We develop a symmetry classification scheme to find ground states of pseudo spin-1/2, spin-1, and spin-2 spin-orbit coupled spinor Bose-Einstein condensates, and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential, examples include two different kagaome lattices for pseudo spin-1/2 condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo spin-1/2 system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a micro-condensate.
By studying the zero-temperature and nonzero-temperature phase diagrams of the ferromagnetic spin-1 Bose-Hubbard model under an external magnetic field, we find that the competition between ferromagnetism and the quadratic Zeeman energy yields two superfluid phases, which feature discontinuous first-order phase transitions between them for a strongly spinor Bose gas such as ${}^7$Li, contrary to the corresponding continuum system.
We establish a theoretical correspondence between spin-one antiferromagnetic spinor condensates in an external magnetic field and quantum rotor models in an external potential. We show that the rotor model provides a conceptually clear picture of the possible phases and dynamical regimes of the antiferromagnetic condensate. We also show that this mapping simplifies calculations of the condensate's spectrum and wavefunctions. We use the rotor mapping to describe the different dynamical regimes recently observed in $^{23}$Na condensates. We also suggest a way to experimentally observe quantum me…
We experimentally study two quantum phase transitions in a sodium spinor condensate immersed in a microwave dressing field. We also demonstrate that many previously unexplored regions in the phase diagram of spinor condensates can be investigated by adiabatically tuning the microwave field across one of the two quantum phase transitions. This method overcomes two major experimental challenges associated with some widely used methods, and is applicable to other atomic species. Agreements between our data and the mean-field theory for spinor Bose gases are also discussed.
We apply the number-conserving Bogoliubov theory to spinor Bose-Einstein condensates and show that the Goldstone magnon leads instability leading to fragmentation. Unlike the dynamical instability, where modes with complex eigenfrequencies grow exponentially, here the zero-energy mode exhibits algebraic growth. We also point out that a small fraction of thermally excited atoms enhances the fragmentation dynamics.
The spinor dynamics of Bose-Einstein condensates of 87Rb atoms with hyperfine spins 1 and 2 were investigated. A technique of simultaneous Ramsey interferometry was developed for individual control of the vectors of two spins with almost the same Zeeman splittings. The mixture of spinor condensates is generated in the transversely polarized spin-1 and the longitudinally polarized spin-2 states. The time evolution of the spin-1 condensate exhibits dephasing and rephasing of the Larmor precession due to the interaction with the spin-2 condensate. The scattering lengths between spin-1 and -2 atom…
We experimentally demonstrate that combining a cubic optical lattice with a spinor Bose-Einstein condensate substantially relaxes three strict constraints and brings spin singlets of ultracold spin-1 atoms into experimentally accessible regions. About 80 percent of atoms in the lattice-confined spin-1 spinor condensate are found to form spin singlets, immediately after the atoms cross first-order superfluid to Mott-insulator phase transitions in a microwave dressing field. A phenomenological model is also introduced to well describe our observations without adjustable parameters.
An overview on the physics of spinor and dipolar Bose-Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor-dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent de…
We study periodic crystalline spin textures in spinor condensates with dipolar interactions via a systematic symmetry analysis of the low-energy effective theory. By considering symmetry operations which combine real and spin space operations, we classify symmetry groups consistent with non-trivial experimental and theoretical constraints. Minimizing the energy within each symmetry class allows us to explore possible ground states.
Using effective field theories dictated by the symmetry of the system, as well as microscopic considerations, we map out the magnetic coupling-temperature phase diagrams of spin-1 Bose gases in both two- and three-dimensions. We also determine the nature of all phase boundaries, and critical properties in the case of 2nd order phase transitions at both zero and finite temperatures.
We study the uniform solutions to the one-dimensional spinor Bose-Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the gauge-spin symmetry. Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional spinor condensates.
We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behaviour over a wide parameter regime using numerical calculations specialised to the case of a spinor condensate confined to be quasi-two…
We present an exact solution to the stationary coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. The solitonic solution is a twisted half-skyrmion in the three-dimension (3D) space. By making a map from and the Cartesian coordinates to the toroidal coordinates, we demonstrate it is a linked half-unknot with a fractional Hopf charge.
