Spinor Bose-Einstein Condensate Research Articles

Stability and dynamics of self-bound state of spin–orbit coupled spin-1 Bose–Einstein condensates

We study self-bound state of spin–orbit (SO) coupled spin-1 BECs under the action of the SO coupling and the density-dependent and spin-dependent interactions. The phase transition conditions from the magnetized phase to the unmagnetized phase are analytically obtained in the self-bound state, and the physical mechanism of the phase transition is revealed. The distinct properties of self-bound state in different ground states are discussed in detail, and static and moving self-bound states are obtained. Then, the stability of the self-bound state is studied, and the unstable threshold caused by the competition among SO coupling, Raman coupling, spin-dependent interaction and density-dependent interaction is obtained analytically and confirmed numerically. Furthermore, the dynamical transition of self-bound state from moving type to static type is studied numerically. Due to the spin momentum locking and the drive of spin dynamics, the self-bound states exhibit distinct dynamical behaviors in different ground state phases. Our study provides theoretical evidence for a deep understanding of the stability and the dynamic of self-bound states in SO coupled spin-1 BECs.

Ground states of a distinct spin–orbit-coupled spin-1 Bose–Einstein Condensate in a toroidal trap

This study delves into the influence of a new type of spin–orbit coupling (SOC) on spin-1 Bose–Einstein condensates (BECs) in quasi-two-dimensional annular regions. The unconventional characteristics of the annular potential trap coupled with innovative artificial gauge field bring about a diverse array of phase diagrams for the ground state behavior of the BECs. In the antiferromagnetic state, we observe a distinct petal-like phase structure with components exhibiting novel density and phase distributions. In the ferromagnetic state, the spin-1 BECs exhibit rich asymmetric states which showcase a new type of vortex-molecule structure with multiple winding numbers in the huge hole. Many other novel breaking structures have also been discovered by modulating the strength of the nonlinear interaction. We contribute the different ground states of distinct spin–orbit couplings to the different symmetries.

Universality class of a spinor Bose–Einstein condensate far from equilibrium

Universality class of a spinor Bose–Einstein condensate far from equilibrium

Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates

Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates

Topological atom optics and beyond with knotted quantum wavefunctions

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose–Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Möbius strips, and a twice-linked Solomon’s knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields—a realization of topological atom-optics.

Cavity-enhanced metrology in an atomic spin-1 Bose–Einstein condensate

Cavity-enhanced metrology in an atomic spin-1 Bose–Einstein condensate

Multiple-quantum-coherence dynamics of spin-1 Bose–Einstein condensate during quantum phase transitions

Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose–Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.

Enhanced measurement precision with continuous interrogation during dynamical decoupling

Dynamical decoupling (DD) is normally ineffective when applied to DC measurement. In its straightforward implementation, DD nulls out DC signal as well while suppressing noise. This work proposes a phase relay method that is capable of continuously interrogating the DC signal over many DD cycles. We illustrate its efficacy when applied to the measurement of a weak DC magnetic field with an atomic spinor Bose–Einstein condensate. Sensitivities approaching standard quantum limit or Heisenberg limit are potentially realizable for a coherent spin state or a squeezed spin state of 10000 atoms, respectively, while ambient laboratory level noise is suppressed by DD. Our work offers a practical approach to mitigate the limitations of DD to DC measurement and would find other applications for resorting coherence in quantum sensing and quantum information processing research.

Bimeron in a ferromagnetic spin-1 Bose–Einstein condensate

The spin degrees of freedom in multicomponent Bose–Einstein condensates allow for various types of topological excitations, such as skyrmions and knots. Systems with high spins offer a broader range of internal symmetries. For instance, in spin-1 Bose–Einstein condensates, one can observe not only the two-dimensional (2D) skyrmion spin texture but also the bimeron spin texture. However, it remains challenging to experimentally create or stabilize a bimeron and identify the conditions that facilitate its formation. In this context, our research predicts a novel form of topological structure known as the domain wall bimeron in ferromagnetic spin-1 Bose–Einstein condensates by manipulating the magnetic field. Unlike conventional 2D skyrmions, this unique bimeron exhibits a non-axisymmetric spin texture and features complex off-axis vortices whose cores are connected by domain walls. This work significantly contributes to the study of 2D topological excitations in quantum matter with high spins.

