Geometric Phase of Two-Level Mixed State and Bloch Sphere Structure

Geometric phase of two-level mixed state is investigated by comparing our approach with kinematic one. The results show that in the kinematic one, the Berry phases emerge discontinuous points because of losing a physical contribution from one of two eigenstates of density matrix. In contrast, our approach is a smooth curve of initial angle, evolving time and decay rate because of the interference between the two eigenstates with the probability ensemble.     

Single-shot electronic optical activity interferometry: power and phase fluctuation-free measurement

We demonstrate that a single-pulse characterization of electronic optical activity-free induction decay, which carries information on both circular dichroism and optical rotatory dispersion, is experimentally feasible. Employing a self-referencing scheme, we show that a highly reliable interferometric chiroptical measurement free from power and phase fluctuations is achievable on a shot-by-shot basis.     

Modulation of optical FID and structure of absorption line due to superhyperfine interaction in ruby

Modulation of optical free induction decay (FID) and structure of R₁ absorption line due to superhyperfine interaction in ruby have been observed by using Stark-switching and Stark-sweeping techniques, respectively. The inhomogeneous broadening is effectively eliminated by a narrow optical hole burning. Frequency and phase characteristics of the FID signal have also been examined. The agreement between experimental results and theoretical calculations is quite satisfactory.     

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     

Berry phase magnification in optical microcoil resonators

We have studied the effects of the Berry phase on the linear transmission properties of optical microcoil resonators and analyzed the resonant behavior for different input polarizations and coil geometries. Contrary to previous expectations, we find that on resonance the size of the Berry phase shift can be magnified significantly, leading to a measurable polarization rotation for some geometries. Our model also considers other polarization effects including elasto-optic bend birefringence and the polarization dependent coupling coefficients, which were also previously neglected, and we still find that observable Berry phase effects persist. For example, in a three turn microcoil with a diameter of 0.2 mm, close to 100% of an initially x polarized light will be coupled into the orthogonal y polarization, due to the optical activity arising from the cumulative effects of Berry phase on resonance. More generally, the cross-polarization coupling also significantly influences the resonance extinction ratio and quality factor.     

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.     

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.     

Optical free induction decay by extracavity laser-frequency switching

In this letter we demonstrate the possibility of performing optical free induction decay by extra-cavity laser-frequency switching. The method is used to study optical dephasing of pentacene in p-terphenyl and the results are found to be consistent with those previously obtained by the intra-cavity switching technique. The prospects of extra-cavity frequency switching as a tool for studying optical dephasing on a subnanosecond time-scale and in the uv spectral range are emphasized.     

等离子体波背景下的光子Berry相位

利用光学度规将强激光脉冲激发的电子等离子体波描述为有效几何背景.借助于广义相对论中弯曲时空下的Maxwell方程组得到了探针光子在等离子体中电子等离子体波背景下(被处理为有效度规)所满足的运动方程及光子的Hamilton表达式.导出了电子等离子体波对光子Berry相位贡献的解析表达式并且对光子在真空中Berry相位的修正做了数值估算. 关键词： 电子等离子体波 等离子体 Berry相位     

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.     

Geometric Phase of Mixed States in the Resonance Fluorescence Spectrum

Berry phase of mixed state is investigated for modified Bloch equation with constant terms, which was used to explain sidebands in the spectrum of fluorescent light. The results show that for the physical phenomenon of sidebands, the Berry phases under the quasicyclic evolution exhibit as a geometric phase transition, where the transition point and region depend fully on the dynamics of population inversion and mixed degree. We find that, furthermore, the transition position is correlated to photon number. Thus the open quantum system preserves indeed a memory of its evolution in terms of the Berry phase, which may provide another clue for looking for devices of quantum memory in terms of geometric sideband approach.     

