An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for...An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.展开更多
We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two indepen...We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan(CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.展开更多
The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived t...The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived through the sense, the spinor method directly converges tracking error in the planning. It promotes the dynamic accuracy of trace operation. It is also suitable to the exerciser with redundant freedom.展开更多
We investigate the internal dynamics of the spinor Bose-Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always...We investigate the internal dynamics of the spinor Bose-Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along a specific orbital in the phase space of （no, O） and display three kinds of dynamical properties including Josephson-like oscil- lation, self-trapping-like oscillation, and ＇running phase＇. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-（-1） dissipate at different rates, the magnetization m will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the ohase soace of （nn, θ, m）.展开更多
We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate（BEC） in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain st...We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate（BEC） in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.展开更多
Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,ea...Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.展开更多
In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST cha...In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.展开更多
The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex soluti...The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.展开更多
We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interac...We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly,it yields the momentum spectrum of the emitted photons and the photon-photon correlations.展开更多
We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demo...We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our resuRs reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.展开更多
Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. Th...Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.展开更多
In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose-Einstein condensates. It is found that there exists the sub-Poissonlan distributions for spin-1 and spin-（-...In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose-Einstein condensates. It is found that there exists the sub-Poissonlan distributions for spin-1 and spin-（-1） components, respectively. There may exist the violation of the Cauchy-Schwartz inequality. For the same atomic numbers, the regions that include violation of the Cauchy-Schwartz inequality will shift rightwards with the increment of the Rabi frequency, whereas for the same Rabi frequency, the regions will shift leftwards with the increment of the atomic numbers.展开更多
We consider two-dimensional spinor F=1 Bose-Einstein condensates in two types of radially-periodic potentials with spin-orbit coupling,i.e.,spin-independent and spin-dependent radially-periodic potentials.For the Bose...We consider two-dimensional spinor F=1 Bose-Einstein condensates in two types of radially-periodic potentials with spin-orbit coupling,i.e.,spin-independent and spin-dependent radially-periodic potentials.For the Bose-Einstein condensates in a spin-independent radially-periodic potential,the density of each component exhibits the periodic density modulation along the azimuthal direction,which realizes the necklacelike state in the ferromagnetic Bose-Einstein condensates.As the spin-exchange interaction increases,the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose-Einstein condensates with larger spin-orbit coupling.The competition of the spin-dependent radially-periodic potential,spin-orbit coupling,and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose-Einstein condensates in a spin-dependent radially-periodic potential.展开更多
In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ...In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.展开更多
A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler meth...A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler method more concise and efficient.A reference system is formed with respect to the mass center of the arms of robot, which simplifies the calculation of inertial lensor and mass center acceleration.And further reduces work load in calculation, and thus ensures a fast real-timecalculation.展开更多
We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder(BHL).For unbiased BHL,we find superfluid(SF)phase and integer fi...We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder(BHL).For unbiased BHL,we find superfluid(SF)phase and integer filling Mott insulator(Int MI)phase.For biased BHL,in addition to the SF and Int MI phases,there appears half-integer filling Mott insulator(HInt MI)phase.The phase transition between the SF and Int MI phases can be first order at a part of phase boundaries,while the phase transition between the SF and HInt MI phases is always second order.By tuning the bias energy,we report on the change of the nature of SF-MI phase transitions.Furthermore,we study the effect of the spin-dependent interaction on the many-body population dynamics.The spin-dependent interaction can lead to rich dynamical behaviors,but does not influence the particle transfer efficiency.Our results indicate a way to tune the nature of the SF-MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.展开更多
We develop a research of spin currents in a^(23)Na spinor Bose–Einstein condensate(BEC)by applying a magnetic field gradient.The spin current is successfully induced by the spin-dependent force arising from the magne...We develop a research of spin currents in a^(23)Na spinor Bose–Einstein condensate(BEC)by applying a magnetic field gradient.The spin current is successfully induced by the spin-dependent force arising from the magnetic field gradient.The dynamics of the spin components under the magnetic force is investigated.The study is promising to be extended to produce a longer spin-coherence and to enhance the sensitivity of the spin-mixing interferometry in a spinor BEC.展开更多
基金supported by National Natural Science Foundation of China under Grant No.10474022
文摘An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.
基金Supported by the National Natural Science Foundation of China under Grant No.11475016by the Scientific Research Foundation for Returned Scholars,Ministry of Education of China
文摘We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan(CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.
文摘The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived through the sense, the spinor method directly converges tracking error in the planning. It promotes the dynamic accuracy of trace operation. It is also suitable to the exerciser with redundant freedom.
基金supported by the National Natural Science Foundation of China(Grant No.11004007)the Fundamental Research Funds for the Central Universities of China
文摘We investigate the internal dynamics of the spinor Bose-Einstein condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along a specific orbital in the phase space of （no, O） and display three kinds of dynamical properties including Josephson-like oscil- lation, self-trapping-like oscillation, and ＇running phase＇. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-（-1） dissipate at different rates, the magnetization m will not conserve and the system transits between different dynamical regions. The dynamical properties can be exhibited in the ohase soace of （nn, θ, m）.
基金Project supported by the National Natural Science Foundation of China(Grant No.11104217)the Natural Science Foundation of Shaanxi Province,China(Grant No.2014JQ1022)the Youth Foundation of XUPT,China(Grant No.ZL2013-36)
文摘We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate（BEC） in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.
