Spinor Bose-Einstein Condensate Research Articles

Six types of spin solitons in three-component Bose–Einstein condensates

Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems. We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose–Einstein condensate. Six types of spin soliton solutions can be obtained, and they exist in different regions. Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise. The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons. These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.

Understanding dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses

Abstract Phase transitions in nonequilibrium dynamics of many body quantum systems, 
known as dynamical phase transitions (DPTs), play an important role for understanding
various dynamical phenomena observed in different branches of physics.
In general, there are two types of DPTs, the first one is characterized by 
distinct evolutionary behaviors of a physical observable, while the second one is marked by 
the vanishing overlap between the time-evolved and initial states. 
Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives 
in a spinor Bose-Einstein condensate (BEC), an ideal platform for
investigating nonequilibrium dynamics.
Utilizing the sudden quench process, we demonstrate that the system exhibits 
both types of DPTs as the control parameter is quenched through
the critical value, referring to as the critical quenching. 
We show analytically how to determine the critical quenching via
the semiclassical approach and carry out a detailed examination of both semiclassical 
and quantum signatures of DPTs. 
In particular, we reveal that the occurrence of DPTs is triggered by
the separatrix in the underlying semiclassical system.
Our findings offer deeper insights into the properties of DPTs and verify the usefulness 
of semiclassical analysis for studying DPTs in quantum systems 
with well-defined semiclassical limit. 

Composite cores of monopoles and Alice rings in spin-2 Bose-Einstein condensates

We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration. Published by the American Physical Society 2024

High-order rogue wave and mixed interaction patterns for the three-component Gross-Pitaevskii equationsin F=1 spinor Bose-Einstein condensates.

Under investigation are the three-component Gross-Pitaevskii equationsin F=1 spinor Bose-Einstein condensates. Various localized waves' generation mechanisms have been derived from plane wave solutions using modulation instability. The perturbed continuous waves produce a large number of rogue wave structures through the split-step Fourier numerical method. Based on the known Lax pair, we construct the generalized iterative (n,N-n)-fold Darboux transformation to generate various high-order solutions, including the bright-dark-bright structure of rogue waves, periodic waves, and their mixed interaction structures. Numerical simulations show that rogue waves with a two-peaked structure have robust noise resistance and stable dynamical behavior. The asymptotic states of high-order rogue waves as the parameter approaches infinity are also predicted using the large parameter asymptotic technique. In addition, the position of these localized wave patterns can be controlled by some special parameters. These results may help us understand the dynamic behavior of spinor condensates for the mean-field approximation.

Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates

Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates

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