Spinor Bose-Einstein Condensate Research Articles

Abundant vortex dynamics in spin-1 Bose–Einstein condensates induced by Rashba spin–orbit coupling

The paper studies the dynamics of vortices evolved from the ring dark solitons (RDSs) in spin-1 Bose–Einstein condensates with Rashba spin–orbit coupling (SOC). We find that the SOC induces abundant vortex dynamic phenomena, and the numbers of vortex dipoles and lump-like solitons are all determined by the initial depths’ weighted average of the three components of RDSs. For a shallow RDS, the ring first expands and then contracts into a mini RDS, eventually evolving into late vortex dipoles. For the RDS with a moderate initial depth, during the contraction of the ring, it evolves into early vortex dipoles or lump-like solitons, and they evolve back into the mini RDS, which then evolves into late vortex dipoles during the expansion process. For the deep and black RDSs, the early vortex dipoles continue to transform between vortex dipoles and lump-like solitons without forming mini RDS. The motions of vortices mentioned above have a higher disorder degree than that in the system without SOC, because the SOC breaks the mirror symmetry of the condensate. Finally, we reveal that the SOC strength only influences the number of late vortex dipoles, while it does not affect the number of early vortex dipoles and lump-like solitons. Stronger SOC intensity results in a shallower critical depth, and vortices form only at or beyond this depth.

Three-component soliton states in spinor F = 1 Bose-Einstein condensates with PT-symmetric generalized Scarf-II potentials

Abstract Introducing PT-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seeking stable soliton states in quasi-one-dimensional spin-1 Bose-Einstein condensates. In scenarios where the spin-independent parameter c_0 and the spin-dependent parameter c_2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c_2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

Fractional-order effects on the dynamics and lifetime of ring dark solitons in spin–orbit coupled spin-1 Bose–Einstein condensate

Fractional-order effects on the dynamics and lifetime of ring dark solitons in spin–orbit coupled spin-1 Bose–Einstein condensate

2D Skyrmion topological charge of spin textures with arbitrary boundary conditions: a two-component spinorial BEC as a case study

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

Phase separation and metastability in a mixture of spin-1 and spin-2 Bose-Einstein condensates

Phase separation and metastability in a mixture of spin-1 and spin-2 Bose-Einstein condensates

Vector rogue waves in spin-1 Bose–Einstein condensates with spin–orbit coupling

Abstract We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose–Einstein condensates with Raman-induced spin–orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions.

Hydrodynamic model of skyrmions and vorticities in the spin-1 Bose–Einstein condensate in ferromagnetic phase at finite temperatures

Quantum hydrodynamic of skyrmions in spinor ultracold bosons at the finite temperature is described. The limit regime of BEC appearing at the zero temperature is discussed either. The skyrmions are found as the solution of the spin evolution equation for the ferromagnetic phase of spin-1 ultracold bosons. It is demonstrated that the quantum part of the spin current gives major contribution in the formation of the skyrmions. The interplay between the quantum (spin) vorticity and the classic vorticity is considered for the finite temperatures. Bosons are presented as two fluids associated with the Bose–Einstein condensate and the normal fluid. All effects are considered for the ferromagnetic phase.

Chaos-assisted turbulence in spinor Bose-Einstein condensates

We present a turbulence-sustaining mechanism in a spinor Bose-Einstein condensate, which is based on the chaotic nature of internal spin dynamics. Magnetic driving induces a complete chaotic evolution of the local spin state, thereby continuously randomizing the spin texture of the condensate to maintain the turbulent state. We experimentally demonstrate the onset of turbulence in the driven condensate as the driving frequency changes and show that it is consistent with the regular-to-chaotic transition of the local spin dynamics. This chaos-assisted turbulence establishes the spin-driven spinor condensate as an intriguing platform for exploring quantum chaos and related superfluid turbulence phenomena. Published by the American Physical Society 2024

Oscillating multi-node solitons in spin-orbit coupled spin-1 Bose–Einstein condensates

Oscillating multi-node solitons in spin-orbit coupled spin-1 Bose–Einstein condensates

Bessel vortices in spin-1 Bose–Einstein condensates with Zeeman splitting and spin–orbit coupling

