The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.     

Geometric quantum discord and Berry phase between two charge qubits coupled by a quantum transmission line

Geometric quantum discord（GQD） and Berry phase between two charge qubits coupled by a quantum transmission line are investigated. We show how GQDs evolve and investigate their dependencies on the parameters of the system.We also calculate the energy and the Berry phase and compare them with GQD, finding that there are close connections between them.     

Berry Phase of Composite System Induced by Time-Dependent Interaction

The Berry phase in a composite system induced by the time-dependent interaction is discussed. We choose two coupled spin-1/2 systems as the composite system： one of the subsystems is subjected to a static magnetic field, and the coupling parameters between two spins are controllable in time. We show that the time-dependent interaction can induce the Berry phase in a similar way as that a spin-1/2 system （qubit） is driven by an effective time-dependent magnetic field. Furthermore, using two consecutive cycles with opposite directions of both the static magnetic field as well as opposite signs of the coupling parameters, a nontrivial two-qubit unitary transformation purely based on Berry phases can be constructed.     

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.     

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.     

Non-Abelian Berry phase in a quantum mechanical environment

We investigate a quantum physical system that can be naturally separated into fast and slow moving components. A modification of the conventional molecular Born-Oppenheimer approximation is considered by taking the intermolecular position vector to be a slowlyvarying quantum mechanical parameter. It is found that the fast motion (electronic degrees of freedom) induces a non-Abelian vector potential (Berry connection) into the dynamics of the slow system (nucleus), thereby modifying the commutation relations of the slow variables.     

Optical tuning of Berry phase effect in topological insulators

We theoretically discuss the influence of driving laser field on the topological nature, one of the manifestation of the electron Berry phase effect, in two-dimensional electronic systems. Adiabatic change of the laser amplitude with circular polarization alters the “order parameter”, termed the Chern number, in topological insulator with broken time-reversal symmetry, resulting in photo-induced phase transition. The finding is an optical analog of the integer quantum Hall effect, that is triggered by the laser field instead of magnetic field. This parallelism suggests the similarity of effects to electron dynamics between circularly polarized light and magnetic field.     

Berry Phases for the L—S Coupled System in a Time—Dependent Magnetic Field

By the unitary transformation method,the instantaneous energy eigenstates of the L-S coupled system in a time-dependent magnetic field,hence the Berry phases,are calculated.     

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.     

Wave-packet dynamics of Bloch electrons—Role of Berry phase

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we reconsidered the problem of adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We showed, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics of Bloch electrons is conveniently described by a set of equations of motion (EOM) in which a non-Abelian Berry phase associated with the internal degree of freedom appears.     

均匀磁场中荷电粒子量子运动的经典对应

荷电粒子在均匀磁场中的运动是螺旋线,在垂直于磁场的平面内为圆轨道.在量子力学中,可以利用规范变换将这个经典圆轨道关系的算符形式推导出来.     

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis–Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.     

Convergence of block spins defined by a random field

We study the asymptotic behavior of families of dependent random variables called block spins, which are associated with random fields arising in statistical mechanics. We give sufficient conditions for these families to converge weakly to products of independent Gaussian random variables. We also estimate the error terms involved. In addition we give some conditions which imply that the block spins can converge weakly only to families of normal or degenerate random variables. Central to our proofs is a mixing property which is weaker than strong mixing and which holds for many random fields studied in statistical mechanics. Finally we give a simple method for determining when a stationary random field does not satisfy a strong mixing property. This method implies that the two-dimensional Ising model at the critical temperature is not strong mixing, a result obtained by a different method by M. Cassandro and G. Jona-Lasinio. The method also shows that a stationary, mean-zero, positively correlated Gaussian process indexed by is not strong mixing if its covariance function decreases liket ^– , 0 < < 1.     

Quantum phase transition in XY spin chain with three-site interaction studied in terms of Loschmidt echo and Berry phase

By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BP?s λ derivative present anomaly behaviors at the critical regions λ₁,λ₂ and λ₃. The model is in the Ferromagnetic phase as λ>λ₁=1+α and in the Spin Liquid I phase as −1+α<λ<1+α. λ₁ and λ₂ are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line λ₃ between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP.     

两网孔介观RLC耦合电路的量子化

从介观电路中经典运动方程出发,运用正则变换的方法对两网孔介观RLC耦合电路的量子化问题进行研究,结果表明其哈密顿量等价于两个独立的谐振子的哈密顿量之和.     

Synthesis of some three-qubit gates and their implementation in a three spins system coupled with Ising interaction

The synthesis of the Toffoli gate, Fredkin gate, three-qubit Inversion-on-equality gate and D(α) gate, as well as their implementation in a three spins system coupled with Ising interaction are investigated. The sequences of the control pulse and the drift process to implement these gates are given. It is revealed that the implementation of some three-qubit gates in a circular spin chain is much better than in a linear spin chain, and every two measurements of the quantum computation complexity are not always consistent. It is significant to directly study the implementation of the multi-qubit gates and even more complicated components of quantum information processing without resorting to their synthesis.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

Switching field behavior in antiparallely coupled sub-micrometer scale magnetic elements

Magnetization process and switching field of sub-micron sized elements for antiparallely coupled ferromagnetic systems (ferromagnet/nonmagnet/ferromagnet) are studied with micromagnetic simulation using Landau–Lifshiz–Gilbert equations. It is found that the switching field of the antiparallel structure of the trilayer is lower than that of the ferromagnetic single film for above aspect RATIO=2 and below WIDTH=150 nm.     

A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

Quantum characteristics of a charged particle subjected to a singular oscillator potential under an external magnetic field is investigated via SU(1,1) Lie algebraic approach together with the invariant operator and the unitary transformation methods. The system we managed is somewhat complicated since we considered not only the time-variation of the effective mass of the system but also the dependence of the external magnetic field on time in an arbitrary fashion. In this case, the system is a kind of time-dependent Hamiltonian systems which require more delicate treatment when we study it. The complete wave functions are obtained without relying on the methods of perturbation and/or approximation, and the global phases of the system are identified. To promote the understanding of our development, we applied it to a particular case, assuming that the effective mass slowly varies with time under a time-dependent magnetic field.     

Impurity bands in a magnetic field of arbitrary strength

On the basis of the self-consistentt-matrix approximation for a system of quasi free electrons interacting with randomly distributed attractive-potentials, we discuss impurity bands in the presence of a magnetic field of arbitrary strength. We compare the results with existing theoretical work on the limiting cases of weak and strong magnetic fields, which are shown to be partly incompatible, and with experimental work onn-type InSb in the magnetic freeze-out regime. Satisfactory agreement is obtained between the thermal ionisation energy, evaluated from experiments, and the calculated gap energy, separating impurity band and conduction band.