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...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.展开更多
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 par...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.展开更多
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 transf...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.展开更多
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 dem...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.展开更多
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 fi...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.展开更多
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（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 s...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.展开更多
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 prop...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.展开更多
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 be...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.展开更多
We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equ...We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.展开更多
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.
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 i...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.展开更多
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...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.展开更多
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 ...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.展开更多
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 phas...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.展开更多
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...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.展开更多
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....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.展开更多
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-...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.展开更多
In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexa...In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].展开更多
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,...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.展开更多
基金Supported by National Natural Science Foundation of China under Grants No.10875026
文摘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.
基金Supported by the National Natural Science Foundation of China under Grants Nos.11075099,11047167,and 11105087
文摘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.
基金Project supported by the National Natural Science Foundation of China （Grant No 10475053）
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774418,11374363,11674317,11974348,11834014,and 21373191)the Strategic Priority Research Program of CAS(Grant Nos.XDB28000000 and XDB33000000)the Training Program of Major Research Plan of NSFC(Grant No.92165105)。
文摘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.
基金Supported by National Natural Science Foundation of China under Grant No. 10974016
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174024)the State Key Laboratory of Low-Dimensional Quantum Physics(Tsinghua University)(Grant No.KF201407)+1 种基金the Fundamental Research Funds for the Central Universities of Beihang University(Grant No.YWF-14-WLXY-017)Beijing City Youth Talent Plan
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62072378)the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JM077)the Xi’an Science and Technology Plan Project, China (Grant No. GXYD20.4)。
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11204012 and 91321103
文摘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.
基金supported in part by Department of Energy under Contract No.DE-FG02-03ER25587by Office of Naval Research under Contract No.N00014-01-1-0674by National Science Foundation grant DMS-0708026
文摘We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 10575040.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10825417)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 10574060 and the Beijing Natural Science Foundation under Grant No 1072010.
文摘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.
文摘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.
基金Project supported by the National Key Basic Research Program of China(Grant Nos.2014CB921103 and 2017YFA0206304)the National Natural Science Foundation of China(Grant Nos.U1732159 and 11274003)Collaborative Innovation Center of Solid-State Lighting and Energy-Saving Electronics,China
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60821061,60776061,10604010 and 60776063)
文摘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.
文摘In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408].
基金Project supported by the State Key Laboratory of Applied Optics(Grant No.SKLA02020001A17)。
文摘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.
