Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates

A numerical scheme for the ground state of rotating spin-1 Bose-Einstein condensates

We study the existence of nontrivial solution branches of three-coupled Gross-Pitaevskii equations (CGPEs), which are used as the mathematical model for rotating spin-1 Bose-Einstein condensates (BEC). The Lyapunov-Schmidt reduction is exploited to test the branching of nontrivial solution curves from the trivial one in some neighborhoods of bifurcation points. A multilevel continuation method is proposed for computing the ground state solution of rotating spin-1 BEC. By properly choosing the constraint conditions associated with the components of the parameter variable, the proposed algorithm can effectively compute the ground states of spin-1 [Formula: see text] and [Formula: see text] under rapid rotation. Extensive numerical results demonstrate the efficiency of the proposed algorithm. In particular, the affect of the magnetization on the CGPEs is investigated.

Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids

Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a one-dimensional quantum gas, modeled by a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to solve and analyze the complete set of nonequilibrium steady states in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. In experimental systems of Lieb-Liniger bosons we predict a change from power-law correlations to dominant collective density wave excitations at the corresponding wave numbers as the frequency is lowered below a characteristic cutoff.

A Dual-Species Bose-Einstein Condensate with Attractive Interspecies Interactions

We report on the production of a 41 K- 87 Rb dual-species Bose–Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime; i.e., for negative values of the interspecies scattering length a 12 . The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of a 12 . After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components possibly experiencing different potentials.

Vortex-lattice in a uniform Bose-Einstein condensate in a box trap

We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose-Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman's universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross-Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state.

Skyrmion lattice structural transition in MnSi

Magnetic skyrmions exhibit particle-like properties owing to the topology of their swirling spin texture, providing opportunities to study crystallization of topological particles. However, they mostly end up with a triangular lattice, and thus, the packing degree of freedom in the skyrmion particles has been overlooked so far. We report a structural transition of the skyrmion lattice in MnSi. By use of small-angle neutron scattering, we explore a metastable skyrmion state spreading over a wide temperature and magnetic field region, after thermal quenching. The quenched skyrmions undergo a triangular-to-square lattice transition with decreasing magnetic field at low temperatures. Our study suggests that various skyrmion lattices can emerge at low temperatures, where the skyrmions exhibit distinct topological nature and high sensitivity to the local magnetic anisotropy arising from the underlying chemical lattice.

Vortex Lattices in the Bose-Fermi Superfluid Mixture

In this Letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to the difference in the vortex core structure of a Fermi superfluid in the BCS regime and in the BEC regime. In the BCS regime the vortex core is nearly filled, while the density at the vortex core gradually decreases until it empties out in the BEC regime. Therefore, with the density-density interaction between the Bose and the Fermi superfluids, interaction between the two sets of vortex lattices gets stronger in the BEC regime, which yields the structure transition of vortex lattices. In view of the recent realization of this superfluid mixture and vortices therein, our theoretical predication can be verified experimentally in the near future.

Possible Demonstration of a Polaronic Bose-Einstein(-Mott) Condensate in UO2(+x) by Ultrafast THz Spectroscopy and Microwave Dissipation

Bose-Einstein condensates (BECs) composed of polarons would be an advance because they would combine coherently charge, spin, and a crystal lattice. Following our earlier report of unique structural and spectroscopic properties, we now identify potentially definitive evidence for polaronic BECs in photo- and chemically doped UO_2(+x) on the basis of exceptional coherence in the ultrafast time dependent terahertz absorption and microwave spectroscopy results that show collective behavior including dissipation patterns whose precedents are condensate vortex and defect disorder and condensate excitations. That some of these signatures of coherence in an atom-based system extend to ambient temperature suggests a novel mechanism that could be a synchronized, dynamical, disproportionation excitation, possibly via the solid state analog of a Feshbach resonance that promotes the coherence. Such a mechanism would demonstrate that the use of ultra-low temperatures to establish the BEC energy distribution is a convenience rather than a necessity, with the actual requirement for the particles being in the same state that is not necessarily the ground state attainable by other means. A macroscopic quantum object created by chemical doping that can persist to ambient temperature and resides in a bulk solid would be revolutionary in a number of scientific and technological fields.

A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose-Einstein condensates

Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations ('ground states') that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N≥7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N=2,…,5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called N+1 configuration). We finally examine the opposite limit of large N and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.

Vortices and turbulence in trapped atomic condensates

After more than a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices, and superfluidity and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates.

Formation and control of Turing patterns in a coherent quantum fluid

Nonequilibrium patterns in open systems are ubiquitous in nature, with examples as diverse as desert sand dunes, animal coat patterns such as zebra stripes, or geographic patterns in parasitic insect populations. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light. The unique features of polaritons in semiconductor microcavities allow us to go one step further and to study Turing patterns in an interacting coherent quantum fluid. We demonstrate formation and control of these patterns. We also demonstrate the promise of these quantum Turing patterns for applications, such as low-intensity ultra-fast all-optical switches.

