循环量子系统中状态演化的Bloch定理和同步几何相位的统一

对于Hamiltonian随时间作周期变化的量子系统中状态的演化，Bloch定理亦成立，并可据此定义一种新的几何相位———Bloch相位．证明用这种新的几何相位可以把迄今发现的所有同步（即量子态演化一周后获得的）几何相位统一起来，即Bloch相位等于Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位，并且在绝热条件下化为Bery相位．为此，先对Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位的定义作等价的改变，使它们变得有物理意义，并把Lewis-Riesenfeld相位和Berry相位推广到简并情形．还讨论了Bloch相位的求解问题 关键词：     

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.     

量子体系演化的几何相位

量子体系在演化过程中,其状态的时间演化因子除众所周知的由系统能谱决定的动力学相位因子外,还会出现与系统演化路径有关的几何相位因子即Berry相位因子。几何相位的存在已为大量实验所证实,在理论上,已确定了其数学基础是纤维丛理论,并发现它与规范场有某些联系。本文评述了有关几何相位研究工作的进展。     

自旋为1粒子在旋转磁场中的几何相位和动力学相位(英文)

文章研究了自旋为1的粒子在旋转磁场中的几何相位和动力学相位.推导出如何计算自旋为1的粒子在绝热和非绝热演化中的几何相位和动力学相位公式,并利用这些公式计算其相位.最后我们讨论了三种情况下的Berry相位,当考虑ω1<<ω时,系统处于绝热近似,此时,几何相位就是Berry相位.     

关于量子几何相位的评注——评三本量子力学教材中一个基本概念

回顾了国内出版的两本量子力学教材和一本参考书中有关贝里相位的章节，指出了其中有关量子几何相位的一些错误概念。     

教科书内容的正确和真实至关重要--关于曾谨言著"量子力学"中量子几何相位概念的再评注

对曾谨言所著的量子力学书中量子几何相位的一些错误概念再次提出了批评,同时针对他在《大学物理》上的《介绍几个量子力学基本概念》一文的有关观点进行了逐点分析批驳,并举出Berry论文中有关论述为证．本文着重从“正确”和“真实”两方面去分析．     

非绝热几何量子逻辑门的脉冲设计

量子逻辑门是实现量子计算的基本组件之一,而高保真度和高鲁棒性是量子逻辑门必不可少的关键性质。在实现量子逻辑门的各种方法中,利用几何相位的全局特性来构造量子逻辑门是一个有效的方法,它可以对一些局域扰动有比较好的容错性。本文在非绝热几何量子计算的框架下,在三能级系统中构造出了任意的单比特量子逻辑门,并创建出在实验中方便实现的脉冲形式。本文进一步研究了量子系统中存在频率失谐和脉冲振幅偏差的情况,并考虑量子系统与环境之间的退相干效应,以设计出具有更好鲁棒性能的脉冲波形。     

量子绝热定理(II):近似和适用条件

文章首先概述了近年国际文献中关于量子绝热近似和绝热条件的不自洽性的研究.叙述了文献中关于绝热近似不自洽性的论证和争论.然后引入文章作者的观点,从不同于国外文献的角度出发指出应当正确地理解瞬时本征函数的相位问题,从这个相位的正确处理,得出结论:(1)MS不自洽的存在,不因计及几何相位而消除;(2)量子几何相位不自洽是不存在;(3)现时的标准的绝热近似条件不是充分条件.     

量子绝热定理（II）：近似和适用条件

文章首先概述了近年国际文献中关于量子绝热近似和绝热条件的不自洽性的研究.叙述了文献中关于绝热近似不自洽性的论证和争论.然后引入文章作者的观点,从不同于国外文献的角度出发指出应当正确地理解瞬时本征函数的相位问题,从这个相位的正确处理,得出结论：（1）MS不自洽的存在,不因计及几何相位而消除;（2）量子几何相位不自洽是不存在;（3）现时的标准的绝热近似条件不是充分条件.     

量子绝热定理(Ⅱ):近似和适用条件

文章首先概述了近年国际文献中关于量子绝热近似和绝热条件的不自洽性的研究．叙述了文献中关于绝热近似不自洽性的论证和争论．然后引入文章作者的观点，从不同于国外文献的角度出发指出应当正确地理解瞬时本征函数的相位问题，从这个相位的正确处理，得出结论：（1）MS不自洽的存在，不因计及几何相位而消除；（2）量子几何相位不自洽是不存在；（3）现时的标准的绝热近似条件不是充分条件．     

激光淬火温度场及材料性能的数值模拟

The nonadiabatic geometric phase(AA phase) generating in the quantum system consisting of a single-mode or many-mode cavity field with a quantized oscillating-mirror has been discussed. The result shows that such a phase only depends on the intensity of the cavity field but not on its photon statistics, which contrasts to these occuring in a Kerr-like medium.     

Geometric Phase of a Coupled System

In this contribution, my main attention is paid to the study of the geometric phase ora two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.     

State-Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.     

General Solutions of Geometric Phase of Neutron in Rotating Magnetic Fields

The exact solutions of the closed evolution of spin states in rotating magnetic fields are described for the most general cases via eigenstate method. A simple algorithm for calculating the geometric phase is exploited.     

Geometric Phase of a Coupled System

In this contribution, my main attention is paid to the study of the geometric phase of a two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.     

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.     

Heisenberg Model in a Rotating Magnetic Field

We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrödinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.     

Nonadiabatic Geometric Phase and Induced Persistent Current in Mesoscopic Square Circuit with Tilted Magnetic Field at Edges

We investigate the geometric phase produced by nonadiabatic transition of spin states at corners of mesoscopic square circuit with tilted magnetic field at its edges, From the Schrodlnger equation, the transitions of electron spin state at corners are described by the transfer matrices. The eigenenergies and eigenstates are obtained from the cyclic condition and the multiplying of the transfer matrices. We show that there exist persistent charge and spin currents in such a system due to the lift of degeneracy between the opposite moving directions in the presence of the tilted magnetic field. The dependences of eigenenergies, geometric phase, charge and spin persistent currents on the tilting angles of magnetic field are analysed.     

The Nonadiabatic Geometric Phase (AA Phase) in a Quantum System Composed of a Cavity Field Interacting with a Quantum Oscillating-mirror

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Nonautonomous deformed solitons in a Bose-Einstein condensate

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.