着Berry发现了量子系统在循环绝热演化下的几何相位.在光子系统中,实验上已经验证了经典光和单光子的几何相位,并观察到几何相位的大小与循环演化过程有关.对于双光子,其几何相位在相同的循环演化下是单光子两倍.我们提出了一种简单的实验方案来观察双光子的几何相位.实验中,通过光路的设计排除了由于光程改变引起的相位改变,直接检测由于几何相位的不同引起的双光子干涉.     

Poincaré sphere representation for three state systems

We point out that the Poincaré sphere can be used to represent the rays of a three state quantum system. Those interested in geometric phase phenomena may find this representation a useful aid to visualize the global structure of ray space.     

Geometric Phase in Fluctuating Magnetic Field

Geometric phase in a two-level atom with a fluctuating magnetic field is calculated by a nonunit vector ray in a complex projective Hilbert space, where the nonunit vector is a map connecting with density matrices of a quantum open system. We find that the Pancharatnam phase oscillates with evolving time. The Berry phase depends on the fluctuating parameter but it is proportional to the area spanned in the Bloch parameter space.     

Nonadiabatic Geometric Phases Induced by Master Equation in Open Quantum System

By seeking for a useful generic solution of Lindblad master equation, we find that the density matrix of mixed state carries with the geometric messages, where the density matrix of mixed state is expanded in terms of a complete set of normalized, traceless and Hermitian matrices together with a unit matrix in a Hilbert space. Our approach to the geometric phases of mixed state are directly from the master equation describing a dynamic evolution of open system and therefore may be conceptually useful in analyzing the geometric phases of mixed state. An example is discussed for the nuclear-magnetic-resonance system interacting with its surrounding environment.     

基于Metasurface的柱矢量光束的产生

本文提出了一种基于Metasurface产生任意柱矢量光束的方法.采用的Metasurface是在熔融石英上刻蚀空间变化的非周期光栅构成.非周期光栅会形成空变的有效双折射,从而对光场的偏振态空间分布进行调制.通过琼斯矩阵的方法分析得出这样的Metasurface可以将入射线偏振光转换为柱矢量光束,并且只需要改变入射线偏振光的偏振方向即可获得高阶庞加莱球赤道上任意一点的柱矢量光束.最后,用Metasurface搭建了一套简单、高效的柱矢量光束产生系统,实验结果与理论分析一致.     

Use of the poincare sphere in polarization optics and classical and quantum mechanics. Review

The method of the Poincaré sphere, which was proposed by Henri Poincaré in 1891–1892, is a convenient approach to represent polarized light. This method is graphical: each point on the sphere corresponds to a certain polarization state. Apart from the obvious representation of polarized light, the method of the Poincaré sphere permits efficient solution of problems that result from the use of a set of phase plates or a combination of phase plates and ideally homogeneous polarizers. Recently, to calculate the geometric phase (which is often called the Berry phase) in polarization optics and quantum and classical mechanics, the method of the Poincaré sphere has drawn much attention, since it allows us to carry out these calculations very efficiently and intuitively using the solid angle resting, on a closed curve on the Poincaré sphere that corresponds to the change in the state of light polarization or in the state of spin of an elementary particle or its orientation in space from the viewpoint of systems in classical mechanics. The review considers papers on the above problems. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 3, pp. 265–307, March. 1997.     

Geometric Phase for Optical Free Induction Decay

Geometric phase is investigated for optical free induction decay with a modified Bloch equation by establishing in connecting density matrices with nonunit vector ray in a complex projective Hilbert space. Under the limiting of pure state, our approach may give out the Berry phase and Aharonov and Anandan one. Furthermore, by comparing our approach with the kinematic one, we find that, after a suitable modification to the kinematic approach, both differences are very small for the Berry phase of mixed states in the optical free induction decay under the case of quasicyclic evolution.     

Poincaré-sphere equivalent for light beams containing orbital angular momentum

The polarization state of a light beam is related to its spin angular momentum and can be represented on the Poincaré sphere. We propose a sphere for light beams in analogous orbital angular momentum states. Using the Poincaré-sphere equivalent, we interpret the rotational frequency shift for light beams with orbital angular momentum [Phys. Rev. Lett. 80, 3217 (1998)] as a dynamically evolving geometric phase.     

光线庞加莱球法构建的结构光场及其传输特性研究

结构光场在光信息传输、显微成像以及微粒俘获中有重要作用.本文基于光线庞加莱球法结合不同花瓣数的梅花曲线构建了一类结构光束.根据光线庞加莱球法可计算这类光束在束腰面上的光强与相位分布,以及光束内外焦散线的分布.这些焦散线的特征表明梅花形结构光束具有无衍射与自修复的特性.进一步采用角谱衍射法和光线追迹研究了这类光束在空间中的传输特性.当梅花花瓣数为0时,该光束退化为拉盖尔-高斯光束;当花瓣数为1时,内焦散线汇集到两点,使光束具有无衍射特性.通过光线庞加莱球法获得其光线在空间传播的轨迹,直观地展示了光束被遮挡后的自修复特性.此外,本文还展示了花瓣数为5的结构光束,其内焦散线为十角星结构,该光束同样具有自修复特性.通过修改梅花曲线参数或选择其他庞加莱球面曲线可以构造更加复杂的结构光场.     

Wigner representation and geometric transformations of optical orbital angular momentum spatial modes

An exact Wigner representation of optical spatial modes carrying orbital angular momentum is found in closed form by exploiting the underlying SU(2) Lie-group algebra of their associated Poincaré sphere. Orthogonality relations and observables of these states are obtained within the phase space picture. Development of geometric phases on mode transformations is also elucidated.     

Harmonic analysis on the Poincaré group

The generalized matrix elements of the unitary representations of the Poincaré group are computed as eigendistributions of a complete commuting set of infinitestimal operators on the group. The unitary representations of the Poincaré group can be reconstructed from these matrix elements in a Hilbert space of square integrable functions over the space of eigenvalues. Some properties of these distributions (which are measures) are given and some characters are computed from the explicit formulae for the matrix elements.