Integer quantum Hall state in two-component Bose gases in a synthetic magnetic field

We study two-component (or pseudospin-1/2) Bose gases in a strong synthetic magnetic field. Using exact diagonalization, we show that a bosonic analog of an integer quantum Hall state with no intrinsic topological order appears at the total filling factor ν=1+1 when the strengths of intracomponent and intercomponent interactions are comparable with each other. This provides a prime example of a symmetry-protected topological phase in a controlled setting of quantum gases. The real-space entanglement spectrum of this state is found to be comprised of counterpropagating chiral modes consistent with the edge theory derived from an effective Chern-Simons theory.

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.

Spin-orbit coupled Bose-Einstein condensate under rotation

We examine the combined effects of Rashba spin-orbit (SO) coupling and rotation on trapped spinor Bose-Einstein condensates. The nature of single particle states is thoroughly examined in the Landau level basis and is shown to support the formation of a half-quantum vortex. In the presence of weak s-wave interactions, the ground state at strong SO coupling develops ringlike structures with domains whose number shows step behavior with increasing rotation. For the fast rotation case, the vortex pattern favors a triangular lattice, accompanied by density depletion in the central region and a weakened Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is facilitated when SO coupling and rotation are both strong.

Texture control in a pseudospin Bose-Einstein condensate

We describe a wave function engineering approach to the formation of textures in nonrotated multicomponent Bose-Einstein condensates. With numerical simulations of a viable two-component condensate experiment, we demonstrate the formation of a ballistically expanding regular lattice texture, composed of half-quantum vortices and spin-2 textures. The formation is described by a linear interference process in which the geometry and phase of three initially separated wave packets provide deterministic control over the resulting lattice texture.

Stable vortex-bright-soliton structures in two-component Bose-Einstein condensates

We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex-bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.

Mixtures of Bose gases confined in a ring potential

The rotational properties of a mixture of two distinguishable Bose gases that are confined in a ring potential provide novel physical effects that we demonstrate in this study. Persistent currents are shown to be stable for a range of the population imbalance between the two components at low angular momentum. At higher values of the angular momentum, even small admixtures of a second species of atoms make the persistent currents highly fragile.

Dissipation-induced coherent structures in Bose-Einstein condensates

We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.

Dynamical creation of fractionalized vortices and vortex lattices

We investigate the dynamic creation of fractionalized half-quantum vortices in Bose-Einstein condensates of sodium atoms. Our simulations show that both individual half-quantum vortices and vortex lattices can be created in rotating optical traps when additional pulsed magnetic trapping potentials are applied. We also find that a distinct periodically modulated spin-density-wave spatial structure is always embedded in square half-quantum vortex lattices. This structure can be conveniently probed by taking absorption images of ballistically expanding cold atoms in a Stern-Gerlach field.

Topological winding and unwinding in metastable Bose-Einstein condensates

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of gray solitons, or density notches, which serve as an experimental signature of this phenomenon.

Nonequilibrium dynamics and superfluid ring excitations in binary Bose-Einstein condensates

We revisit a classic study [D. S. Hall, Phys. Rev. Lett. 81, 1539 (1998)10.1103/PhysRevLett.81.1539] of interpenetrating Bose-Einstein condensates in the hyperfine states |F=1,m{f}=-1 identical with |1 and |F=2,m{f}=+1 identical with |2 of 87Rb and observe striking new nonequilibrium component separation dynamics in the form of oscillating ringlike structures. The process of component separation is not significantly damped, a finding that also contrasts sharply with earlier experimental work, allowing a clean first look at a collective excitation of a binary superfluid. We further demonstrate extraordinary quantitative agreement between theoretical and experimental results using a multicomponent mean-field model with key additional features: the inclusion of atomic losses and the careful characterization of trap potentials (at the level of a fraction of a percent).

Two-dimensional discrete solitons in rotating lattices

We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance R from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities S=1 and 2 . At a fixed value of rotation frequency Omega , a stability interval for the FSs is found in terms of the lattice coupling constant C , 0<C<C_{cr}(R) , with monotonically decreasing C_{cr}(R) . VSs with S=1 have a stability interval, C[over ]_{cr};{(S=1)}(Omega)<C<C_{cr};{(S=1)}(Omega) , which exists for Omega below a certain critical value, Omega_{cr};{(S=1)} . This implies that the VSs with S=1 are destabilized in the weak-coupling limit by the rotation. On the contrary, VSs with S=2 , that are known to be unstable in the standard DNLS equation, with Omega=0 , are stabilized by the rotation in region 0<C<C_{cr};{(S=2)} , with C_{cr};{(S=2)} growing as a function of Omega . Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by Omega not equal 0 .

Mixtures of Bose gases under rotation

We examine the rotational properties of a mixture of two Bose gases. Considering the limit of weak interactions between the atoms, we investigate the behavior of the system under a fixed angular momentum. We demonstrate a number of exact results in this many-body system.

Vortex lattices in planar Bose-Einstein condensates with dipolar interactions

In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.

Vortex lattices in rotating atomic bose gases with dipolar interactions

We show that dipolar interactions have dramatic effects on the ground states of rotating atomic Bose gases in the weak-interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean field, or high filling factor, ground state undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, "stripe," and "bubble" phases. We also study the effects of dipolar interactions on the quantum fluids at low filling factors. We show that the incompressible Laughlin state at filling factor nu = 1/2 is replaced by compressible stripe and bubble phases.