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.

Dynamical and Geometric Phases of a Two Energy-Level Bose-Einstein Condensate Interacting with a Laser Field

By using of the invariant theory, we study a two energy-level Bose-Einstein condensate interacting with a timedependent laser field, the dynamical and geometric phases are given respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.

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.

Remark on Relations Between Different Non-integrable Phases

There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.

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.

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.

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.

Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition

There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the generaltime-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.

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.

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.

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.

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.

Quantum oscillations and nontrivial transport in (Bi0.92In0.08)2Se3

Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications. Here we report the magnetotransport properties of single crystalline （Bi0.92In0.08）2Se3. The average mobility of^1000 cm2·V-1·s-1 is obtained from the Lorentz law at the low field （〈 3 T） up to 50 K. The quantum oscillations rise at a field of^5 T, revealing a high mobility of^1.4×104 cm2·V-1·s-1 at 2 K. The Dirac surface state is evident by the nontrivial Berry phase in the Landau-Fan diagram. The properties make the （Bi0.92In0.08）2Se3 a promising platform for the investigation of quantum phase transition in topological insulators.

Necessity of Integral Formalism

To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 （1974） 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 （1975） 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation （i.e., differential formalism for wave function） shall lead to vanishing Berry phase and that the Schroedinger integral equation （i.e., integral formalism for wave function）, in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion： There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.

Orbital magnetization in semiconductors

This paper theoretically investigates the orbital magnetization of electron-doped （n-type） semiconductor het-erostructures and of hole-doped （p-type） bulk semiconductors, which are respectively described by a two-dimensional electron/hole Hamiltonian with both the included Rashba spin-orbit coupling and Zeeman splitting terms. It is the Zeeman splitting, rather than the Rashba spin-orbit coupling, that destroys the time-reversal symmetry of the semiconductor systems and results in nontrivial orbital magnetization. The results show that the magnitude of the orbital magnetization per hole and the Hall conductance in the p-type bulk semiconductors are about 10^-2-10^-1 effective Bohr magneton and 10^-1-1 e^2/h, respectively. However, the orbital magnetization per electron and the Hall conductance in the n-type semiconductor heterostructures are too small to be easily observed in experiment.

Multiple bottle beams based on metasurface optical field modulation and their capture of multiple atoms

Compared to conventional devices, metasurfaces offer the advantages of being lightweight, with planarization and tuning flexibility. This provides a new way to integrate and miniaturize optical systems. In this paper, a metasurface capable of generating multiple bottle beams was designed. Based on the Pancharatnam–Berry(P–B) phase principle, the metasurface lens can accurately control the wavefront by adjusting the aspect ratio of the titanium dioxide nanopillars and the rotation angle. When irradiated by left-handed circularly polarized light with a wavelength of 632.8 nm, the optical system can produce multiple micron bottle beams. Taking two bottle beams as examples, the longitudinal full widths at half-maximum of the optical tweezers can reach 0.85 μm and 1.12 μm, respectively, and the transverse full widths at half-maximum can reach 0.46 μm and 0.6 μm. Also, the number of generated bottle beams can be varied by controlling the size of the annular obstacle. By changing the x-component of the unit rotation angle, the metasurface can also change the shape of the bottle beam - the beam cross-section can be changed from circular to elliptical. This paper also analyzes the trapping of ytterbium atoms by the multi bottle beam acting as optical tweezers. It is found that the multi bottle beam can cool and trap multiple ytterbium atoms.

New method for calculating the Berry connection in atom-molecule systems

In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.

A method for generating double-ring-shaped vector beams

We propose a method for generating double-ring-shaped vector beams. A step phase introduced by a spatial light modulator（SLM） first makes the incident laser beam have a nodal cycle. This phase is dynamic in nature because it depends on the optical length. Then a Pancharatnam–Berry phase（PBP） optical element is used to manipulate the local polarization of the optical field by modulating the geometric phase. The experimental results show that this scheme can effectively create double-ring-shaped vector beams. It provides much greater flexibility to manipulate the phase and polarization by simultaneously modulating the dynamic and the geometric phases.

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter,yet the study of topological circuits in the strongly nonlinear regime,has been lacking.We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors.Nonlinear topological interface modes arise on domain walls of the circuit lattices,whose topological phases are controlled by the amplitudes of nonlinear voltage waves.Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory.Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.

具有高阶范霍夫奇点的自选轨道耦合体系中的鲁棒拓扑超导

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities.It is also known that a nontrivial Berry phase derived from spin–orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena.However,it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities(VHSs)and the Berry phase.Here,based on a general Rashba model on the square lattice,we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis.Despite the existence of a variety of comparable fluctuations in the particle–particle and particle-hole channels associated with higher-order VHSs,we find that the chiral p±ip pairings emerge as two stable fixed trajectories within the generic interaction parameter space,namely the system becomes a robust topological superconductor.The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase.The possible experimental realization and implications are discussed.Our work sheds new light on the correlated states in quantum materials with strong spin–orbit coupling(SOC)and offers fresh insights into the exploration of topological superconductivity.