Ground states of helicoidal spin-orbit-coupled spin-1 bosons

The ground states of spin-1 Bose–Einstein condensate under helicoidal spin–orbit-coupling are investigated, by solving the corresponding Gross–Pitaevskii equations, and via the time-splitting Fourier pseudospectral method. Taking into account the ferromagnetic interaction as well as the antiferromagnetic case, we identify some novel structures on the ground states, including the spot phase, particle-like supersolid phase, hole-like supersolid phase, particle-hole-like supersolid phase, and wave-shaped stripe phase. With the variance of helicoidal gauge potential, the system would undergo abundant quantum phases.

Integrator for general spin-s Gross-Pitaevskii systems.

We provide an algorithm, i-SPin 2, for evolving general spin-s Gross-Pitaevskii or nonlinear Schrödinger systems carrying a variety of interactions, where the 2s+1 components of the "spinor" field represent the different spin-multiplicity states. We consider many nonrelativistic interactions up to quartic order in the Schrödinger field (both short and long range, and spin-dependent and spin-independent interactions), including explicit spin-orbit couplings. The algorithm allows for spatially varying external and/or self-generated vector potentials that couple to the spin density of the field. Our work can be used for scenarios ranging from laboratory systems such as spinor Bose-Einstein condensates (BECs), to cosmological or astrophysical systems such as self-interacting bosonic dark matter. As examples, we provide results for two different setups of spin-1 BECs that employ a varying magnetic field and spin-orbit coupling, respectively, and also collisions of spin-1 solitons in dark matter. Our symplectic algorithm is second-order accurate in time, and is extensible to the known higher-order-accurate methods.

Phase characterization of spinor Bose-Einstein condensates: A Majorana stellar representation approach

We study the variational perturbations for the mean-field solution of an interacting spinor system with underlying rotational symmetries. An approach based upon the Majorana stellar representation for mixed states and group theory is introduced to this end. The method reduces significantly the unknown degrees of freedom of the perturbation, allowing us a simplified and direct exploration on emergent physical phenomena. We apply it to characterize the phases of a spin-1 Bose-Einstein condensate and to study the behavior of these phases with entropy. The spin-2 phase diagram was also investigated within the Hartree-Fock approximation, where a non-linear deviation of the cyclic-nematic phase boundary with temperature is predicted.

Three-dimensional solitons in Rydberg-dressed cold atomic gases with spin–orbit coupling

We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose–Einstein condensates of Rydberg atoms under the action of the spin–orbit coupling (SOC). By means of systematic numerical computations, we demonstrate that the interplay of SOC and long-range spherically symmetric Rydberg interactions stabilize the 3D solitons, improving their resistance to collapse. We find how the stability range depends on the strengths of the SOC and Rydberg interactions and the soft-core atomic radius.

Winding real and order-parameter spaces via lump solitons of spinor BEC on sphere

The three condensate wavefunctions of a F = 1 spinor Bose–Einstein condensate on a spherical shell can map the real space to the order-parameter space that also has a spherical geometry, giving rise to topological excitations called lump solitons. The homotopy of the mapping endows the lump solitons with quantized winding numbers counting the wrapping between the two spaces. We present several lump-soliton solutions to the nonlinear coupled equations minimizing the energy functional. The energies of the lump solitons with different winding numbers indicate coexistence of lumps with different winding numbers and a lack of advantage to break a higher-winding lump soliton into multiple lower-winding ones. Possible implications are discussed since the predictions are testable in cold-atom experiments.

Vortex Lattice Formation in Spin–Orbit-Coupled Spin-2 Bose–Einstein Condensate Under Rotation

Vortex Lattice Formation in Spin–Orbit-Coupled Spin-2 Bose–Einstein Condensate Under Rotation

Long-Lived Squeezed Ground States in a Quantum Spin Ensemble.