We implement full polarization tomography on the photon correlations in a spinor exciton-polariton condensate. Our measurements reveal condensate pseudospin mean-field dynamics spanning from stochastic switching between linear polarization components, limit cycles, and stable fixed points, and their intrinsic relation to the condensate photon statistics. We optically harness the cavity birefringence, polariton interactions, and the optical orientation of the photoexcited exciton background to engineer photon statistics with precise control. Our results demonstrate a smooth transition from a hi…
We study the spontaneous spin textures induced by magnetic dipole-dipole interaction in ferromagnetic spinor condensates under various trap geometries. At the mean-field level, we show the system is dual to a Dirac string gas with a negative string tension in which the ground state spin texture can be easily determined. We find that three-dimensional condensates prefer a meron-like vortex texture, quasi one-dimensional condensates prefer the axially polarized flare texture, while condensates in quasi two dimensions exhibit either a meron texture or an in-plane polarized texture.
An inequality for spin-$F$ Bose-Einstein condensates (BECs) $ F^2(ρ^2-|Θ|^2)-\boldsymbol{M}^2\ge0 $ is reported, where $ρ$, $Θ$, and $\boldsymbol{M}$ represent the density, singlet pair amplitude, and magnetization vector, respectively. The distribution of high-symmetry spinors in the allowed region by the inequality is elucidated with using the Majorana representation. The result is illustrated by the example of spin-2 BECs.
We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of $F=1$ spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the po…
We present a derivation of the low energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate, for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet, for which the low energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas.
We propose a method to analytically solve the one-dimensional coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. In a uniform external potential, the Hamiltonian comprises the kinetic energy, the linear and the quadratic Zeeman energies. Several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates. These solutions are general that contain neither approximations nor constraints on the system parameters.
We study the low-energy effective theory of spinor condensate ferromagnets for the superfluid velocity and magnetization degrees of freedom. This effective theory describes the competition between spin stiffness and a long-ranged interaction between skyrmions, topological objects familiar from the theory of ordinary ferromagnets. We find exact solutions to the non-linear equations of motion describing neutral configurations of skyrmions and anti-skyrmions. These analytical solutions provide a simple physical picture for the origin of crystalline magnetic order in spinor condensate ferromagnets…
We theoretically and numerically study spin-wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates, finding direct and inverse cascades with power-law behavior. To derive these power exponents analytically, the conventional weak wave turbulence theory is applied to the spin-1 spinor Gross-Pitaevskii equation. Thus, we obtain the $-7/3$ and $-5/3$ power laws in the transverse spin correlation function for the direct and inverse cascades, respectively. To confirm these power laws, numerical calculations are performed that obtain results consistent with these power laws.
Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.
We theoretically and numerically investigate the generation of fractional-charge vortex dipoles in spinor condensates with non-zero magnetization. We find that in the antiferromagnetic phase of spin-1 and spin-2 and the cyclic phase of spin-2 condensate with non-zero magnetization coupling of the density (phonon) and a spin-excitation mode results in two critical speeds for vortex-antivortex pair creation in the condensate. As a result, a Gaussian obstacle potential moving across the antiferromagnetic spin-1 or spin-2 and cyclic spin-2 spinor condensates with non-zero magnetization can lead to…
Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximating model by replacing the optical lattice with a Harmonic trap, we demonstrate the physical origination of these two families. For a large negative quadratic Zeeman shift, we also find…
We study numerically the spin turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates (BECs). Spin turbulence (ST) is characterized by a -7/3 power law in the spectrum of the spin-dependent interaction energy. The direction of the spin density vector is spatially disordered but temporally frozen in ST, showing some analogy with the spin glass state. Thus, we introduce the order parameter of spin glass into ST in spinor BECs. When ST develops through some instability, the order parameter grows with a -7/3 power law, thus succeeding in describing ST well.
