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.     

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.     

Coreless vortex formation in a spinor Bose-Einstein condensate

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.     

Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates

We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.     

Polarized nonequilibrium Bose-Einstein condensates of spinor exciton polaritons in a magnetic field

The effect of a magnetic field on a spinor exciton-polariton condensate has been investigated. A quenching of a polariton Zeeman splitting and an elliptical polarization of the condensate have been observed at low magnetic fields B<2 T. The effects are attributed to a competition between the magnetic field induced circular polarization buildup and the spin-anisotropic polariton-polariton interaction which favors a linear polarization. The sign of the circular polarization of the condensate emission at B<3 T is negative, suggesting that a dynamic condensation in the excited spin state rather than the ground spin state takes place in this magnetic field range. From about 2T on, the Zeeman splitting opens and from then on the slope of the circular polarization degree changes its sign. For magnetic fields larger than the 3 T, the upper spin state occupation is energetically suppressed and circularly polarized condensation takes place in the ground state.     

梯度磁场中自旋-轨道耦合旋转两分量玻色-爱因斯坦凝聚体的基态研究

利用准二维Gross-Pitaevskii方程,研究了在梯度磁场中具有自旋-轨道耦合的旋转两分量玻色-爱因斯坦凝聚体的基态结构.探索了自旋-轨道耦合作用和梯度磁场对基态的影响.结果发现,在梯度磁场下,随着自旋-轨道耦合强度增大,基态结构由skyrmion格子逐渐过渡为skyrmion列.对于弱自旋-轨道耦合和小旋转频率情况,增大磁场梯度强度可导致基态由平面波相转变为half-skyrmion;对于强自旋-轨道耦合和大旋转频率情况,梯度磁场可诱导hidden涡旋的产生.梯度磁场、自旋-轨道耦合和旋转作为体系的调控参数,可用于控制不同基态相间的转化.     

Spin current in a spinor Bose-Einstein condensate induced by a gradient magnetic field

We develop a research of spin currents in a ²³Na 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.     

Beliaev theory of spinor Bose–Einstein condensates

By generalizing the Green’s function approach developed by Beliaev [S.T. Beliaev, Sov. Phys. JETP 7 (1958) 299; S.T. Beliaev, Sov. Phys. JETP 7 (1958) 289], we study effects of quantum fluctuations on the energy spectra of spin-1 spinor Bose–Einstein condensates, in particular, of a ⁸⁷Rb condensate in the presence of an external magnetic field. We find that due to quantum fluctuations, the effective mass of magnons, which characterizes the quadratic dispersion relation of spin-wave excitations, increases compared with its mean-field value. The enhancement factor turns out to be the same for two distinct quantum phases: the ferromagnetic and polar phases, and it is a function of only the gas parameter. The lifetime of magnons in a spin-1 ⁸⁷Rb spinor condensate is shown to be much longer than that of phonons due to the difference in their dispersion relations. We propose a scheme to measure the effective mass of magnons in a spinor Bose gas by utilizing the effect of magnons’ nonlinear dispersion relation on the time evolution of the distribution of transverse magnetization. This type of measurement can be applied, for example, to precision magnetometry.     

Spontaneously modulated spin textures in a dipolar spinor bose-einstein condensate

Helical spin textures in a 87Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. The formation of this modulated phase is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. The reduction of dipolar interactions by a sequence of rf pulses results in a suppression of the modulated phase, thereby confirming the role of dipolar interactions in this process. This study demonstrates the significance of magnetic dipole interactions in degenerate 87Rb F=1 spinor gases.     

由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内逐渐重合,向上和向下的凸起被拉长,最终自旋向上态在z轴上呈线状分布,这与理论分析预测得到的孤立狄拉克弦相对应.最后,通过计算凝聚体的超流涡度给出磁单极的表征图.结果显示,凝聚体在磁场的两个零点处形成正、负磁单极对,分别对应着自旋向上态在z轴上向上和向下的凸起.随着磁场的两个零点重合,正、负磁单极对中的两条狄拉克弦逐渐靠近,之后大约经5 ms,它们完全相连,最终形成孤立的狄拉克弦.     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Stable striped state in a rotating two-dimensional spin–orbit coupled spin-1/2 Bose–Einstein condensate

We consider an effective two-dimensional Bose–Einstein condensate with some spin–orbit coupling (SOC) and a rotation term in an external harmonic potential. We find the striped state, and analyze the effects of SOC, the external potential, and the rotation frequency/direction on the profile and the stability of the striped state. Without the rotation term, the two spinor components exhibit striped pattern, and the numbers of stripes in the two components are always an odd–even or an even–odd. With the increase of the SOC strength, the number of stripes in both components increases, while the difference of the striped numbers is always one. After adding the rotation term, the profiles of the spinor components change qualitatively, and the change regulation of the striped numbers differs, while the difference of the striped numbers is still one. In addition, we find that the rotation direction only makes the striped state of the two spinor components exchange each other, though the clockwise and counterclockwise rotation directions are inequivalent with the presence of SOC. Such regulation is different from the previous study. And the rotation frequency gives rise to the transition from the striped state to a mixture of the striped state and vortex state. Furthermore, we prove the stability of these states by the evolution and linear stability analysis.     

Quantum tunneling of a vortex between two pinning potentials

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.     

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.     

The non-Abelian bosonic quantum ring

We investigate the dynamics of a spinor Bose-Einstein condensate which is governed by an optically induced non-Abelian gauge potential. Using a ring shaped trap to confine the atoms and a hydrodynamic ansatz, nonlinear Josephson type equations are found to describe the system. The degenerate eigenstates which show rotation are solved exactly. We consider a homogenous filled ring and observe population dynamics between the two quasi-spin components but also space dependent Josephson oscillations. Stable mass currents can be observed which are induced by the constant non-Abelian effective magnetic field in the limit of weak interactions. For strong interactions the appearance of two-component dark soliton-like objects are observed.     

Interaction of $F=2$ Spinor Bose Condensate with Driven External Magnetic Fields

We have studied the interaction of $F=2$ spinor Bose condensate with a combination of static and sinusoidal magnetic field $b_l(t)=b_0+b\cos(\omega t)$. We find that the tunneling current among spin 0 and spin $\pm1$, spin 0 and spin $\pm2$, spin $\pm1$ and spin $\pm2$ may exhibit the incremental oscillation behavior, which depends on the field parameters of the reduced amplitudes of the transverse and the longitudinal magnetic fields respectively. This means that the dynamics spin localization can be adjusted experimentally by selecting the less values of the reduced amplitudes of the transverse magnetic field $b_x/\omega$ and those of the longitudinal magnetic field $b/\omega$.     

Topological defects and the superfluid transition of the s=1 spinor condensate in two dimensions

The s=1 spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We analyze the topological defects of the polar condensate, correcting previous studies, and show that the polar condensate in two dimensions is unstable at any finite temperature; instead, there is a nematic or paired superfluid phase with algebraic order in exp(2itheta), where theta is the superfluid phase, and no magnetic order. The Kosterlitz-Thouless transition out of this phase is driven by unbinding of half-vortices (the spin-disordered version of the combined spin and phase defects found by Zhou), and the anomalous universal 8T(c)/pi stiffness jump at the transition is confirmed in numerical simulations. The anomalous stiffness jump is a clear experimental signature of this phase and the corresponding phase transition.     

Persistent and enhanced spin-nematic squeezing in a spinor Bose-Einstein condensate

We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.     

Einstein-de Haas effect in dipolar Bose-Einstein condensates

The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a nonsingular vortex via spin-orbit interactions--a phenomenon reminiscent of the Einstein-de Haas effect in ferromagnets.