从一维光晶格中释放的任意子噪声关联函数研究

首先求解具有delta函数型相互作用的任意子气体的含时薛定谔方程,给出了其多体波函数的解析解,并在此基础上详细分析了无相互作用情形和有相互作用情形下任意子噪声关联函数的特性。对于有相互作用的任意子气体,其噪声关联呈现出与无相互作用情形下不同的特性：散射相位具有一定的空间分布,一系列线性而不是尖峰出现在噪声关联函数中;线性的宽度、取向以及位置与任意子的统计参数和粒子间相互作用强度的关系都非常密切。特别地,在TG极限下,也就是相互作用趋于无限大的情形下,任意子的噪声关联函数图样与无相互作用情形下的图样完全相反。     

一维晶格中全同任意子的量子动力学与关联

任意子介于玻色子与费米子之间,遵从奇特的分数统计,隐含着许多有趣的物理特性.本文研究了一维晶格中相互作用全同任意子的少体量子动力学及其量子关联性质.基于严格的数值方法,分析了任意子在晶格中局域粒子密度分布的动力学演化过程.结果表明,分数统计可以明显影响任意子动力学演化过程中实空间的局域粒子密度分布,产生新的动力学结构.特别地,当存在相互作用时,分数统计粒子的局域粒子密度分布会呈现有趣的依赖于相互作用性质的不对称性.最后计算了任意子的密度密度关联,分析了粒子统计性质和相互作用对体系量子关联的调制,同时进一步证实了任意子分数统计在实空间中的动力学效应.     

从光晶格中释放的超冷玻色气体密度-密度关联函数研究

利用量子旋转场理论详细研究了从光晶格中释放的超冷玻色气体的空间密度-密度关联函数.由于量子旋转场理论充分考虑了光晶格中冷原子气体的粒子数涨落和相位效应,该理论能有效应用于具有强相互作用的冷原子系统,从而光晶格处于超流态到绝缘态逐渐过渡过程中的超冷原子气体的关联特性在这一理论体系下都得到了很好的描述.结果表明:随着超冷玻色气体逐渐从绝缘态向超流态过渡,其密度-密度关联图样中连续对角斜线也逐渐向分散的尖峰过渡,理论结果与目前实验观测到的结果符合.除此以外,上述密度-密度关联的结果中还包含了超冷原子系统量子耗散效应,相关结论与目前已有的理论和实验一致.     

基于时域有限差分法的非球型气溶胶和卷云粒子散射特性研究

本文选取3种气溶胶粒子和3种卷云粒子,利用时域有限差分法,对椭球型气溶胶粒子和六棱柱卷云粒子在不同波长下散射相位函数进行了仿真分析,并讨论了入射方向对粒子散射特性的影响。仿真结果表明,尺寸参数较小时散射相位函数变化较平稳,尺寸参数较大时曲线出现震荡,且随尺寸参数增大震荡剧烈;粒子单次散射能量主要集中在前向散射,随散射角增大呈指数下降;气溶胶粒子散射相位函数在90~150°之间出现明显的波谷;卷云粒子散射相位函数一般不出现明显波谷。当入射角度改变时,气溶胶粒子在整个0~180°之内的散射相位函数都有101数量级的变化,卷云粒子则在0~90°前向散射内保持稳定。本文的研究方法和结论可以为研究天空偏振光模式的形成机理和变化规律提供参考。     

关联噪声对单模激光动力学性质的影响

应用线性近似方法,计算了具有指数形式关联的两白噪声驱动下的单模激光光强的关联函数、功率谱及关联时间。根据计算结果讨论了噪声间的关联程度和噪声间互联时间对以上各量的影响,并和噪声间具有δ函数关联形式的情况进行了比较     

参考光干涉提取复振幅的散斑统计函数的实验研究

由散斑场和参考光的干涉图样提取散斑场复振幅、相位和强度的数值分布,并对其统计特性进行实验研究,消除了散斑场强度统计函数特别是概率密度函数的传统测量方法中噪声引起的偏差,并实现了散斑场复振幅和相位统计特性的实验研究.通过对不同散射角处散斑场的研究发现随着散射角度的增大散斑颗粒逐渐呈现出横向展宽的现象,且其平均宽度表现为各向异性,但是其概率密度函数并没有发生变化,与小角度情况一样属于圆形高斯散斑场. 关键词： 散斑 概率密度 干涉     

一种可能存在的两分量任意子模型

本文提出了一个可能存在的两分量任意子模型,在玻色表象下给出了多体波函数的一般形式.我们分析了规范矢势引起的相互作用,通过将规范矢势类比于一个二维静电场,发现这个两分量任意子模型近似等价于一个二维两分量库仑气体,在低温下可能发生 Kosterlitz-Thouless 相变.     