基金Supported partially by National Key Research and Development Project(2020YFA0712300)。
文摘Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.
基金The project supported by National Natural Science Foundation of China under Grant No. 10275030. It is a pleasure to thank Prof. Y.S. Duan and Dr. H. Wei for useful discussions. We have also made extensive use of a Mathematica package for calculating 0PEs, written by Prof. K. Thielemans.
文摘In this paper, we investigate the spinor field realizations of the W2,4 algebra, making use of the fact that the W2,4 algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical W2,4 string were built with these realizations.
基金Project supported by the Beijing Natural Science Foundation, China (Grand No. 1182009)the National Natural Science Foundation of China (Grant No. 11471182).
文摘The three-component Gross–Pitaevskii equation with an angular momentum rotational term can be served as a model to study spinor Bose–Einstein condensates (BECs) with time–space modulated interactions. Vortex solutions of the spinor BECs with spatiotemporally modulated interactions are worked out by similarity transformation. Theoretical analysis and numerical simulation of vortex states are demonstrated. Stable vortex states are obtained by adjusting the frequency of the external potential and the spatiotemporally modulated interaction.
基金Supported by National Natural Science Foundation of China under Grant Nos.11434011,11674334,11421063,and 11674393National Key Basic Research Special Foundation of China under Grant No.2012CB922104+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant Nos.16XNLQ03 and 17XNH054
文摘We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly,it yields the momentum spectrum of the emitted photons and the photon-photon correlations.
基金Supported by the National Natural Science Foundation of China under Grant No.11274095the Program of USTITSPHP under Grant No.13IRTSTHN016
文摘We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our resuRs reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 11274378 and 10404037
文摘Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.
基金The project supported partly by the Natural Science Foundation of Shandong Province of China under Grant No. Y2003A02
文摘In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose-Einstein condensates. It is found that there exists the sub-Poissonlan distributions for spin-1 and spin-（-1） components, respectively. There may exist the violation of the Cauchy-Schwartz inequality. For the same atomic numbers, the regions that include violation of the Cauchy-Schwartz inequality will shift rightwards with the increment of the Rabi frequency, whereas for the same Rabi frequency, the regions will shift leftwards with the increment of the atomic numbers.
基金supported by the National Natural Science of China(Grant Nos.11904242 and 12004264)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2019210280 and A2019210124)。
文摘We consider two-dimensional spinor F=1 Bose-Einstein condensates in two types of radially-periodic potentials with spin-orbit coupling,i.e.,spin-independent and spin-dependent radially-periodic potentials.For the Bose-Einstein condensates in a spin-independent radially-periodic potential,the density of each component exhibits the periodic density modulation along the azimuthal direction,which realizes the necklacelike state in the ferromagnetic Bose-Einstein condensates.As the spin-exchange interaction increases,the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose-Einstein condensates with larger spin-orbit coupling.The competition of the spin-dependent radially-periodic potential,spin-orbit coupling,and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose-Einstein condensates in a spin-dependent radially-periodic potential.
文摘In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.
文摘A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler method more concise and efficient.A reference system is formed with respect to the mass center of the arms of robot, which simplifies the calculation of inertial lensor and mass center acceleration.And further reduces work load in calculation, and thus ensures a fast real-timecalculation.
基金Project supported by the Key-Area Research and Development Program of Guang Dong Province,China(Grant No.2019B030330001)the National Natural Science Foundation of China(Grant Nos.11874434 and 11574405)+1 种基金the Science and Technology Program of Guangzhou,China(Grant No.201904020024)the Guangzhou Science and Technology Projects(Grant No.202002030459)。
文摘We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose-Hubbard ladder(BHL).For unbiased BHL,we find superfluid(SF)phase and integer filling Mott insulator(Int MI)phase.For biased BHL,in addition to the SF and Int MI phases,there appears half-integer filling Mott insulator(HInt MI)phase.The phase transition between the SF and Int MI phases can be first order at a part of phase boundaries,while the phase transition between the SF and HInt MI phases is always second order.By tuning the bias energy,we report on the change of the nature of SF-MI phase transitions.Furthermore,we study the effect of the spin-dependent interaction on the many-body population dynamics.The spin-dependent interaction can lead to rich dynamical behaviors,but does not influence the particle transfer efficiency.Our results indicate a way to tune the nature of the SF-MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFA0304203)the National Natural Science Foundation of China(Grant Nos.62020106014,62175140,61901249,92165106,12104276,and 62011530047)+4 种基金PCSIRT(Grant No.IRT17R70)the Educational Reform and Innovation Project of Higher Education in Shanxi Province,China(Grant Nos.Z20220001 and Z20220013)111 Project(Grant No.D18001)the Applied Basic Research Project of Shanxi Province(Grant Nos.201901D211191 and 201901D211188)the Shanxi 1331 KSC。
文摘We develop a research of spin currents in a^(23)Na spinor Bose–Einstein condensate(BEC)by applying a magnetic field gradient.The spin current is successfully induced by the spin-dependent force arising from the magnetic field gradient.The dynamics of the spin components under the magnetic force is investigated.The study is promising to be extended to produce a longer spin-coherence and to enhance the sensitivity of the spin-mixing interferometry in a spinor BEC.
