Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

Topological excitations in rotating spin–orbit-coupled spin-1 Bose–Einstein condensates with in-plane gradient magnetic field

We investigate the topological excitations of rotating spin-1 ferromagnetic Bose–Einstein condensates with spin–orbit coupling (SOC) in an in-plane quadrupole field. Such a system sustains a rich variety of exotic vortex structures due to the spinor order parameter and the interplay among in-plane quadrupole field, SOC, rotation, and interatomic interaction. For the nonrotating case, with the increase of the quadrupole field strength, the system experiences a transition from a coreless polar-core vortex with a bright soliton to a singular polar-core vortex with a density hole. Without rotation but with a fixed quadrupole field, when the SOC strength increases, the system transforms from a central Mermin–Ho vortex into a criss-crossed vortex–antivortex string lattice. For the rotating case, we give a phase diagram with respect to the quadrupole field strength and the SOC strength. It is shown that the rotating system supports four typical quantum phases: vortex necklace, diagonal vortex chain cluster, single diagonal vortex chain, and few vortex states. Furthermore, the system favors novel spin textures and skyrmion excitations including an antiskyrmion, a criss-crossed half-skyrmion–half-antiskyrmion lattice, a skyrmion-meron necklace, a symmetric half-skyrmion lattice, and an asymmetric skyrmion-meron lattice.     

Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: scenario for Cs2CuCl4

Motivated by inelastic neutron scattering data on Cs2CuCl4, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel critical spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a noncompact U(1) gauge field. This "algebraic vortex liquid" supports gapless spin excitations and universal power-law correlations in the dynamical spin structure factor which are consistent with those observed in Cs2CuCl4. We suggest future neutron scattering experiments that should help distinguish between the algebraic vortex liquid and other spin liquids and quantum critical points previously proposed in the context of Cs2CuCl4.     

具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构研究

通过虚时演化方法研究了具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构.结果发现:面内四极磁场和旋转双重作用可导致中央Mermin-Ho涡旋的产生;随着磁场梯度增强,Mermin-Ho涡旋周围环绕的涡旋趋向对称化排布;在四极磁场下,密度相互作用和自旋交换相互作用作为体系的调控参数,可以控制Mermin-Ho涡旋周围的涡旋数目;该体系自旋结构中存在双曲型meron和half-skyrmion两种拓扑结构.     

A Rotating Bose-Einstein Condensation in a Toroidal Trap

We have studied the ground state configurations of a rotating Bose-Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the
gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.     

Manipulating vortices in F=2 Bose-Einstein condensates through magnetic field and spin-orbit coupling

We investigate the vortex structures excited by Ioffe-Pritchard magnetic field and Dresselhaus-type spin-orbit coupling in F=2 ferromagnetic Bose-Einstein condensates. In the weakly interatomic interacting regime, an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero. With the combined effect of spin-orbit coupling and magnetic field, the ground state experiences a transition from polar-core vortex to Mermin-Ho vortex, in which the canonical particle current is anticlockwise. For fixed spin-orbit coupling strengths, the evolution of phase winding, magnetization, and degree of phase separation with magnetic field are studied. Additionally, with further increasing spin-orbit coupling strength, the condensate exhibits symmetrical density domains separated by radial vortex arrays. Our work paves the way to explore exotic topological excitations in high-spin systems.     

自旋轨道耦合的23Na自旋-1玻色-爱因斯坦凝聚体中的涡旋斑图的研究

利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 ²³Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词： 玻色-爱因斯坦凝聚体 自旋 涡旋     

Spin-orbit-coupled dipolar Bose-Einstein condensates

We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. By employing the linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudospin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. We show that, in addition to the stripe structures induced by the spin-orbit coupling, the magnetic dipole-dipole interaction gives rise to the vortex phase, in which a spontaneous spin vortex is formed.     

