Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates

Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.     

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

<正>研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.     

Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

We study the properties of two dimensional topological spin Hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have an electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of Skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the Skyrmion gap. In the latter case the superconductor-spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.     

The excitonic insulator route through a dynamical phase transition induced by an optical pulse

We consider a dynamical phase transition induced by a short optical pulse in a system prone to thermodynamical instability. We address the case of pumping to excitons whose density contributes directly to the order parameter. To describe both thermodynamic and dynamic effects on equal footing, we adopt a view of the excitonic insulator for the phase transition and suggest a formation of the Bose condensate for the pumped excitons. The work is motivated by experiments in donor–acceptor organic compounds with a neutral- ionic phase transition coupled to the spontaneous lattice dimerization and to charge transfer excitons. The double nature of the ensemble of excitons leads to an intricate time evolution, in particular, to macroscopic quantum oscillations from the interference between the Bose condensate of excitons and the ground state of the excitonic insulator. The coupling of excitons and the order parameter also leads to self-trapping of their wave function, akin to self-focusing in optics. The locally enhanced density of excitons can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The system is stratified in domains that evolve through dynamical phase transitions and sequences of merging. The new circumstances in experiments and theory bring to life, once again, some remarkable inventions made by L.V. Keldysh.     

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.     

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

We study the exact Bloch states of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) held in an optical lattice. Under a natural condition of the symmetry between the two species, we obtain two different forms of exact solutions corresponding to different existing conditions. Then, we analytically demonstrate that (a) the average atomic number per well can enlarge the region area (consisting of instability and stability parameter regions) existing exact solutions; (b) the sizes of the instability and stability parameter regions exhibit opposite variation trend with the increase in Rabi coupling strength, and the results of different solutions are just opposite. Besides, we find that spin-orbit coupling (SOC) results in the generation of spin-motion entanglement for the Bloch states, the SOC strength and lattice depth can influence the population transfer between two BEC components, and varying the SOC strength and lattice depth can also reveal the dynamical superfluid-insulator transition from the superfluid state to the critical insulating state. These results present a feasible scheme to manipulate the stable superfluid currents, which will be useful to control quantum transport of BEC.

     

偶极相互作用对自旋轨道耦合自旋-1凝聚体中磁畴分布的影响

研究准一维简谐势阱中存在自旋轨道耦合（SOC）的自旋-1偶极玻色-爱因斯坦凝聚体,数值求解旋量Gross-Pitaevskii方程,给出磁畴的分布。计算结果表明：磁畴结构与偶极-偶极相互作用（DDIs）密切相关,随着自旋轨道耦合强度和磁化强度的增强,原来的空间对称分布被破坏,随之出现新的分布模式。     

Spin-orbit coupling, spin relaxation, and spin diffusion in organic solids

We develop a systematic approach of quantifying spin-orbit coupling (SOC) and a rigorous theory of carrier spin relaxation caused by the SOC in disordered organic solids. The SOC mixes up and down spin in the polaron states and can be characterized by an admixture parameter γ2. This mixing effects spin flips as polarons hop from one molecule to another. The spin relaxation time is τ(sf) = R2/(16γ2 D), and the spin diffusion length is L(s) = R/4|γ|, where R is the mean polaron hopping distance and D the carrier diffusion constant. The SOC in tris-(8-hydroxyquinoline) aluminum (Alq3) is particularly strong due to the orthogonal arrangement of the three ligands. The theory quantitatively explains the temperature-dependent spin diffusion in Alq3 from recent muon measurements.     

XAuBi (X=Eu, Ba)拓扑nodal chain半金属的第一性原理研究

由于在磁性材料体系中缺失时间反演对称性,导致nodal chain被破坏,所以nodal chain通常存在于非磁材料中。但是,磁性材料EuAuBi是与常规磁性材料不同。本工作以第一性原理计算为研究方法,预言了在不考虑自旋轨道相互作用时,磁性材料EuAuBi体系为新型拓扑nodal chain半金属;当考虑自旋轨道耦合时,EuAuBi会退化为外尔半金属。对于非磁材料BaAuBi来说,在不考虑自旋轨道相互作用时,它同样是一种拓扑nodal chain半金属;当考虑自旋轨道相互作用时,由于C3旋转对称性的存在,BaAuBi会退化为狄拉克半金属。在XAuBi (X=Eu, Ba)中发现nodal chain半金属,会促进对六角材料的拓扑性质研究以及开拓其新实际应用领域。     

Bose-Einstein condensation in nonequilibrium systems

The properties of quantum statistically degenerate systems of Bosons which are created by an external pump field and decay within a finite lifetime are investigated by means of a Green's function treatment. These investigations help to understand the physical properties of such condensed Bose-systems as excitons, excitonic molecules and spin aligned hydrogen atoms. As an example, recent experiments by Hulin et al. on degenerate excitons in Cu₂O are analyzed and a condensate fraction of about 5% is obtained.     

The quark condensate from K(e(4)) decays

We show that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave pipi scattering lengths. In view of this constraint, the new precision data on K(e(4)) decay allow a remarkably accurate determination of these quantities. The result confirms the hypothesis that the quark condensate is the leading order parameter.     

