Manipulating atomic states via optical orbital angular-momentum

Optical orbital angular-momentum (OAM) has more complex mechanics than the spin degree of photons, and may have a broad range of application. Manipulating atomic states via OAM has become an interesting topic. In this paper, we first review the general theory of generating adiabatic gauge field in ultracold atomic systems by coupling atoms to external optical fields with OAM, and point out the applications of the generated adiabatic gauge field. Then, we review our work in this field, including the generation of macroscopic superposition of vortex-antivortex states and spin Hall effect (SHE) in cold atoms.     

Manipulating atomic states via optical orbital angular-momentum

Optical orbital angular-momentum (OAM) has more complex mechanics than the spin degree of photons, and may have a broad range of application. Manipulating atomic states via OAM has become an interesting topic. In this paper, we first review the general theory of generating adiabatic gauge field in ultracold atomic systems by coupling atoms to external optical fields with OAM, and point out the applications of the generated adiabatic gauge field. Then, we review our work in this field, including the generation of macroscopic superposition of vortex-antivortex states and spin Hall effect (SHE) in cold atoms.      

Gauge potential formulations of the spin Hall effect in graphene

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣.基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径.然而,在具有自旋轨道耦合的系统中,自旋流并不守恒.如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一.本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展.引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性.利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的白旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力.由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累.自旋霍尔效应已经在半导体和金属材料中被观察到.虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注.通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释.此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象.在能量简并点附近,自旋霍尔电导率和隧穿白旋电导率均会出现共振现象.当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应.     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣。基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径。然而,在具有自旋轨道耦合的系统中,自旋流并不守恒。如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一。本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展。引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性。利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的自旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力。由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累。自旋霍尔效应已经在半导体和金属材料中被观察到。虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注。通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释。此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象。在能量简并点附近,自旋霍尔电导率和隧穿自旋电导率均会出现共振现象。当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应。     

Quantum Spin Hall Effect in a Triple-Well Quantum Dot System

A scheme for generating a quantum spin Hall effect for an ensemble of electrons trapped in a triple-well quantum dot system is proposed. Light-induced effective spin-dependent gauge potential and gauge filed are both given in a real Gaussian pulses space. In our scheme, the spin Hall effect can be demonstrated by electronic population without spin-orbit coupled interaction in the absence of any magnetic fields.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Spinor bosonic atoms in optical lattices: symmetry breaking and fractionalization

We study superfluid and Mott insulator phases of cold spin-1 Bose atoms with antiferromagnetic interactions in an optical lattice, including a usual polar condensate phase, a condensate of singlet pairs, a crystal spin nematic phase, and a spin singlet crystal phase. We suggest a possibility of exotic fractionalized phases of spinor Bose-Einstein condensates and discuss them in the language of Z2 lattice gauge theory.     

U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics,and generalized Hall effects

We show that the non-relativistic quantum mechanics of particles with spin coupled to an electromagnetic field has a naturalU(1)×SU(2) gauge invariance. Ward identities reflecting this gauge invariance combined with an assumption of incompressibility of a system of such particles in an appropriate external field and for suitable values of the particle density permit us to determine the form of the effective action of the system as a functional of small fluctuations in the electromagnetic field, in the large-distance-, adiabatic limit. In this limit, the action is found to have a universal form. We present explicit results for two-dimensional, incompressible electron fluids and apply them to derive the equations of linear response theory, describing a variety of generalized Hall effects. Sum rules for the Hall conductivities, magnetic susceptibilities and other quantities of physical interest are found.     

Spin Hall effect and Berry phase of spinning particles

We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non-Abelian Berry gauge connection making the quantum mechanical algebra noncommutative. A generalization to any known spinning particles is possible by using the Bargmann–Wigner equation of motions. The noncommutativity of the coordinates is responsible for the topological spin transport of spinning particles similarly to the spin Hall effect in spintronic physics or the Magnus effect in optics. As an application we predict new dynamics for nonrelativistic particles in an electric field and for photons in a gravitational field.     

Berry effect in unmagnetized inhomogeneous cold plasmas

The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.     

Spin Hall effect in noncommutative coordinates

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter θ. The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and θ deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting θ different formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.     

Quantum anomalous hall effect in Hg1-yMnyTe quantum wells

The quantum Hall effect is usually observed when a two-dimensional electron gas is subjected to an external magnetic field, so that their quantum states form Landau levels. In this work we predict that a new phenomenon, the quantum anomalous Hall effect, can be realized in Hg{1-y}Mn{y}Te quantum wells, without an external magnetic field and the associated Landau levels. This effect arises purely from the spin polarization of the Mn atoms, and the quantized Hall conductance is predicted for a range of quantum well thickness and the concentration of the Mn atoms. This effect enables dissipationless charge current in spintronics devices.     

Spin and spin-valley Hall effects in a honeycomb lattice with antiferromagnetism and spin-orbit couplings

We study linear response to a longitudinal electric field on an antiferromagnetic honeycomb lattice with intrinsic and Rashba spin-orbit couplings (SOCs). It is found that the spin-valley Hall effect could emerge alone or coexist with the spin Hall effect. The spin and spin-valley Hall conductivities exhibit some peculiarities that depend on the distinct topological states of the graphene lattice. Furthermore, the spin and spin-valley Hall conductivities could be remarkably modulated by changing the Fermi level. Our findings suggest that the antiferromagnetic honeycomb lattice with SOCs is an excellent platform for potential applications of spintronics and valleytronics.     

Spin-orbit gauge and quantum spin Hall effect

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.     

Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.     

Reprint of : Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.     

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.     

Spin Hall effect induced by a gravitational field

The experiment by Collela et al. (1975) [1] evidenced in a striking manner how the gravitational field appears in quantum mechanics. Within the modern framework of gauge theories, one can ascribe such effect as due to gauge fields originated from fundamental symmetries of spacetime: local transformations of the Lorentz-Poincaré group. When this gauge principle is applied to the Dirac equation, we obtain kinematical correlations between the gravitational field and the spin of the particles. The phenomenon is similar to the spin Hall effect found in condensed matter systems, although much smaller in magnitude. Actual measurements may require highly precision interferometric techniques with spin-polarized neutrons.