大N近似下旋量玻色-爱因斯坦凝聚的基态能级分裂

采用超越单模近似,研究了纯光学势阱中自旋s=1的旋量BEC对单模的模式偏离效应.通过对有效哈密顿量的能量泛函变分,给出了模式偏离修正因子ε,并计算了模式偏离修正因子和分裂能随凝聚体粒子数N的变化关系. 关键词： 玻色-爱因斯坦凝聚 GP泛函 单模近似     

Dzyaloshinsky-Moriya anisotropy in the spin-1/2 kagome compound ZnCu3(OH)6Cl2

We report the determination of the Dzyaloshinsky-Moriya interaction, the dominant magnetic anisotropy term in the kagome spin-1/2 compound ZnCu3(OH)6Cl2. Based on the analysis of the high-temperature electron spin resonance (ESR) spectra, we find its main component |Dz|=15(1) K to be perpendicular to the kagome planes. Through the temperature dependent ESR linewidth, we observe a building up of nearest-neighbor spin-spin correlations below approximately 150 K.     

Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein condensates

We measure spin mixing of F=1 and F=2 spinor condensates of 87Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from the F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.     

Low temperature limit of the vortex core radius and the kramer-pesch effect in NbSe2

Muon spin rotation ( &mgr;SR) has been used to measure the magnetic field distribution in the vortex state of the type-II superconductor NbSe2 ( T(c) = 7.0 K) below T = 2 K. The distribution is consistent with a highly ordered hexagonal vortex lattice with a well resolved high-field cutoff associated with the finite size of the vortex cores. The temperature dependence of the core radius is much weaker than the temperature dependence predicted from the Bogoliubov-de Gennes theory. Furthermore, the vortex radius measured by &mgr;SR near the low temperature quantum limit is about an order of magnitude larger than predicted.     

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry

We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=?/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.     

Spinor dynamics in an antiferromagnetic spin-1 condensate

We observe coherent spin oscillations in an antiferromagnetic spin-1 Bose-Einstein condensate of sodium. The variation of the spin oscillations with magnetic field shows a clear signature of nonlinearity, in agreement with theory, which also predicts anharmonic oscillations near a critical magnetic field. Measurements of the magnetic phase diagram agree with predictions made in the approximation of a single spatial mode. The oscillation period yields the best measurement to date of the sodium spin-dependent interaction coefficient, determining that the difference between the sodium spin-dependent s-wave scattering lengths a(f=2) - a(f=0) is 2.47+/-0.27 Bohr radii.     

Complex quantum gases: spinor Bose–Einstein condensates of trapped atomic vapors

We discuss the energy eigenstates, ground and spin mixing dynamics of a spin-1 spinor Bose–Einstein condensate for a dilute atomic vapor confined in an optical trap. Our results go beyond the mean field picture and are developed within a fully quantized framework.     

The spin evolution of spin-3 52Cr Bose–Einstein condensate

This paper studies theoretically the spin evolution of a Bose--Einstein condensate starting from a mixture of two or three groups of ⁵²Cr (spin-3) atoms in an optical trap. The initial state is so chosen that the condensate has total magnetization zero so that the system does not distinguish up and down. It is assumed that the system is very dilute (particle number is very small), the temperature is very low, and the frequency of the harmonic trap is large enough. In these situations, the deviation caused by the neglect of the dipole--dipole interaction and by using the single-mode approximation is reduced. A theoretical calculation beyond the mean field theory is performed and the numerical results are helpful for the evaluation of the unknown strength g0.     

Analytic relations between localizable entanglement and string correlations in spin systems

We study the relation between the recently defined localizable entanglement and generalized correlations in quantum spin systems. Differently from the current belief, the localizable entanglement is always given by the average of a generalized string. Using symmetry arguments we show that in most spin-1/2 and spin-1 systems the localizable entanglement reduces to the spin-spin or string correlations, respectively. We prove that a general class of spin-1 systems, which includes the Heisenberg model, can be used as a perfect quantum channel. These conclusions are obtained in analytic form and confirm some results found previously on numerical grounds.     

Monopole core instability and Alice rings in spinor Bose-Einstein condensates

We show how the length scale hierarchy, resulting from different interaction strengths in an optically trapped spin-1 23Na Bose-Einstein condensate, can lead to intriguing core deformations in singular topological defects. In particular, a point defect can be unstable with respect to the formation of a stable half-quantum vortex ring (an "Alice ring"), providing a realistic scheme to use dissipation as a sophisticated state engineering tool. We compute the threshold for stability of the point monopole, which is beyond the current experimental regime.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.