压缩光透过克尔介质时光场的相位和压缩特性及其关联

用Pegg-Barnett理论研究了压缩真空态光与克尔介质的相互作用对光场相位特性的影响,讨论了光场的压缩和高阶压缩与相位特性之间的关联.光场相位正交分量的各阶矩呈现周期性的振荡,与相位分布函数密切相关.     

包容性非球形气溶胶粒子的散射特性及其对激光传输的影响研究

针对局部地域大气气溶胶的生成、演化的特点,在分析典型对称结构的包容性非球形气溶胶粒子的形态学特征基础上,利用T矩阵法进行了椭球形粒子含非球形粒子的包容性粒子光散射特性计算和分析.以1 064nm波长激光传输为例分别计算了两种典型分布状况的包容性非球形粒子的散射相函数等散射特性,并针对稠密气溶胶大气路径上激光传输的多散射现象,利用蒙特卡罗方法进行了典型大气状况下包容性粒子多次散射对激光信号大气传输中脉冲展宽的应用分析,在传输3km和5km距离时多次散射效应造成激光脉冲峰值半宽分别为3μs和4μs左右.指出气溶胶的基本散射特性与粒子的形态学特征、尺度因子、化学成分及颗粒密度等有密切的关系,其散射特性对激光信号的大气传输具有明显的影响.     

量子理想气体中粒子间的统计关联作用

在量子理想气体中，虽然粒子间没有动力学互作用力，但由于粒子全同性原理的影响，在粒子间存在着统计关联，这种统计关联来源于波函数的对称性．对于费米子，统计关联表现为统计排斥作用；对于玻色子，统计关联表现为统计吸引作用． 本文以气体的物态方程、内能和熵为例，把粒子间的统计关联作用和动力学相互作用对气体性质的影响进行分析对比．在弱简并条件下的讨论表明，统计排斥和统计吸引作用对气体物态方程和内能的影响与动力学互作用的排斥作用和吸引作用相当；但统计关联作用与动力学工作用对气体的熵有不同的影响：动力学工作用不论是斥力还是引力）都使气体的熵减少，但统计吸引作用使气体的熵减少，而统计排斥作用使气体的熵增加（相对于经典理想气体的熵值）．     

Interacting anyons in topological quantum liquids: the golden chain

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.     

Anyonic quantum walks

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system’s Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors. The position distribution of the walker is related to Jones polynomials, topological invariants of the links created by the anyonic world-lines during the walk. Several examples such as the SU(2)_k and the quantum double models are considered that provide insight to the rich diffusion properties of anyons.     

Engineering complex topological memories from simple Abelian models

In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.     

Implementation of single-qubit and CNOT gates by anyonic excitations of two-body topological color code

The anyonic excitations of topological two-body color code model are used to implement a set of gates. Because of two-body interactions, the model can be simulated in optical lattices. The excitations have nontrivial mutual statistics, and are coupled to nontrivial gauge fields. The underlying lattice structure provides various opportunities for encoding the states of a logical qubit in anyonic states. The interactions make the transition between different anyonic states, so being logical operation in the computational bases of the encoded qubit. Two-qubit gates can be performed in a topological way using the braiding of anyons around each other.     

Anyon-fermion mapping and applications to ultracold gases in tight waveguides

The Fermi-Bose mapping method for one-dimensional Bose and Fermi gases with zero-range interactions is generalized to an anyon-fermion mapping and applied to exact solution of several models of ultracold gases with anyonic exchange symmetry in tight waveguides: anyonic Calogero-Sutherland model, anyons with point hard-core interaction (anyonic Tonks-Girardeau gas), and spin-aligned anyon gas with infinite zero-range odd-wave attractions (attractive anyonic Tonks-Girardeau, or AATG, gas). It is proved that for even N>or=4 there are states of the AATG gas on a ring, with anyonic phase slips which are odd integral multiples of pi/(N-1), of energy lower than that of the corresponding fermionic ground state. A generalization to a spinor Fermi gas state with anyonic symmetry under purely spatial exchange enables energy lowering by the same mechanism.     

Dynamical role of anyonic excitation statistics in rapidly rotating bose gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.     

Interferometry of non-Abelian anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at ν=5/2 and Read-Rezayi state at ν=12/5.