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.     

Berry's Phases of the Alkali Atom in a SlowlyChanging Strong Magnetic Field and Non-Adiabatic Transition

In this paper the high-order adiabatic approximation (HOAA) method is formulated in a new form ko that the calculation is greatly simplified. using this improved HOAA method, we study the Berry phase effects of the Alkali atom in a slowly-changing strong magnetic field and also the non-adiabatic transitions between the instantaneous angular momentum states. The possible observability is also pointed out.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

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.     

动边界量子含时谐振子系统的Lewis-Riesenfeld相位与Berry相位

根据Lewis-Riesenfeld的量子不变量理论,计算了一维动壁无限深势阱内频率随时间变化的谐振子的Lewis-Riesenfeld相位,发现刘登云文中“非绝热Berry相位”与Lewis-Riesenfeld相位中的几何部分完全一致.也许更为重要的是,证明了至少对于做正弦振动的边界,在绝热近似下,该系统不存在非零的Berry相位. 关键词： Berry相位 Lewis-Riesenfeld相位 量子不变量 动边界     

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.     

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.     

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.     

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.     

Landau electron in a rotating environment: A general factorization of time evolution

For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.     

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.     

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     

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.     

Aharonov-Anandan Phase and Superadiabatic Approximaton

In this paper, the exact evolving state for a two-level quantum system is found by making use of the Lewis-Riesenfeld invariant theory. In principle, the correction to an arbitrary order in the adiabatic approximation parameter c can be obtained from this exact evolving state. To the n-th order in ∈, it is shown that the exact evolving state reduces to the superadiabatic basis introduced by Berry recently. The Aharonov-Anandan phase and its adiabatic limit (Berry phase for the system) are also calculated. e for the system) are also calculated.     

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：     

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.     

Non-adiabatic geometric phases and dephasing in an open quantum system

We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of both weak short-correlated noise and slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit.     

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.     

Low energy position-hydrogen scattering

The positron-hydrogen scattering problem has been investigated using an integral approach at low incident positron energies. The effects of adiabatic and non-adiabatic potentials in both the direct and the rearrangement channels have been considered. The present values of the elastic S-wave phase shifts are found to be in reasonable agreement with the exact results.     

Born-oppenheimer revisited

An algebraic approach to solving degenerate perturbation theory is exhibited. This approach is used to solve the canonical Berry phase problem in the Born-Oppenheimer approximation, as well as the analogous classical problem. The show variables need not commute. Non-abelian phases and field theory anomalies are treated as examples. A non-adiabatic extension is suggested.