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 ease 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-Adiabatic Geometric Phase in a Dispersive Interaction System

We investigate the geometric phase and dynamic phase of a two-level fermionic system with dispersive interaction, driven by a quantized bosonic field which is simultaneously subjected to parametric amplification. It is found that the geometric phase is induced by a counterpart of the Stark shift. This effect is due to distinct shifts in the field frequency induced by interaction between different states （｜e〉 and ｜g〉 ） and cavity field, and a simple geometric interpretation of this phenomenon is given, which is helpful to understand the natural origin of the geometric phase.

A 9×9 Matrix Representation of Birman-Wenzl-Murakami Algebra and Berry Phase in Yang-Baxter System

We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.

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 tlme-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.

Circular Polarization Hologram Realized by Pancharatnam-Berry Phase in Microwave Frequency

Metasurfaces have shown great potential in controlling the propagation of electromagnetic waves, making them suitable for holographic beam-shaping elements. Using the principle of array synthesis, holograms have been realized in microwave frequency to manipulate electromagnetic waves to generate specific field patterns. However, current research is almost based on linear polarization and has little analysis on the circular polarization microwave hologram. Herein, we propose a circular polarization hologram realized by sub-wavelength units with self-adaptively phase profiles of electromagnetic waves. The full, continuous control of the phase is achieved by using a single structure unit based on the Pancharatnam-Berry phase. The inhomogeneity of wave-front is considered through amplitude and phase compensation which are essential to improve the quality of microwave hologram. The model achieves circular polarization hologram in microwave frequency and the clear field pattern is generated. The circular polarization hologram enriched the research field of microwave imaging, thus providing more inspirations for the development of various related techniques.

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.

Quantum Phase of a Moving Dipole and Berry’s Phase

The quantum phase of a moving dipole as it encircles an infinite line of magnetic charge,recently discovered by Wilkens(Phys.Rev.Lett.72(1994)5),is derived as a special case of Berry’s phase.

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.

Chiral current regulation and detection of Berry phase in triangular triple quantum dots

Based on the hierarchical equations of motion(HEOM)calculation,we theoretically investigate the corresponding control of a triangular triple-quantum-dots(TTQD)ring which is connected to two reservoirs.We initially demonstrate by adding bias voltage and further adjusting the coupling strength between quantum dots,the chiral current induced by bias will go through a transformation of clockwise to counterclockwise direction and an unprecedented effective Hall angle will be triggered.The transformation is very rapid,with a corresponding characteristic time of 80-200 ps.In addition,by adding a magnetic flux to compensate for the chiral current in the original system,we elucidate the relationship between the applied magnetic flux and the Berry phase,which can realize direct measurement of the chiral current and reveal the magnetoelectric coupling relationship.

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.

An ultra-wideband 2-bit coding metasurface using Pancharatnam–Berry phase for radar cross-section reduction

An ultra-wideband 2-bit coding metasurface is designed for radar cross-section(RCS) reduction. The design process is presented in detail, in which a polarization conversion metasurface(PCM) is first proposed. The proposed PCM can realize ultra-wideband circular polarization(CP) maintaining reflection. Moreover, Pancharatnam–Berry(PB) phase will be generated in the co-polarized reflection coefficient by rotating the metallic patches in its unit cells. Thus, based on the PCM, the four coding elements of a 2-bit coding metasurface are constructed using PB phase, and an ultra-wideband PB 2-bit coding metasurface is proposed according to an appropriate coding sequence. The simulated and experimental results show that the coding metasurface has obvious advantages of wideband and polarization-insensitivity. Compared to a metallic plate of the same size, it can achieve more than 10 dB RCS reduction in the frequency band from 9.8 GHz to 42.6 GHz with a relative bandwidth of 125.2% under normal incidence with arbitrary polarizations.

