Antiferromagnetic Spin-1 Bose-Einstein Condensate Research Articles

Vortex-lattice formation in a spin–orbit coupled rotating spin-1 condensate

We study the vortex-lattice formation in a rotating Rashba spin–orbit (SO) coupled quasi-two-dimensional (quasi-2D) hyper-fine spin-1 spinor Bose–Einstein condensate (BEC) in the x–y plane using a numerical solution of the underlying mean-field Gross–Pitaevskii equation. In this case, the non-rotating Rashba SO-coupled spinor BEC can have topological excitation in the form of vortices of different angular momenta in the three components, e.g. the (0, +1, +2)- and (−1, 0, +1)-type states in ferromagnetic and anti-ferromagnetic spinor BEC: the numbers in the parenthesis denote the intrinsic angular momentum of the vortex states of the three components with the negative sign denoting an anti-vortex. The presence of these states with intrinsic vorticity breaks the symmetry between rotation with vorticity along the z and −z axes and thus generates a rich variety of vortex-lattice and anti-vortex-lattice states in a rotating quasi-2D spin-1 spinor ferromagnetic and anti-ferromagnetic BEC, not possible in a scalar BEC. For weak SO coupling, we find two types of symmetries of these states − hexagonal and ‘square’. The hexagonal (square) symmetry state has vortices arranged in closed concentric orbits with a maximum of 6, 12, 18… (8, 12, 16…) vortices in successive orbits. Of these two symmetries, the square vortex-lattice state is found to have the smaller energy.

Interlocked knot in spinor Bose-Einstein condensates

Abstract The physics of topological defects have been extensively studied by theory and experiment in recent years. Vortex rings especially linking vortex rings are difficult to create and stabilize in experiments. We study a new structure of knot called interlocked knot in the antiferromagnetic spin-1 Bose-Einstein condensate, which has never been studied before. The interlocked knot differs from the conventional knot with linking vortex rings that are connected by a Mobius strip. It cannot be converted to untwisted rings without cutting them. We propose two schemes to generate the interlocked knot in experiments either by using an external magnetic field, or alternatively, by the spin-orbit coupling in spin-1 condensates. Our results open a new perspective for the study of knot and extend the application of experimental technique.

Efficient Generation of Many-Body Entangled States by Multilevel Oscillations.

We generate high-fidelity massively entangled states in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC) by utilizing multilevel oscillations. Combining the multilevel oscillations with additional adiabatic drives, we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting, from microgauss to milligauss, for a ^{23}Na spinor BEC. The achieved high fidelities over 96% show that two kinds of massively entangled states, the many-body singlet state and the twin-Fock state, are almost perfectly generated. The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of atom number fluctuations and stray magnetic fields, illustrating the robustness of our protocol under real experimental conditions. The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science.

Observation of dynamical quantum phase transitions in a spinor condensate

A dynamical quantum phase transition can be characterized by a nonanalytic change in the quench dynamics when a parameter in the governing Hamiltonian is varied. Such a transition typically only shows up in long-time dynamics for extensive systems with short-range couplings. We analyze a model Hamiltonian of spin-1 particles with effectively infinite-range couplings and demonstrate that for this system the nonanalytic transition occurs for local observables in short-time durations even when the system is of a large size. We experimentally realize this model Hamiltonian and observe the dynamical quantum phase transition in an antiferromagnetic spinor Bose-Einstein condensate of around ${10}^{5}$ sodium atoms. Our observations agree well with the theoretical prediction. We also analyze the scaling exponent near the dynamical phase transition and discuss its relation with the excited-state spectrum of the system.

Mesoscopics of half-quantum vortex pair deconfinement in a trapped spin-one condensate

Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein condensate of ${}^{23} \textrm{Na}$ atoms, we study the energetical stability of a singly quantum vortex injected into the center of a quasi-two-dimensional gas with zero total spin against dissocation into a pair of half-quantum vortices. We find that the critical dissociation point of this confinement-deconfinement type phase transition can be expressed in terms of the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants. The transition of bound to unbound vortices, in particular, sensitively depends on (1) the ratio of system size ($R$) to density healing length ($\xi_d$), and (2) the trap potential. Specifically, the critical ratio $(c_2 / c_0)_{\textrm{cr}}$ increases when $R / \xi_d$ decreases, and is relatively larger in a harmonic trap than in a box trap. Dissociation is energetically generally favored for $c_2 / c_0 < (c_2 / c_0)_{\textrm{cr}}$, which as a corollary implies that vortex dissociation is observed as well for negative $c_2 < 0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC ($c_2>0$) it is energetically blocked above the critical ratio $(c_2 / c_0)_{\textrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave control techniques, the dependence of the deconfinement phase transition on coupling parameters, density, and system size we predict, can be verified in experiments with ultracold spinor gases.

Hanbury Brown–Twiss correlations and multi-mode dynamics in quenched, inhomogeneous density spinor Bose–Einstein condensates

We have studied the effects of 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 were both observed experimentally and deduced theoretically are intimately connected to the inhomogeneous density profile of the condensate. Unique features were observed not present in a homogeneous system, including unstable modes located near the center of the cloud, where the dynamics were initiated.

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.

Critical Spin Superflow in a Spinor Bose-Einstein Condensate.