We experimentally demonstrate that spin dynamics and the phase diagram of spinor condensates can be conveniently tuned by a two-dimensional optical lattice. Spin population oscillations and a lattice-tuned separatrix in phase space are observed in every lattice where a substantial superfluid fraction exists. In a sufficiently deep lattice, we observe a phase transition from a longitudinal polar phase to a broken-axisymmetry phase in steady states of lattice-confined spinor condensates. The steady states are found to depend sigmoidally on the lattice depth and exponentially on the magnetic fiel…
We study the thermal activation of spin fluctuations in dynamically-stable spinor Bose-Einstein condensates. We analyze the specific cases of a non-dipolar spin-1 condensate in m = 0, where thermal activation results from spin-changing collisions, and of a Chromium condensate in the maximally stretched state m = -3, where thermal spin fluctuations are due to dipole-induced spin- relaxation. In both cases, we show that the low energy associated to the spinor physics may be employed for thermometry purposes down to extremely low temperatures, typically impossible to measure in BECs with usual th…
The response of spinor Bose-Einstein condensates to dynamical modulation of magnetic fields is discussed with linear response theory. As an experimentally measurable quantity, the energy absorption rate (EAR) is considered, and the response function is found to access quadratic spin correlations which come from the perturbation of the quadratic Zeeman term. By applying our formalism to spin-1 condensates, we demonstrate that the EAR spectrum as a function of the modulation frequency is able to characterize the different magnetically ordered phases.
We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of a cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds a new dimension to the study of spinor condensates both within and beyond the single-mode approximation. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down …
We study the effects of an on-site disorder potential in a gas of spinor (spin-1) ultracold atoms loaded in an optical lattice corresponding to both ferromagnetic and antiferromagnetic spin dependent interactions. Starting with a disordered spinor Bose-Hubbard model (SBHM) on a two dimensional square lattice, we observe the appearance of a Bose glass phase using the fraction of the lattice sites having finite superfluid order parameter and non integer local densities as an indicator. A precise distinction between three different types of phases namely, superfluid (SF), Mott insulator (MI) and …
Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein condensates is theoretically and numerically studied by using the spinor Gross-Pitaevskii (GP) equations. SST is turbulence in which the disturbed spin and superfluid velocity fields are coupled. Applying the Kolmogorov-type dimensional scaling analysis to the hydrodynamic equations of spin and velocity fields, we theoretically find that the -5/3 and -7/3 power laws appear in spectra of the superflow kinetic and the spin-dependent interaction energy, respectively. Our numerical calculation of the GP equations confirms…
We present an experimental study on the interaction and dynamics of half-quantum vortices (HQVs) in an antiferromagnetic spinor Bose-Einstein condensate. By exploiting the orbit motion of a vortex dipole in a trapped condensate, we perform a collision experiment of two HQV pairs, and observe that the scattering motions of the HQVs is consistent with the short-range vortex interaction that arises from nonsingular magnetized vortex cores. We also investigate the relaxation dynamics of turbulent condensates containing many HQVs, and demonstrate that spin wave excitations are generated by the coll…
We introduce a novel mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that Kolmogorov 5/3 law is obeyed in the turbulent region. As the stirring is turned off, the flow decays to an agitated non-equilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled 3D Gross-Pitaevskii equa…
We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using in situ magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The dynamics of HQV pair formation is characterized by measuring the temporal evolutions of the pair separation distance and the core magnetization, which reveals the short-range nature of the repulsive interactions between the HQVs. We find that spin fluct…
We propose a pump scheme for quantum circulations, including counter-circulations for superposition states, of a spinor Bose-Einstein condensate. Our scheme is efficient and can be implemented within current experimental technologies and setups. It remains valid for non-classical atomic states, such as pseudo-spin squeezed states and maximal entangled N-GHZ or NooN states. Moreover, it is capable of transforming several enhanced sensing protocols relying on reduced fluctuations from quantum correlation and entanglement of atomic internal states to enhanced measurement of spatial interference a…
We study a spinor condensate of alkali atoms in F = 1 hyperfine state under the presence of an oscillating magnetic field. We find resonances which, due to the dipolar interactions, magnify the transfer of atoms from mF = 1 to mF = 0 Zeeman sublevel. These resonances occur at magnetic fields of the order of milligaus and are broad enough to enable observation of the famous Einstein-de Haas effect, which is solely a dipolar effect, in systems of cold alkali gases.