Abstract We investigate the ground states of spin–orbit coupled spin-1 Bose–Einstein condensates in the presence of Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system is solved exactly, yielding a set of Bessel vortices. Additionally, based on linear solution and using variational approximation, the solutions for the full nonlinear system and their ground state phase diagrams are derived, including the vortex states with quantum numbers m = 0, 1, as well as mixed states. In this work, mixed states in spin-1 spin–orbit coupling (SOC) BEC are interpreted for the first time as weighted superpositions of three vortex states. Furthermore, the results also indicate that under strong Zeeman splitting, the system cannot form localized states. The variational solutions align well with numerical simulations, showing stable evolution and meeting the criteria for long-term observation in experiments.

The synthetic gauge field and exotic vortex phase with spin-orbital-angular-momentum coupling

Ultracold atoms endowed with tunable spin-orbital-angular-momentum coupling (SOAMC) represent a promising avenue for delving into exotic quantum phenomena. Building on recent experimental advancements, we propose the generation of synthetic gauge fields, and by including exotic vortex phases within spinor Bose–Einstein condensates, employing a combination of a running wave and Laguerre–Gaussian laser fields. We investigate the ground-state characteristics of the SOAMC condensate, revealing the emergence of exotic vortex states with controllable orbital angular momenta. It is shown that the interplay of the SOAMC and conventional spin-linear-momentum coupling induced by the running wave beam leads to the formation of a vortex state exhibiting a phase stripe hosting single multiply quantized singularity. The phase of the ground state will undergo the phase transition corresponding to the breaking of rotational symmetry while preserving the mirror symmetry. Importantly, the observed density distribution of the ground-state wavefunction, exhibiting broken rotational symmetry, can be well characterized by the synthetic magnetic field generated through light interaction with the dressed spin state. Our findings pave the way for further exploration into the rotational properties of stable exotic vortices with higher orbital angular momenta against splitting in the presence of synthetic gauge fields in ultracold quantum gases.

Improving metrology with quantum scrambling in a spin-1 Bose-Einstein condensate coupled to a cavity.

Spinor Bose-Einstein condensate is an ideal candidate for implementing the many-body entanglement, quantum measurement and quantum information processing owing to its inherent spin-mixing dynamics. Here we present a system of an 87Rb atomic spin-1 Bose-Einstein condensate coupled to an optical ring cavity, in which cavity-mediated nonlinear interactions give rise to saddle points in the semiclassical phase space, providing a general mechanism for exponential fast scrambling and metrological gain augment. We theoretically study metrological gain and fidelity out-of-time-ordered correlator based on time-reversal protocols and demonstrate that exponential rapid scrambling dynamics can enhance quantum metrology. In addition, we use the out-of-time-ordered correlator to probe dynamical phase transitions. This work is useful to understand the intrinsic relation between the concepts from different subfields of quantum science.

Dynamics of Ring Dark Solitons and the Following Vortices in Spin-1 Bose–Einstein Condensates

Abstract This work focuses on the evolution behaviors of ring dark solitons (RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose-Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis. For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally. Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.

Elementary excitations in a spin–orbit-coupled Floquet spinor Bose–Einstein condensate

We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.

Fast transport and splitting of spin-orbit-coupled spin-1 Bose-Einstein condensates

Fast transport and splitting of spin-orbit-coupled spin-1 Bose-Einstein condensates

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

Phase transitions in nonequilibrium dynamics of quantum many-body system, 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.

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.

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

Superfluid transition of a ferromagnetic Bose gas

The strongly ferromagnetic spin-1 Bose-Einstein condensate has recently been realized with atomic Li7. It was predicted that a strong ferromagnetic interaction can drive the normal gas into a magnetized phase at a temperature above the superfluid transition, and Li7 likely satisfies the criterion. We reexamine this theoretical proposal employing the two-particle-irreducible effective potential, and conclude that there exists no stable normal magnetized phase for a dilute ferromagnetic Bose gas. For Li7, we predict that the normal gas undergoes a joint first-order transition and jumps directly into a state with finite condensate density and magnetization. We estimate the size of the first-order jump and examine how a partial spin polarization in the initial sample affects the first-order transition. We propose a qualitative phase diagram at fixed temperature for the trapped gas. 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.