Dynamics of Spin-2 Bose-Einstein Condensates

We numerically simulate the dynamics of a spin-2 Bose-Einstein condensate. We find that the initial phase plays an important role in the spin component oscillations. The spin mixing processes can fully cancel out due to quantum interference when taking some initial special phase. In all the spin mixing processes, the total spin is conversed. When the initial population is mainly occupied by a component with the maximal or minimal magnetic quantum number, the oscillations of spin components cannot happen due to the total spin conversation. The presence of quadratic Zeeman energy terms suppresses some spin mixing processes so that the oscillations of spin components are suppressed in some initial spin configuration. However, the linear Zeeman energy terms have no effects on the spin mixing processes.     

Fragmented and single condensate ground states of spin-1 bose Gas

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order N) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.     

Strong quantum spin correlations observed in atomic spin mixing

We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of -7 dB (-10 dB corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of 100 μs.     

Anderson localization of a spin-orbit coupled Bose-Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin-orbit coupled Bose-Einstein condensate expanding in a speckle disorder potential by employing the Gross-Pitaevskii equation. Localization properties of a spin-orbit coupled Bose-Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose-Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose-Einstein condensate will experience spin relaxation in disorder potential.     

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.     

Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Schr odinger equations with the variational method and the imaginary time evolution method,fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength.The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.     

Observation of topologically stable 2D Skyrmions in an antiferromagnetic spinor Bose-Einstein condensate

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.     

Polar-Core Spin Vortex of Quasi-2D Spin-2 Condensate in a Flat-Bottomed Optical Trap

Motivated by the recent experiments realized in a flat-bottomed optical trap [Science 347(2015) 167;Nat. Commun. 6(2015) 6162], we study the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a homogeneous trap plus a weak magnetic field. The exact spatial distribution of local spin is obtained and the vortex core are observed to decrease with the growth of the effective spin-spin interaction. For the larger effective spin-spin interaction, the spatial distribution of spin magnitude in spin-2 condensate we obtained agrees well with that of spin-1 condensate in a homogeneous trap, where a polar-core spin vortex was schematically demonstrated as a fully-magnetized planar spin texture with a zero-spin core. The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap, simultaneously. Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.     

Excitonic condensation under spin-orbit coupling and BEC-BCS crossover

The condensation of electron-hole pairs is studied at zero temperature and in the presence of a weak spin-orbit coupling (SOC) in coupled quantum wells. Under realistic conditions, a perturbative SOC can have observable effects in the order parameter of the condensate. First, the fermion exchange symmetry is absent. As a result, the condensate spin has no definite parity. Additionally, the excitonic SOC breaks the rotational symmetry yielding a complex order parameter in an unconventional way; i.e., the phase pattern of the order parameter is a function of the condensate density. This is manifested through finite off-diagonal components of the static spin susceptibility, suggesting a new experimental method to confirm an excitonic condensate.     

Radiative dark–bright instability and the critical Casimir effect in DQW exciton condensates

It is already well known that radiative interband interaction in the excitonic normal liquid in semiconducting double quantum wells is responsible for a negligible splitting between the energies of the dark and bright excitons enabling us to consider a four fold spin degeneracy. This has also lead many workers to naively consider the same degeneracy in studying the condensate. On the other hand, the non-perturbative aspects of this interaction in the condensed phase, e.g. its consequences on the order parameter and the dark–bright mixture in the ground state have not been explored. In this work, we demonstrate that the ground state concentrations of the dark and the bright exciton condensates are dramatically different beyond a sharp interband coupling threshold where the contribution of the bright component in the ground state vanishes. This shows that the effect of the radiative interband interaction on the condensate is nonperturbative.We also observe in the free energy a discontinuous derivative with respect to the layer separation at the entrance to the condensed phase, indicating a strong critical Casimir force. An estimate of its strength shows that it is measurable. Measuring the Casimir force is challenging, but at the same time it has a conclusive power about the presence of the long sought for condensed phase.     

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.     

New non-Goldstone collective mode of BEC of magnons in superfluid 3He-B

Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.     

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     

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.     

Influence of External Magnetic Fields on Tunneling of Spin-1 Bose Condensate

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.     

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.     

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.     

Superfluid bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He

One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.