We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a non-inert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2 and 3 cases at zero magnetic field, and find a new phase in the last case. Properties of vortices in the spin-3 system are also discussed.
We investigate the internal dynamics of the spinor Bose-Einstein Condensates subject to dissipation by solving the Lindblad master equation. It is shown that for the condensates without dissipation its dynamics always evolve along specific orbital in the phase space of ($n_0$, $θ$) and display three kinds of dynamical properties including Josephson-like oscillation, self-trapping-like oscillation and 'running phase'. In contrast, the condensates subject to dissipation will not evolve along the specific dynamical orbital. If component-1 and component-(-1) dissipate in different rates, the magne…
The properties of an F=1 spinor Bose-Einstein condensate trapped in a double-well potential are discussed using both a mean-field two-mode approach and a simplified two-site Bose-Hubbard Hamiltonian. We focus in the region of phase space in which spin effects lead to a symmetry breaking of the system, favoring the spatial localization of the condensate in one well. To model this transition we derive, using perturbation theory, an effective Hamiltonian that describes N/2 spin singlets confined in a double-well potential.
We present an experimental study on non-equilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized t…
We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature $T_c$. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below $T_c$ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.
We used the Gross--Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose--Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.
It is argued that a continuous quantum phase transition between different ordered phases in spinor Bose-Einstein condensates predicted by the mean-field theory is vulnerable to quantum fluctuations. By analyzing Lee-Huang-Yang corrections in the condensate, we demonstrate that the so-called Coleman-Weinberg mechanism takes place in such a transition, that is, the transition becomes of the first order by quantum fluctuations. A jump to be expected in this first-order transition is induced by a correction from density fluctuations despite a transition between different magnetic properties with k…
We propose a protocol which utilises radio frequency magnetic pulses in order to tune the effective two-particle scattering amplitudes for alkali atoms in the $F=1$ hyperfine ground state. Unlike the Feshbach resonance method, the proposed protocol preserves with controllable accuracy the global rotational symmetry in the spin space offering access to a broad region of the phase diagram of the rotationally-symmetric spinor Bose condensate. Examples of $^{41}$K and $^{7}$Li are considered and it is shown that for these atoms sufficient variation in the effective coupling constants can be achiev…
We introduce equations of motion for spin dynamics in a ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction, written using a vector expressing the superfluid velocity and a complex scalar describing the magnetization. This simple hydrodynamical description extracts the dynamics of spin wave and affords a straightforward approach by which to investigate the spin dynamics of the condensate. To demonstrate the advantages of the description, we illustrate dynamical instability and magnetic fluctuation preference, which are expressed in analytical forms.
We study the textures of F=2 spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) due to the SOC. In particular, the cyclic OP consists of two-dimensional lattice textures, such as the hexagonal lattice and the 1/3-vortex lattice, commonly understandable as the two-dimensional network of the helical modulations.
We develop time-splitting finite difference methods, using implicit Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to study the spin-orbit coupled spinor Bose Einstein condensates with coherent coupling in quasi-one and quasi-two-dimensional traps. The split equations involving kinetic energy and spin-orbit coupling operators are solved using either time-implicit Backward-Euler or semi-implicit Crank-Nicolson methods. We explicitly develop the method for pseudospin-1/2, spin-1, and spin-2 condensates. The results for ground states obtained with time-splitting Backward-…
Quantum degenerate Bose gases with an internal degree of freedom, known as spinor condensates, are natural candidates to study the interplay between magnetism and superfluidity. In the spinor condensates made of alkali atoms studied so far, the spinor properties are set by contact interactions, while magnetization is dynamically frozen, due to small magnetic dipole-dipole interactions. Here, we study the spinor properties of S=3 $^{52}$Cr atoms, in which relatively strong dipole-dipole interactions allow changes in magnetization. We observe a phase transition between a ferromagnetic phase and …
We show that the easy-axis (EA) magnetic domains formed in a quenched ferromagnetic spinor condensate are described by percolation theory. We introduce a generalized spin rotation to vary the proportion of positive and negative EA domains, allowing us to explore domain percolation. Using simulations we investigate the finite-size scaling behaviour to extract the correlation length critical exponent and the transition point. We analyse the sensitivity of our results to the early-time dynamics of the system, the quadratic Zeeman energy, and the threshold condition used to define the positive (pe…
By generalizing the Green's function approach proposed by Beliaev [1, 2], we investigate the effect of quantum depletion on the energy spectra of elementary excitations in an F = 1 spinor Bose-Einstein condensate, in particular, of 87Rb atoms in an external magnetic field. We find that quantum depletion increases the effective mass of magnons in the spin-wave excitations with quadratic dispersion relations. The enhancement factor turns out to be the same for both ferromagnetic and polar phases, and also independent of the magnitude of the external magnetic field. The lifetime of these magnons …
Motivated by the recent experiment performed by the Berkeley group [G. E. Marti {\it et al.}, Phys. Rev. Lett. {\bf 113}, 155302 (2014)], we consider the dynamics of magnons in a spin-1 spinor-dipolar Bose-Einstein condensate, using mean-field theory. We show that the effective mass of a magnon is increased by the magnetic dipole-dipole interaction, as observed in the experiment. The magnon mass is also decreased by changing the direction of the magnetic field. The increase and decrease in the magnon mass manifest themselves in the acceleration of the magnons.