We investigate the critical dynamics of spin superflow in an easy-plane antiferromagnetic spinor Bose-Einstein condensate. Spin-dipole oscillations are induced in a trapped condensate by applying a linear magnetic field gradient and we observe that the damping rate increases rapidly as the field gradient increases above a certain critical value. The onset of dissipation is found to be associated with the generation of dark-bright solitons due to the modulation instability of the counterflow of two spin components. Spin turbulence emerges as the solitons decay because of their snake instability. We identify another critical point for spin superflow, in which transverse magnon excitations are dynamically generated via spin-exchanging collisions, which leads to the transient formation of axial polar spin domains.

Stable 2D skyrmion and half-skyrmion in three-component Bose–Einstein condensates

Skyrmion spin textures were experimentally created in an antiferromagnetic spin-1 Bose–Einstein condensate by Choi et al. However, the stability of 2D skyrmion excitations is still controversial. Theoretical calculations show that 2D skyrmion excitations are energetically unstable. However, we find that the 2D skyrmion as well as the half-skyrmion can be naturally generated from a vortex-free Gaussian wave packet by incorporating spin–orbit coupling into three-component Bose–Einstein condensates.

Stable double-pair skyrmion in an antiferromagnetic F = 1 Bose–Einstein condensate

The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.

Emergence and scaling of spin turbulence in quenched antiferromagnetic spinor Bose-Einstein condensates

We investigate the phase transition dynamics of a quasi-2D antiferromagnetic spin-1 Bose-Einstein condensate from the easy-axis polar phase to the easy-plane polar phase, which is initiated by suddenly changing the sign of the quadratic Zeeman energy $q$. We observe the emergence and decay of spin turbulence and the formation of half-quantum vortices (HQVs) in the quenched condensate. The characteristic time and length scales of the turbulence generation dynamics are proportional to $|q|^{-1/2}$ as inherited from the dynamic instability of the initial state. In the evolution of the spin turbulence, spin wave excitations develop from large to small length scales, suggesting a direct energy cascade, and the spin population for the axial polar domains exhibit a nonexponential decay. The final equilibrated condensate contains HQVs, and the number is found to increase and saturate with increasing $|q|$. Our results demonstrate the time-space scaling properties of the phase transition dynamics near the critical point and the peculiarities of the spin turbulence state of the antiferromagnetic spinor condensate.

On the spin-1 Bose–Einstein condensates in the presence of Ioffe–Pritchard magnetic field

We study the Cauchy problem of an antiferromagnetic spin-1 Bose–Einstein condensate under Ioffe–Pritchard magnetic field [Formula: see text]. We then address the existence of ground state solutions and characterize the orbit of standing waves.

First-order superfluid-to-Mott-insulator phase transitions in spinor condensates

We observe evidence of first-order superfluid to Mott-insulator quantum phase transitions in a lattice-confined antiferromagnetic spinor Bose-Einstein condensate. The observed signatures include hysteresis effect and significant heatings across the phase transitions. The nature of the phase transitions is found to strongly depend on the ratio of the quadratic Zeeman energy to the spin-dependent interaction. Our observations are qualitatively understood by the mean field theory, and in addition suggest tuning the quadratic Zeeman energy is a new approach to realize superfluid to Mott-insulator phase transitions.

Magnetic-field-induced dynamical instabilities in an antiferromagnetic spin-1 Bose-Einstein condensate

We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type $I_O$, in an anti-ferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability $I_O$ to a uniform one $III_O$ occurs at a critical magnetic field. All the four types of dynamical instability and the pattern transition are ready to be detected in $^{23}$Na condensates within the availability of the current experimental techniques.

Collisional Dynamics of Half-Quantum Vortices in a Spinor Bose-Einstein Condensate.

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 collisional motions of the HQVs. The short-range vortex interaction and the HQV-magnon coupling represent two characteristics of the HQV dynamics in the spinor superfluid.

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate.

We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using insitu 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 fluctuations arising from thermal population of transverse magnon excitations do not significantly affect the HQV pair formation dynamics. Our results demonstrate the instability of a singly charged vortex in the antiferromagnetic spinor condensate.

Superfluid–Mott-insulator transition of spin-1 bosons in optical resonators

We consider an antiferromagnetic spin-1 Bose-Einstein condensate confined in a Fabry-P\'erot optical resonator in which the intracavity light field forms an optical lattice potential for the atoms. Special emphasis is paid to the cavity-mediated superfluid--Mott-insulator transition. We find that exotic phase diagrams can appear due to the competition between cavity-induced nonlinear interactions and the atomic spin-dependent collision interactions.

Dynamics and complex structure of two-dimensional skyrmions in antiferromagnetic spin-1 Bose-Einstein condensates

Motivated by the recent experiment of Choi et al. [Phys. Rev. Lett. 108, 035301 (2012)], we simulate, within the Gross-Pitaevskii equation, the process of creating a skyrmion in an antiferromagnetic spin-1 Bose-Einstein condensate via the magnetic-field rotation method. Complex skymion structures are found and the factors influencing them are discussed. The dynamics of the system is mainly quasiperiodic. When the center of the skyrmion is displaced from the trap center, half vortices can be found at an intermediate stage of the dynamical evolution, but they do not necessarily lead to the destruction of the skyrmions.

Optical control of a quantum rotor

The possibility to coherently control a quantum rotor is investigated theoretically. The rotor is realized by an antiferromagnetic spin-1 Bose-Einstein condensate, trapped in the optical field of a Fabry-P\'erot resonator. By tuning the pumping field of the resonator, coherent control over the rotor is achieved. The technique is illustrated by the numerical simulation of a protocol that transforms the rotor's ground state into a squeezed state. The detection of the squeezed state via measurement of intensity correlations of the cavity field is proposed.

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.