Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角

研究了Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角, 通过理论计算得到了其表达式, 并讨论了这二者之间的半经典关系.结果表明, 这一量子Born-Oppenheimer复合系统的Berry相包含两部分: 第一部分与通常几何相的定义相同, 另一项则是由耦合造成的有效规范式引入的.这一量子修正可以被看作一个等效的Aharonov-Bohm效应.不仅如此, 其对应经典系统的Hannay角的定义中也存在类似的现象. 由此可见, 这一复合系统的Berry相与Hannay角之间也存在半经典关系, 并与文献[16] 中通常情况下的半经典关系相同.此外, 上述理论也可以运用于解决产生中性原子的人造规范势等物理问题. 关键词： Berry相 Hannay角 量子经典对应 Born-Oppenheimer近似     

Ballistic Quantum Transport: Effect of Geometrical Phases

We study the influence of nonuniform magnetic fields on the magneto conductance of mesoscopic microstructures. We show that the coupling of the electron spin to the inhomogenous field gives rise to effects of the Berry phase on ballistic quantum transport and discuss adiabaticity conditions required to observe such effects. We present numerical results for different ring geometries showing a splitting of Aharonov–Bohm conductance peaks for single rings and corresponding signatures of the geometrical phase in weak localization. The latter features can be qualitatively explained in a semiclassical approach to quantum transport.     

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice

Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson–hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.     

Berry effect in unmagnetized inhomogeneous cold plasmas

The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.     

Berry phase and Hannay’s angle in the Born–Oppenheimer hybrid systems

In this paper, we investigate the Berry phase and Hannay’s angle in the Born–Oppenheimer (BO) hybrid systems and obtain their algebraic expressions in terms of one form connection. The semiclassical relation of Berry phase and Hannay’s angle is discussed. We find that, besides the usual connection term, the Berry phase of quantum BO composite system also contains a novel term brought forth by the coupling induced effective gauge potential. This quantum modification can be viewed as an effective Aharonov–Bohm effect. Moreover, the similar phenomenon is founded in Hannay’s angle of classical BO composite system, which indicates that the Berry phase and Hannay’s angle possess the same relation as the usual one. An example is used to illustrate our theory. This scheme can be used to generate artificial gauge potentials for neutral atoms. Besides, the quantum–classical hybrid BO system is also studied to compare with the results in full quantum and full classical composite systems.     

Temperature compensation techniques for resonantly enhanced sensors and devices based on optical microcoil resonators

It is well known that environmental effects have a major influence on the optical stability of resonantly enhanced sensors and devices based on optical microfiber, namely in the configuration of a microcoil resonator. We propose a geometric design to reduce such effects by chirping the refractive index of successive paired turns in the microcoil resonator. The resistance to external effects such as temperature drifts can be considerably improved by optimizing the coupling coefficients and chirping profile, such that the wavelength span of the resonant condition is maximized without compensating its sensitivity to the desired measurand. We also demonstrate another technique based on resonant wavelength tuning using a compact piezoelectric ceramic disk measuring 3 mm in diameter and 1 mm in thickness, attaining tunability as high as 6.5 pm/100 V.     

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.     

Towards a dephasing diode: asymmetric and geometric dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.     

Geometric Phase for Optical Free Induction Decay

Geometric phase is investigated for optical free induction decay with a modified Bloch equation by establishing in connecting density matrices with nonunit vector ray in a complex projective Hilbert space. Under the limiting of pure state, our approach may give out the Berry phase and Aharonov and Anandan one. Furthermore, by comparing our approach with the kinematic one, we find that, after a suitable modification to the kinematic approach, both differences are very small for the Berry phase of mixed states in the optical free induction decay under the case of quasicyclic evolution.     

Transition of Bery Phase and Pancharatnam Phase and Phase Change

Berry Phase and time-dependent Pancharatnam phase are investigated for nuclear spin polarization in a liquid by a rotation magnetic field, where two-state mixture effect is exactly included in the geometric phases. We find that when the system of nuclear spin polarization is in the unpolarized state, the transitive phenomena of both Berry phase and Pancharatnam phase are taken place. For the polarized system, in contrast, such a transition is not taken place. It is obvious that the transitions of geometric phase correspond to the phase change of physical system.     