We have studied the interaction between multiple, competing spatial modes that are excited by a quantum quench of an antiferromagnetic spinor Bose-Einstein condensate. We observed Hanbury Brown-Twiss correlations and associated super-Poissonian noise in the mode populations. The decay of these correlations was consistent with experimentally observed spin domain patterns. Data were compared with a real-space Bogoliubov theory as well as numerical solution of the coupled Gross-Pitaevskii equations that were seeded by quantum noise via the truncated Wigner approximation. The spatial modes that we…
Symmetry-breaking magnetization dynamics of a spin-1 Bose-Einstein condensate (BEC) due to the dipole-dipole interaction are investigated using the mean-field and Bogoliubov theories. When a magnetic field is applied along the symmetry axis of a pancake-shaped BEC in the m = 0 hyperfine sublevel, transverse magnetization develops breaking the chiral or axial symmetry. A variety of magnetization patterns are formed depending on the strength of the applied magnetic field. The proposed phenomena can be observed in 87Rb and 23Na condensates.
We investigate the ground-state and magnetic properties of a dipolar spin-1 Bose-Einstein condensate trapped in a symmetric double-well potential. In particular, we focus on the spin-vortex states by assuming that each potential well is highly pancake shaped. We show that the presence of the double-well potential gives rise to two different spin configurations for the spin-vortex pair states. We also study the response of the coupled spin-vortex pair to static transverse magnetic fields.
Motivated by a recent experiment [S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabic, PRL 110, 025301 (2013)] we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a two-component condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe persistent currents, if the spin-population imbalance is above some well-defined `critical' value. The triply charged vortices decay in quantized steps. The vortex lines escape from t…
We summarize the recent theoretical and numerical works on spin turbulence (ST) in spin-1 spinor Bose-Einstein condensates. When the system is excited from the ground state, it goes through hy- drodynamic instability to ST in which the spin density vector has various disordered direction. The properties of ST depend on whether the spin-dependent interaction is ferromagnetic or antiferro- magnetic. ST has some characteristics different from other kinds of turbulence in quantum fluids. Firstly, the spectrum of the spin-dependent interaction energy exhibits the characteristic power law different …
Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 Rb-87 condensate. Interatomic interactions lead to correlated pair creation in the m_F= +/- 1 states from an initial unstable m_F=0 condensate, which acts as a vacuum for m_F unequal 0. Although this pair creation from a pure m_F=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial m_F= +/- 1 atoms induce a classical seed w…
In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical m…
We numerically study spin turbulence in a two-dimensional trapped spin-1 spinor Bose--Einstein condensate, focusing on the energy spectrum. The spin turbulence in the trapped system is generated by instability of the helical structure of the spin density vector in the initial state. Our numerical calculation finds that in the trapped system the spectrum of the spin-dependent interaction energy in the ferromagnetic case exhibits a -7/3 power law, which was confirmed in a uniform system by our previous study. The relation between the -7/3 power law and the motion of the spin density vector is di…
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of t…
