强磁场中碱金属原子的演化和Aharonov－Anandan相因子

利用量子不变量理论研究了任意随时间变化的强磁场中碱金属原子系统的演化问题，得到了此系统精确的演化态，并利用此精确的演化态求出了相应的Ａｎａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化态按哈密顿量的瞬时本征态展开，可以得到绝热近似的任意阶修正。     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLY-CHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR

By using group representation theory,the quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper.We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation,but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated.It is pointed out that this universal Berry phase factor has observable effects.     

非线性系统的非对角Berry相

研究了非线性系统中非对角情况的Berry相位, 给出了非线性非对角Berry相位的计算公式. 结果表明, 在非线性非对角情况下, 总相位包含有动力学相位, 通常意义的Berry相位, 以及非线性引起的附加相位. 此外, 还包含有非对角情况时所特有的新的附加项. 这新的一项表示, 当系统哈密顿慢变时产生的Bogoliubov涨落, 与另一个瞬时本征态之间的交叉效应, 进而对总的Berry相位产生影响. 作为应用, 对二能级玻色爱因斯坦凝聚体系, 具体计算了非线性非对角的Berry相位. 关键词： Berry 相位 非对角 绝热演化 玻色爱因斯坦凝聚     

Adiabatic and Non-Adiabatic Berry Phases in Generalized J-C Model of Multi-Photon Process

We derive the adiabatic and non-adiabatic Berry phases in the generalized Jaynes-Cummings model of multi-photon process. The results show that the adiabatic Berry phase is kept a constant π independent of all the parameters, while the non-adiabatic approximate Berry phase is parameter-dependent, proportional to the average photon number m, and tends to be constant with the increasing detuning. In the case of exact n-photon resonance and an integer ratio of m/n, the two results coincide with each other, otherwise there appears an additional non-trivial phase factor.     

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.     

Berry phase of coupled two arbitrary spins in a time-varying magnetic field

In this paper, we investigate the Berry phase of two coupled arbitrary spins driven by a time-varying magnetic field where the Hamiltonian is explicitly time-dependent. Using a technique of time-dependent gauge transform the Berry phase and time-evolution operator are found explicitly in the adiabatic approximation. The general solutions for arbitrary spins are applied to the spin-1/2\ system as an example of explanation.     

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.     

Geometric Phase for High-Temperature Master Equation

Geometric phase of mixed state is investigated for three-level system obeying a high-temperature master equation. The results show the Berry phase of mixed phase is strongly dependent on the initial condition. For the different initial angle, the turning region is different. In addition, the decrease of Berry phase is most slow around the coupling strength α=5 with an increasing of evolving time.     

Adiabatic Berry phase in an atom-molecule conversion system

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schrödinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole. We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.     

Nonadiabatic Berry Phase of a Two-State System and Nonstationarity of Quantum States

The nonadiabatic Berry phases in the magnetic resonance under .various initial conditions are investigated and compared with ,the adiabatic Berry phase. The generaJ formalism for calculating the nonadiabatic Berry phase of a two-state system in terpls of the expansion of instantaneous energy eigenstates is presented. Some numerical calculations and discussions are made. The Berry phase of a two-statesystem under an impulsive interaction is addressed.     

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：     

Aharonov-Anandan Phases in Lipkin-Meskov-Glick Model

In the system of several interacting spins, geometric phases have been researched intensively. However, the studies are mainly focused on the adiabatic case (Berry phase), so it is necessary for us to study the non-adiabatic counterpart (Aharonov and Anandan phase). In this paper, we analyze both the
non-degenerate and degenerate geometric phase of Lipkin-Meskov-Glick type model, which has many application in Bose-Einstein condensates and entanglement theory. Furthermore, in order to calculate degenerate geometric phases, the Floquet theorem and decomposition of operator are generalized. And the general formula is achieved.     

On spin evolution in a time-dependent magnetic field: Post-adiabatic corrections and geometric phases

We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the usual adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.     

The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.     

The Exact Solution,Berry's Phase and Coherent State for the Driven Generalized Time-Dependent Harmonic Oscillator

The Lewis'invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for thirr system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adiabatic limit. The relation between the exact Lewis'phase and the corresponding classical phase angle L'discusrred.     

Bery相与AB相的关系

Ｂｅｒｒｙ曾经论证，Ａｈａｒｏｎｏｖ-Ｂｏｈｍ相可以看成是Ｂｅｒｙ相．在论证中放弃了绝热近似，也未涉及量子态的非定态性．重新探讨了此论证，表明Ｂｅｒｙ的结论是正确的，但在该论证过程中需要作绝热近似．ＡＢ效应中运动电子是用一个运动波包（非定态）来描述的，ＡＢ相的出现，是要求波包的演化必须满足Ｓｃｈｒ?ｄｉｎｇｅｒ方程的结果，但ＡＢ相的出现不受绝热条件的限制 关键词：     

Berry phase of many-body system: time-dependent representation method

In this paper, we investigate the Berry phase of many-body system in the time-dependent representation. The formula of Berry phase of many-body system calculating in the time-dependent representation is derived. In this scenario, the Berry phase can be decomposed into two terms, which have different physical meanings respectively. Using these formula, we calculated the Berry phase for the many-spin system coupled by the XXZ exchange interaction. The results show that the Berry phase consists of two contributions which can be interpreted as the flux of a nonquantized monopole and the flux of a Dirac ring respectively.     

Experimental determination of the berry phase in a superconducting charge pump

We present the first measurements of the Berry phase in a superconducting Cooper pair pump. A fixed amount of Berry phase is accumulated to the quantum-mechanical ground state in each adiabatic pumping cycle, which is determined by measuring the charge passing through the device. The dynamic and geometric phases are identified and measured quantitatively from their different response when pumping in opposite directions. Our observations, in particular, the dependencies of the dynamic and geometric effects on the superconducting phase bias across the pump, agree with the basic theoretical model of coherent Cooper pair pumping.     

Pumping in quantum dots and non-Abelian matrix Berry phases

We have investigated pumping in quantum dots from the perspective of non-Abelian (matrix) Berry phases by solving the time-dependent Schrödinger equation exactly for adiabatic changes. Our results demonstrate that a pumped charge is related to the presence of a finite matrix Berry phase. When consecutive adiabatic cycles are performed the pumped charge of each cycle is different from that of the previous ones.