Non-trivial Berry phase for an asymmetric one-dimensional potential in the free electron limit

We find a non-trivial Berry phase for a finite potential, even in the delocalized-electron limit. We obtain this result for a one-dimensional, periodic sawtooth potential, though our analysis is applicable to other systems. We show that this result is due to both the periodicity of the time-independent wave function and the effects of interband degeneracies. We also find, for the sawtooth potential, that each band is uniquely characterized by its Berry phase’s functional dependence on the potential’s parameters. Thus, each band may be identified by the behavior of its Berry phase.     

Theory of electric polarization in multiorbital Mott insulators

The interaction between the electric field E and spins in multiorbital Mott insulators is studied theoretically. We find a generic coupling mechanism, which works for all crystal lattices and which does not involve relativistic effects. It couples E to the "internal" electric field e originating from the dynamical Berry phase. We discuss several effects of this interaction: (i) an unusual electron spin resonance, (ii) the displacement of spin textures in an applied electric field, and (iii) the resonant absorption of circularly polarized light by Skyrmions, magnetic bubbles, and magnetic vortices.     

Thomas rotation and polarized light: A non-abelian geometric phase in optics

We describe anon-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.     

Paraxial propagation in disclinated amorphous media

We study paraxial beam propagation along the wedge axis of a disclinated amorphous medium. The defect-induced inhomogeneity results in Berry phase and curvature that are affected by the induced uniaxial anisotropy. The Berry phase manifests itself as a precession of the polarization vector. The Berry curvature is responsible for the optical spin Hall effect in the disclinated medium, where beam deflection varies sinusoidally along the paraxial direction. Its application in determining the birefringence and the magnitude of the Frank vector is explained.     

Bistable polarization switching in mutually coupled vertical-cavity surface-emitting lasers

We theoretically investigate the polarization-resolved dynamics of two vertical-cavity surface-emitting semiconductor lasers that are mutually coupled through coherent optical injection. We find a sequence of bistable polarization switchings that can be induced by changing either the coupling strength or the optical propagation phase. The successive polarization switchings are correlated with the creation of new compoundcavity modes when these parameters are continuously varied.     

First principles calculations of magnetism, dielectric properties and spin-phonon coupling in double perovskite Bi(2)CoMnO(6)

First principles electronic structure calculations have been performed for the double perovskite Bi(2)CoMnO(6) in its non-centrosymmetric polar state using the generalized gradient approximation plus the Hubbard U approach. We find that the ferromagnetic state is more favored compared to the ferrimagnetic state with both Co and Mn in high spin states. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. The magnetic structure dependent phonon frequencies indicate the presence of a weak spin-phonon coupling. Using the Berry phase method, we obtain a spontaneous ferroelectric polarization of 5.88?μC?cm(-2), which is close to the experimental value observed for a similar compound, Bi(2)NiMnO(6).     

非线性光学超构表面

在线性光学范畴内,人们已经通过亚波长尺度的超薄超构表面成功实现了对光的众多新颖特性的调控功能.其主要理念是通过对具有亚波长尺度且空间方向变化的超构功能基元进行特定的排列,从而实现对光的偏振、相位和振幅的有效控制.近来,超构表面上的非线性光学特性也引起了大家的广泛关注.在本综述中,我们对非线性光学超构表面的设计、超构功能单元的材料和对称性选择、非线性手性光学、非线性贝里几何相位和非线性波前整形等内容进行了总结;最后对非线性光学超构表面在调控光与物质的相互作用中面临的挑战和前景进行了展望.     

Effects of the Berry phase and instantons in one-dimensional Kondo-Heisenberg model

Motivated by the global phase diagram of antiferromagnetic heavy-fermion metals, we study the Kondo effect from the perspective of a nonlinear sigma model in the one-dimensional Kondo-Heisenberg model away from half-filling. We focus on the effects of the instanton configurations of the sigma-model field and the associated Berry phase. Guided by the results derived using bosonization methods, we demonstrate that the Kondo-singlet formation is accompanied by an emergent Berry phase. This Berry phase also captures the competition between the Kondo-singlet formation and spin-Peierls correlations. Related effects are likely to be realized in Kondo lattice systems in higher dimensions.     

Ferroelectricity due to orbital ordering in E-type undoped rare-earth manganites

Aiming at understanding the origin of the electronic contribution to ferroelectric polarization in undoped manganites, we evaluate the Berry phase of orbital-polarizable Bloch electrons as an orbital ordering (OO) establishes in the background of an antiferromagnetic E-type configuration. The onset of OO is tuned by the Jahn-Teller (JT) interaction in a tight-binding model for interacting electrons moving along zigzag chains. A finite polarization is found as soon as the JT coupling is strong enough to induce OO, supporting the large electronic contribution predicted from first principles.