Knots in a spinor Bose-Einstein condensate

We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.     

Dynamics of Skyrmion crystals in metallic thin films

We study the collective dynamics of the Skyrmion crystal in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. It is shown that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in noncollinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the Skyrmion crystal, and discuss the effects of impurity pinning of Skyrmions.     

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.     

Universal probes of two-dimensional topological insulators: dislocation and π flux

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.     

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.     

Spin-wave modes and their intense excitation effects in Skyrmion crystals

We theoretically study spin-wave modes and their intense excitations activated by microwave magnetic fields in the Skyrmion-crystal phase of insulating magnets by numerically analyzing a two-dimensional spin model using the Landau-Lifshitz-Gilbert equation. Two peaks of spin-wave resonances with frequencies of ～1 GHz are found for in-plane ac magnetic field where distribution of the out-of-plane spin components circulates around each Skyrmion core. Directions of the circulations are opposite between these two modes, and hence the spectra exhibit a salient dependence on the circular polarization of irradiating microwave. A breathing-type mode is also found for an out-of-plane ac magnetic field. By intensively exciting these collective modes, melting of the Skyrmion crystal accompanied by a redshift of the resonant frequency is achieved within nanoseconds.     

Energetically stable particlelike skyrmions in a trapped Bose-Einstein condensate

We numerically show that a topologically nontrivial 3D Skyrmion can be energetically stable in a trapped two-component atomic Bose-Einstein condensate, for the parameters of 87Rb condensate experiments. The separate conservation of the two atomic species can stabilize the Skyrmion against shrinking to zero size, while drift of the Skyrmion due to the trap-induced density gradient can be prevented by rotation or by a laser potential.     

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.     

Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates

We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.     

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.     

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.     

Spontaneous spin textures in dipolar spinor condensates

We have mapped out a detailed phase diagram that shows the ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the interplay between the dipolar and the spin-exchange interactions induces a rich variety of quantum phases that exhibit spontaneous magnetic ordering in the form of intricate spin textures.     

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.     

Thermodynamic phase diagram of the quantum hall skyrmion system

We numerically study the interacting quantum Hall Skyrmion system based on the Chern-Simons action. By noticing that the action is invariant under global spin rotations in the spin space with respect to the magnetic field direction, we obtain the low-energy effective action for a many-Skyrmion system. Performing extensive molecular dynamics simulations, we establish the thermodynamic phase diagram for a many-Skyrmion system.     

Giant Skyrmions stabilized by dipole-dipole interactions in thin ferromagnetic films

Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivial spin texture such as a giant Skyrmion. We derive an analytic formula for the Skyrmion radius. The radius is controllable by the external magnetic field. It is intriguing that a Skyrmion may have already been observed as a magnetic domain. A salient feature is that a single Skyrmion can be created or destroyed experimentally. An analysis is made also on Skyrmions in chiral magnets.     

Vortex quantum creation and winding number scaling in a quenched spinor Bose gas

Motivated by a recent experiment, we study nonequilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and we establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.     

Topological defect formation in rotating binary dipolar Bose–Einstein condensate

We investigate the topological defects and spin structures of a rotating binary Bose–Einstein condensate, which consists of both dipolar and scalar bosonic atoms confined in spin-dependent optical lattices, for an arbitrary orientation of the dipoles with respect to their plane of motion. Our results show that the tunable dipolar interaction, especially the orientation of the dipoles, can be used to control the direction of stripe phase and its related half-vortex sheets. In addition, it can also be used to obtain a regular arrangement of various topological spin textures, such as meron, circular and cross disgyration spin structures. We point out that such topological defects and regular arrangement of spin structures arise primarily from the long-range and anisotropic nature of dipolar interaction and its competition with the spin-dependent optical lattices and rotation.     

Skyrmion burst and multiple quantum walk in thin ferromagnetic films

We propose a new type of quantum walk in thin ferromagnetic films. A giant Skyrmion collapses to a singular point in a thin ferromagnetic film, emitting spin waves, when external magnetic field is increased beyond the critical one. After the collapse the remnant is a quantum walker carrying spin S. We determine its time evolution and show the diffusion process is a continuous-time quantum walk. We also analyze an interference of two quantum walkers after two Skyrmion bursts. The system presents a new type of quantum walk for S>1/2, where a quantum walker breaks into 2S quantum walkers.     

Phase Coherence and Spin Squeezing in One-Axis Twisting Model with Decay

We investigate phase coherence and spin squeezing of a collective spin governed by one-axis twisting Hamiltonian with decay. Here we are interested in the dependence of phase coherence and spin squeezing parameter on the decay. The analytical expressions of phase coherence and spin squeezing parameter are obtained. The stronger decay can induce a stronger spin squeezing, and the squeezing can maintain a longer time interval. Moreover, more squeezing can be achieved by increasing the number of particles.     

Manipulation of Persistent Spin Helix States by Weak External Magnetic Fields

We study theoretically the effect of weak external magnetic fields on persistent spin helix states in semi- conductor two-dimensional electron gases with both Rashba and linear-in-momentum Dresselhaus spin-orbit coupling. We show that in the presence of weak external magnetic fields, some basic properties of a persistent spin helix state, including the dispersion relation between the decay time and the magnitude of the wavevector, the maximum decay time and the value of the characteristic magnitude of the wavevector at which the maximum decay time occurs, will all depend sensitively on the directions of applied external magnetic fields.