Cooper pairs? magnetic moment in MCFL color superconductivity

We investigate the effect of the alignment of the magnetic moments of Cooper pairs of charged quarks that form at high density in three-flavor quark matter. The high-density phase of this matter in the presence of a magnetic field is known to be the Magnetic Color-Flavor-Locked (MCFL) phase of color superconductivity. We derive the Fierz identities of the theory and show how the explicit breaking of the rotational symmetry by the uniform magnetic field opens new channels of interactions and allows the formation of a new diquark condensate. The new order parameter is a spin-1 condensate proportional to the component in the field direction of the average magnetic moment of the pairs of charged quarks. The magnitude of the spin-1 condensate becomes comparable to the larger of the two scalar gaps in the region of large fields. The existence of the spin-1 condensate is unavoidable, as in the presence of a magnetic field there is no solution of the gap equations with nonzero scalar gaps and zero magnetic moment condensate. This is consistent with the fact that the extra condensate does not break any symmetry that has not already been broken by the known MCFL gaps. The spin-1 condensate enhances the condensation energy of pairs formed by charged quarks and the magnetization of the system. We discuss the possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density.     

Spontaneous breaking of spatial and spin symmetry in spinor condensates

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously formed patterns in the longitudinal magnetization.     

Spin Josephson current in a ferromagnet/noncentrosymmetric superconductor junction

We investigate the equilibrium spin transport in a ferromagnet/noncentrosymmetric superconductor (FM/NCS) junction where the NCS has a dominant triplet order parameter and helical edge state. Based on the symmetry analysis and numerical calculation, we demonstrate that there is a nonzero spin supercurrent flowing in the junction, which stems from the exchange coupling between the FM magnetization and triplet Cooper-pair spin. It is also found that a transverse spin current other than the helical edge spin current is flowing along the interface of the junction, and its polarization is related to the longitudinal spin supercurrent. Besides, an equilibrium Hall current is also shown to flow along the junction’s interface due to the broken time-reversal symmetry from the FM.     

Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate (ψψ)fo r any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.     

金属表面Rashba自旋轨道耦合作用研究进展

自旋轨道耦合是电子自旋与轨道相互作用的桥梁, 它提供了利用外电场来调控电子的轨道运动、进而调控电子自旋状态的可能. 固体材料中有很多有趣的物理现象, 例如磁晶各向异性、自旋霍尔效应、拓扑绝缘体等, 都与自旋轨道耦合密切相关. 在表面/界面体系中, 由于结构反演不对称导致的自旋轨道耦合称为Rashba自旋轨道耦合, 它最早在半导体材料中获得研究, 并因其强度可由栅电压灵活调控而备受关注, 成为电控磁性的重要物理基础之一. 继半导体材料后, 金属表面成为具有Rashba自旋轨道耦合作用的又一主流体系. 本文以Au(111), Bi(111), Gd(0001)等为例综述了磁性与非磁性金属表面Rashba自旋轨道耦合的研究进展, 讨论了表面电势梯度、原子序数、表面态波函数的对称性, 以及表面态中轨道杂化等因素对金属表面Rashba自旋轨道耦合强度的影响. 在磁性金属表面, 同时存在Rashba自旋轨道耦合作用与磁交换作用, 通过Rashba自旋轨道耦合可能实现电场对磁性的调控. 最后, 阐述了外加电场和表面吸附等方法对金属表面Rashba自旋轨道耦合的调控. 基于密度泛函理论的第一性原理计算和角分辨光电子能谱测量是金属表面Rashba自旋轨道耦合的两大主要研究方法, 本文综述了这两方面的研究结果, 对金属表面Rashba自旋轨道耦合进行了深入全面的总结和分析.     

52Cr spinor condensate: a biaxial or uniaxial spin nematic

We show that the newly discovered 52Cr Bose condensate in zero magnetic field can be a spin nematic of the following kind: a "maximum" polar state, a "colinear" polar state, or a biaxial nematic ferromagnetic state. We also present the phase diagram with a magnetic field in the interaction subspace containing the chromium condensate. It contains many uniaxial and biaxial spin nematic phases, which often but not always break time reversal symmetry, and can exist with or without spontaneous magnetization.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

A full potential all-electron calculation on electronic structure of NiO

We perform a first principle calculation on NiO system, a prototypical correlated electronic system due to partial filled 3d electronic shell, using various density functional theory (DFT) and hybrid functional methods inclusion of spin polarization (SP), on-site Coulomb repulsion U and spin–orbit coupling (SOC) effects. It is shown that localized spin density approximation (LSDA) plus U (LSDA?+?U) correctly reproduce experimental lattice parameter, while spin polarization generalized gradient approximation (SP?+?GGA?+?U) obviously overestimates lattice parameter. LSDA?+?U/SP?+?GGA?+?U band gaps and magnetic moments are in agreement with experimental data, and correctly predict NiO to be an insulator. NiO undergoes a Mott–Hubbard metal–insulator transition (MIT) by addition of Coulomb interaction U. Our LSDA?+?SOC calculation shows that SOC further splitting of Ni d e_g and t_2g orbitals into d_z2, d_xy, d_x2y2 and d_xz?+?d_yz orbitals, and SP nearly cancels out SOC effect, giving rise to symmetry of density of states (DOS) for spin-up and spin-down states, hence appearance of zero net magnetic moment. For LSDA?+?U?+?SOC calculation, combination effect of SP, U and SOC results in non-occupying of spin-up conduction band and a negligible density of states for spin-down states.     

DOES PARISI'S SOLUTION OF THE SHERRINGTON-KIRKPATRICK MODEL LOCATE ON THE ABSOLUTEMAXIMUM OF THE FREE ENERGY?

In the spin glass phase near the critical temperature we find in aparticular replica symmetry breaking pattern an order parameter with free energy greater than that of the Parisi's.