Optical vortices in low-mode fibers: III. Dislocation reactions, phase transitions, and topological birefringence

Topological birefringence of waves in optical fibers resulting from the spin-orbit interaction in the field of optical vortices is manifested, as a rule, in the form of Rytov-Magnus unified optical effect. At the same time, the field transformations caused by this effect are not explicitly related to the evolution of phase dislocations of longitudinal and transverse components of the electric and the magnetic fields. This relation can be provided by the dislocation reactions proposed by Berry. As opposed to the Berry’s approach, where dislocation reactions at the wavefront surface are considered, it is suggested in this work that topological reactions at the specific characteristic surface of the wave field formed by the coordinate representation of the transverse components of the Poynting vector be considered. Using the action of topological birefringence in a low-mode optical fiber as an example, it is shown that the course of a topological reaction in a vector optical field is accompanied by rigorous conservation of the total topological index of the characteristic surface and does not depend on the presence of an interface (where topological charges can originate and annihilate). The total topological index of a dislocation reaction is found to be equal to the absolute value of the sum of the topological charge and the spirality of the vector wave field.     

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.     

Geometric Phase Based Circular Array for Multimode Vortex Beam Generation

A geometric phase model for electromagnetic radiating elements is proposed. By rotation of the radiating element, a frequency‐independent geometric phase occurs for circularly polarized components of radiation field along every direction in far field. In addition, the geometric phase is equal to the rotation angle for a circularly polarized source, which enables phase modulation ranging from 0 to 2π. In contrast, the Pancharatnam–Berry phase for circular polarization conversion components brought by optical element rotation is twice the rotation angle and is applicable only for the scattering waves propagating along the rotation axis. As a proof of principle, an antenna array is designed and fabricated in microwave regime to verify the phase modulation approach. Both the calculated and measured results verify that three different orbital angular momentum modes are generated simultaneously at 8.5 GHz and 11.5 GHz.     

Pulsed optically detected NMR of single GaAs/AlGaAs quantum wells

While nuclear magnetic resonance (NMR) is one of the most important experimental tools for the analysis of bulk materials, the low sensitivity of conventional NMR makes it unsuitable for the investigation of small structures. We introduce an experimental scheme that makes NMR spectra of single, nanometer-sized quantum wells possible with excellent sensitivity and selectivity while avoiding the spectral broadening associated with some alternative techniques. The scheme combines optical pumping and pulsed radiofrequency excitation of the nuclei with time-resolved detection of the free induction decay through the polarization of the photoluminescence.     

DIGITAL QUADRATURE DETECTION IN HIGH FIELD NMR

在核磁共振中,常规的正交检测技术采用两路相敏检波.因为两路相检波的相位和幅度存在不平衡而引起谱失真,所以必须用相位循环来消除.这增加了实验时间.本文提出并在MSL-300 NMR谱仪上实现了一种数字正交检波方法.这种方法使用单路相检波,避免了两路不平衡而引起的谱线失真,因此不需要相位循环技术.     

Berry phase in a composite system

The Berry phase in a composite system with one driven subsystem has been studied in this Letter. We choose two coupled spin-1 / 2 systems as the composite system; one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and the relation between the Berry phases of the composite system and those of its subsystems.     

掺Er^3＋石英光纤中的共振增强受激四光子混频

首次实验观察到在1064nm激光泵浦下掺Er~(3+)石英光纤中的共振增强受激四光子混频现象和光学自由感应衰减过程.在频域和时域上实验证明了Er~(3+)的~4I_(11/2)激发态能级对受激四光子混频产生的反斯托克斯谱线的增强效应.     

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

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 studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a non-Abelian gauge field associated with a geometric Berry phase.

Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields non-Abelian.

For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal (T) and space inversion (I). The result of these analyses was summarized as a set of cancellation rules. We also introduced the concept of parity polarization current, which may embody the physics of orbital current. Together with charge/spin Hall/polarization currents, this type of orbital current is expected to be a potential probe for detecting and controlling Berry phase.