We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum-critical point separating the different spin phases of the interacting ensemble using a novel nonadiabatic technique. In contrast to typical nonequilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time stationary with a constant quadrature squeezing angle. A squeezed ground state with 6-8dB of squeezing and a constant squeezing angle is demonstrated. The long-term evolution of the squeezed ground state is measured and shows gradual decrease in the degree of squeezing over 2s that is well modeled by a slow tuning of the Hamiltonian due to the loss of atomic density. Interestingly, modeling the gradual decrease does not require additional spin decoherence models despite a loss of 75% of the atoms.

Quantum double structure in cold atom superfluids

The theory of topological quantum computation is underpinned by two important classes of models. One is based on non-abelian Chern–Simons theory, which yields the so-called SU(2)k anyon models that often appear in the context of electrically charged quantum fluids. The physics of the other is captured by symmetry broken Yang–Mills theory in the absence of a Chern–Simons term and results in the so-called quantum double models. Extensive resources have been invested into the search for SU(2)k anyon quasi-particles, in particular, the so-called Ising anyons (k = 2) of which Majorana zero modes are believed to be an incarnation. In contrast to the SU(2)k models, quantum doubles have attracted little attention in experiments despite their pivotal role in the theory of error correction. Beyond topological error correcting codes, the appearance of quantum doubles has been limited to contexts primarily within mathematical physics, and as such, they are of seemingly little relevance for the study of experimentally tangible systems. However, recent works suggest that quantum double anyons may be found in spinor Bose–Einstein condensates. In light of this, the core purpose of this article is to provide a self-contained exposition of the quantum double structure, framed in the context of spinor condensates, by constructing explicitly the quantum doubles for various ground state symmetry groups and discuss their experimental realisability. We also derive analytically an equation for the quantum double Clebsch–Gordan coefficients from which the relevant braid matrices can be worked out. Finally, the existence of a particle-vortex duality is exposed and illuminated upon in this context.

Stationary and moving bright solitons in Bose–Einstein condensates with spin–orbit coupling in a Zeeman field

We explore the existence and stability domains of stationary and moving bright solitons in spin–orbit-coupled spin-1 Bose–Einstein condensates in an external Zeeman field. Two families of bell-shape bright solitons (plane-wave (PW) phases) and two families of stripe-shape bright solitons (standing-wave (SW) phases) are obtained. We find a relation between the existence of these bright solitons and the single-particle energy spectrum, as well as the requirements of their existence for atomic interactions. The stability of four families of bright solitons is systematically analyzed using the linear stability analysis method. For two families of PW bright solitons, they are unstable only when the strength of the Zeeman field is above a critical value. The critical value is affected by the spin–orbit coupling and hardly affected by atomic interactions. When the velocities of solitons are zero (nonzero), the critical values of these two families are equal (unequal). For two families of SW bright solitons, their stability domains are identical in the absence of the Zeeman field, and they are unstable when the ferromagnetic interaction is strong. In the presence of the Zeeman field, their stability domains are complementary and complex, and one family of SW bright solitons can exist stably in the area with stronger ferromagnetic interaction. Furthermore, we find the collisions of stable bright solitons with different velocities can generate intriguing dynamics.

Spin–orbital angular momentum coupling in Bose–Einstein condensate and its spin dynamics

We examine the use of Laguerre–Gaussian (LG) laser beams in the tripod scheme to create the coupling between spin and orbital angular momentum in a Bose–Einstein condensate (BEC) confined by a harmonic trap. We derive and solve the Gross–Pitaevskii equation numerically to obtain the density distribution of the BEC. Orbital angular momentum from the LG beam is transferred to the BEC, inducing the formation of a giant vortex at the BEC’s centre. The macroscopic flow of spinor BEC around the vortex leads to a persistent spin current in the BEC.

Patterns, spin-spin correlations, and competing instabilities in driven quasi-two-dimensional spin-1 Bose-Einstein condensates

Patterns, spin-spin correlations, and competing instabilities in driven quasi-two-dimensional spin-1 Bose-Einstein condensates