Exact soliton solutions of spinor Bose-Einstein condensates

We study matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom and present a class of exact solutions based on the inverse scattering method. The one-soliton solutions are classified with respect to the spin states. We analyze collisional effects between solitons in the same or different spin state(s), which reveals a very interesting possibility: we can manipulate the spin dynamics by controlling the parameters of colliding solitons.     

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.     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.     

Spin-orbit coupled spinor Bose-Einstein condensates

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.     

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.     

The dynamics of ring dark soliton in inhomogeneous Bose-Einstein condensates

The dynamics of the ring dark soliton in an inhomogeneous Bose-Einstein condensates (BEC) with thin disk-shaped potential trapping is investigated analytically and numerically. Analytical result shows that the ring dark soliton is governed by a variable coefficients Korteweg-de Vries (KdV) equation. The effect of the ring curvature (nonplanar geometry) and the inhomogeneous of the background on soliton amplitude and the emitted radiation profiles are obtained analytically. The theoretical results are confirmed by the direct numerical results.     

Mermin-ho vortex in ferromagnetic spinor Bose-Einstein condensates

The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along the z axis and comparing the energies of other competing non-axis-symmetric or singular vortices. The phase diagram is thereby established in a plane of the rotation drive vs the total magnetization. Their stability is also checked by calculating collective modes based on the Bogoliubov equations.     

Collective spin tunneling in spinor Bose-Einstein condensates

We investigate a novel aspect of rotational tunneling of the macroscopic spin for multicomponent spinor Bose-Einstein condensate (BEC). The Lagrangian is deduced from the multi-component BEC system formalism, and is written in terms of spin coherent states. From the effective Hamiltonian for the collective spin, the tunneling rate is obtained through a functional integral of the spin variable. It is pointed out that the cooperative effect between the Zeeman energy and the anisotropic nature of the spin-dependent inter-atomic interaction plays a key role for occurrence of collective spin tunneling.     

Spontaneous circulation in ground-state spinor dipolar Bose-Einstein condensates

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the nonlocal Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 87Rb condensate by changing the number of atoms or the trap frequency.     

Dynamics of F=2 spinor Bose-Einstein condensates

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of 10(-12) cm(3) s(-1) for spin-changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10(-13) cm(3) s(-1) for hyperfine-changing collisions. We observe polar behavior in the F=2 ground state of 87Rb, while we find the F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.     

Spontaneous macroscopic spin polarization in independent spinor Bose-Einstein condensates

We present experimental evidence for the spontaneous formation of a macroscopic spin polarization in overlapping regions of two independent Bose-Einstein condensates produced in different hyperfine states of 87Rb. The condensates are independent in the sense that we do not explicitly introduce a relative phase between them. A single "spin-tip" pulse maps the transverse spin polarization into longitudinal spin polarization, and the atomic density distributions are measured with a Stern-Gerlach imaging method. The resulting matter-wave interference patterns are anticorrelated.     

Bright soliton trains of trapped Bose-Einstein condensates

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.     

How to observe dipolar effects in spinor Bose-Einstein condensates

We propose an experiment which proves the possibility of spinning gaseous media via dipolar interactions in the spirit of the famous Einstein-de Haas effect for ferromagnets. The main idea is to utilize resonances that we find in spinor condensates of alkali atoms while these systems are placed in an oscillating magnetic field. A significant transfer of angular momentum from spin to motional degrees of freedom observed on resonance is a spectacular manifestation of dipolar effects in spinor condensates.     

Spin correlation and discrete symmetry in spinor Bose-Einstein condensates

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal 2 channel. We show that the low energy spin dynamics in the system can be mapped into an o(n) nonlinear sigma model. n = 3 at the zero magnetic field limit and n = 2 in the presence of weak magnetic fields. In an ordered phase, the ground state has a discrete Z2 symmetry and is degenerate under the group [U(1)xS(n-1)]/Z(2). We explore consequences of the discrete symmetry and propose some measurements to probe it.     

Magnons interaction of spinor Bose-Einstein condensates in an optical lattice

We study the interaction of magnons in dipolar spinor Bose-Einstein condensates in an optical lattice. By means of Holstein-Primakoff and Fourier transformations the energy spectra of the ground and the excited states is obtained analytically. Our results show that the collision of magnons is elastic which is expressed by the conservation of wave numbers in the process of collision. At last, we found that the interaction of magnons is attractive which tends to self-localization to form spin waves, i.e., a cluster of a macroscopic number of coherent magnons. Because of the attraction, the instability of spin wave brings about the existence of solitary wave.     

Weakly interacting spinor Bose–Einstein condensates with three-dimensional spin–orbit coupling

Starting from the Hamiltonian of the second quantization form, the weakly interacting Bose-Einstein condensate with spin-orbit coupling of Weyl type is investigated. It is found that the SU(2) nonsymmetric term, i.e., the spin-dependent interaction, can lift the degeneracy of the ground states with respect to the z component of the total angular momentum J_z, casting the ground condensate state into a configuration of zero J_z. This ground state density profile can also be affirmed by minimizing the full Gross-Pitaevskii energy functional. The spin texture of the zero J_z state indicates that it is a knot structure, whose fundamental group is π₃(M)？？？040305？？？？π₃(S²)=Z.     

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.     

Fractional spin-vortex states in F = 2 spinor Bose-Einstein condensates

Stable fractional vortices are numerically generated in the two-dimensional rotating $F=2$ spinor Bose-Einstein condensates. We demonstrate the existence of $\frac{1}{4}$-vortex state or $\frac{1}{2}$-vortex state in the biaxial nematic phase, and $\frac{1}{3}$-vortex state in the cyclic phase. At fast rotation a lattice of fractional vortex in the spin space emerges. Intriguingly, the integral spin-winding of the whole system does not increase with the rotation speed but equals to a simple fraction.     

Observation of hybrid soliton vortex-ring structures in Bose-Einstein condensates

We present the experimental discovery of compound structures comprising solitons and vortex rings in Bose-Einstein condensates. We examine both their creation via soliton-vortex collisions and their subsequent development, which is largely governed by the dynamics of interacting vortex rings. A theoretical model in three-dimensional cylindrical symmetry is also presented.