Non-Abelian Berry phase Factor of the Degenerate states

Suppose the degenerate states wave function of a Hamitonian operatorHis accompanied by a natural phase factor, then we can own it to the role of sometransformation generator played by some non--degenerate Hermitian operator containedin the complete set of conserved mechanical quantities. When this idea is extended tothe spece coordinated by parameters and the momentum--like operator is introduced,thenon-Abelian Berry phose factor of degenerate wave function can be easily gotter afterthe system evolves along a closed adiabatic curve.

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

基于Pancharatnam-Berry相位调控产生贝塞尔光束

提出了一种基于Pancharatnam-Berry相位设计制作的超表面平面轴棱锥透镜产生贝塞尔光束的方法.理论分析表明:由于Pancharatnam-Berry相位的自旋相关性,设计的平面轴棱锥透镜需采用左旋圆偏振光入射才能有效地产生贝塞尔光束.超表面微结构单元的旋转率与最大无衍射距离成反比,这提供了一个获得更大无衍射距离的方便的途径.最后,搭建了一套基于平面轴棱锥透镜的贝塞尔光束产生系统,实验结果与数值模拟结果一致.这些结论有助于设计制作更多新颖的基于Pancharatnam-Berry相位的平面光子学器件.

谐振子系统的量子-经典轨道、Berry相及Hannay角

从量子-经典轨道和几何相两方面,研究了二维旋转平移谐振子系统的量子-经典对应.通过广义规范变换得到了Lissajous经典周期轨道和Hannay角.另外,使用含时规范变换解析推导了旋转平移谐振子系统Schr?dinger方程的本征波函数和Berry相,得出结论:原规范中的非绝热Berry相是经典Hannay角的-n倍.最后,使用SU(2)自旋相干态叠加,构造一稳态波函数,其波函数的概率云很好地局域于经典轨道上,满足几何相位和经典轨道同时对应.

静态规范变换和Berry相因数

静态规范变换既不是么正变换也不是一种严格的规范变换，互为静态规范变换的两个动力学系统是规范不等价的，但它们绝热循回演化的Ｂｅｒｒｙ位相却存在一个非常简单的关系．

隧穿量子点分子Jaynes-cummings模型的Berry相位

为了给量子系统的几何相位调控提供建议,利用全量子理论研究了一个隧穿双量子点分子与量子化单模场相互作用系统的Berry相位,探讨了量子场平均光子数、场-量子点失谐量、隧穿能级失谐量、隧穿强度以及场-量子点线性和非线性耦合对系统几何相位的影响.数值计算结果表明,在系统本征能级反交差区域附近,可以通过调节外加在量子点分子上的电压方便地对系统的Berry相位实现高效调控,这一结论在实现量子计算方面有潜在应用价值.

高阶量子绝热近似方法和Berry相因子的性质

本文详细介绍了具有缓交参数量子体系的高阶绝热近似方法。并讨论了解的性质和相关的Berry相因子的复数性。由此,我们研究了一个有具体物理意义的例子。

高自旋粒子在旋转磁场中的演化及Berry相

对于自旋为 1/2的粒子在旋转磁场中的演化及Berry相问题 ,可用直接求解薛定谔方程的方法进行计算 ,但是用这种方法讨论高自旋粒子的演化问题时会出现数学计算上的困难 .而自旋粒子各能级之间都有一定的间隔 ,根据这个特点 ,文中用“尝试”波函数的方法求解了绝热近似下自旋粒子在旋转磁场中演化的薛定谔方程 ,得到系统的演化波函数和系统在完成一个演化周期后的Berry相 .此方法在求解高自旋问题时不会出现高阶的微分方程 。

量子Rabi模型中的Berry相的解析解

利用光子Fock态,给出量子Rabi模型的数值严格解,其结果比推广的转动波近似有很大改进.截取两个Fock态,可以给出简单明了的解析结果,在很大的耦合区间里,非常接近严格解,包含了主要的非旋波效应.我们获得Berr相的简明解析结果,与数值严格解在很大区间内吻合.