Ring Dark Solitons Research Articles

Stabilization of two-dimensional dark and anti-dark solitons in a nonlocal media

The existence and elastic collision of ring dark and anti-dark solitons in a nonlocal media with an exponential nonlocal response function was first investigated by Horikis and Frantzeskakis (2016 Opt. Lett. 41 583), who found that the initial rings expand outward, keeping their shape during evolution for relatively short propagation distances. In this paper, we study the stability of two-dimensional dark and anti-dark soliton in a nonlocal media by direct numerical simulations. We found that the shapes of the nonlocal response function have a great effect on the propagation of these solitons. In particular, the ring dark solitons can be completely stabilized in a nonlinear media with a cylindrical nonlocal response function due to the boundary force. We also investigate the dynamics of gray ring dark solitons and elliptic dark solitons in detail.

Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates

Multi-component Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work, the notion of magnetic solitons has been introduced. Here we generalize this concept to vector dark-antidark solitary waves in multi-component Bose-Einstein condensates. We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and inter-component repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform numerical continuation studies, investigate the existence of these states and examine their stability using the method of Bogolyubov-de Gennes analysis. Dark-antidark and vortex-antidark states are found to be stable for broad parametric regimes. In the case of ring dark solitons, where the single-component ring state is known to be unstable, the vector entity appears to bear a progressively more and more stabilizing role as the inter-component coupling is increased.

Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited in order to analyze their existence, as well as that of topologically charged variants of the structures, and, importantly, to identify their linear stability Bogolyubov-de Gennes spectrum. We compare our effective 1D spherical and 2D cylindrical computations with the full 3D numerics. An important conclusion is that such spherical shell solitons can be stable sufficiently close to the linear limit of the isotropic condensates considered herein. We have also identified their instabilities leading to the emergence of vortex line and vortex ring cages. In addition, we generalize effective particle pictures of lower dimensional dark solitons and ring dark solitons to the spherical shell solitons concerning their equilibrium radius and effective dynamics around it. In this case too, we favorably compare the resulting predictions such as the shell equilibrium radius, qualitatively and quantitatively, with full numerical solutions in 3D.

Ring dark and antidark solitons in nonlocal media.

Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.

Stabilization of ring dark solitons in Bose-Einstein condensates

Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensate are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. We also explore different proposed particle pictures considering the ring as a moving particle and find, where appropriate, results in very good qualitative and also reasonable quantitative agreement with the numerical findings.

Self-interference of a toroidal Bose–Einstein condensate

We demonstrate the self-interference of a single Bose–Einstein condensate on a non-simply connected geometry, focussing on a toroidally trapped ring-shaped condensate. First, we show how the opposite parts of the ring can interfere using the Wigner function representation. Then, using analytical expressions for the time-evolution of a freely expanding ring-shaped condensate with and without a persistent current, we show that the self-interference of the ring-shaped condensate is possible only in the absence of the persistent current. We conclude by proposing an experimental protocol for the creation of ring dark solitons using the toroidal self-interference.

Reversible decay of ring dark solitons

We show how boundary effects can cause a Bose–Einstein condensate to periodically oscillate between a (circular) array of quantized vortex–antivortex pairs and a (ring) dark soliton. If the boundary is restrictive enough, the ring dark soliton becomes long-lived.

Creation and revival of ring dark solitons in an annular Bose–Einstein condensate

We propose a protocol for the simultaneous controlled creation of multiple concentric ring dark solitons in a toroidally trapped flat Bose–Einstein condensate. The decay of these solitons into a vortex–antivortex necklace shows revivals of the soliton structure, but eventually becomes an example of quantum turbulence.

Generating ring dark solitons in two-component Bose–Einstein condensates

Abstract The dynamical evolution of two-component Bose–Einstein condensates trapped in cylindrical well is numerically investigated by solving the coupled Gross–Pitaevskii equations. We illustrate that, due to intercomponent interaction and different initial component populations ( n 1 n 2 ), different numbers of ring dark (gray) solitons are generated in two components at same time. These solitons have density zeros (minima) accompanied with phase jumps, which cause large superfluid velocities. We also illustrate that at phase jump points ring dark solitons have zero superfluid currents, while ring gray solitons have large superfluid currents. They are unstable and will evolve into other soliton states after a brief time.

Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates

We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.

Snake instability of ring dark solitons in toroidally trapped Bose-Einstein condensates

We show that the onset of the snake instability of ring dark solitons requires a broken symmetry. We also elucidate explicitly the connection between imaginary Bogoliubov modes and the snake instability, predicting the number of vortex-anti-vortex pairs produced. In addition, we propose a simple model to give a physical motivation as to why the snake instability takes place. Finally, we show that tight confinement in a toroidal potential actually enhances soliton decay due to inhibition of soliton motion.

Generation of ring dark solitons by phase engineering and their oscillations in spin-1 Bose-Einstein condensates

The ring dark solitons in spin-1 ${}^{23}$Na and ${}^{87}$Rb Bose-Einstein condensates are studied numerically in the framework of the time-dependent Gross-Pitaevskii equations. By simulating the phase engineering technique in real experiments, we explore the roles of the parameters characterizing the far-off resonant laser pulse which can be used to generate the ring dark solitons. The variations of these parameters have a dramatic effect on the lifetime and the decay profiles of the ring dark solitons. If only one ring dark soliton is generated in one component of the condensate, then ring dark solitons in other components are inclined to be induced, resulting in a coexistence state composed of interdependent ring dark solitons coming from different components of the condensate. Ring dark solitons in this coexistence state exhibit dynamical oscillations for hundreds of milliseconds. By studying the lifetime and decaying profiles of ring dark solitons, we explore the similarities and differences of ${}^{23}$Na and ${}^{87}$Rb condensates. In addition, taking into account the fact that the center of the ring may not coincide with that of the trap, we study the dynamics and decaying profiles of the off-centered ring dark solitons in the presence of the symmetry-breaking effect.

Nucleation in Finite Topological Systems During Continuous Metastable Quantum Phase Transitions

Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit global breaking of the rotational symmetry. This could be realized with current experimental technology.

Soliton characteristics of two-dimensional condensates with two- and three-body interaction

By using multiple-scale method, we study analytically the soliton characteristics of the two-dimensional condensates with two- and three-body interaction. The results show that a ring dark soliton can be found in the condensates when the two-body interaction is repulsive and three-body interaction is attractive. With the strength of the three-body interaction decreasing, the height of the center peak of the ring dark soliton decreases. When the three-body interaction vanishes, the ring dark soliton becomes a perfect dark soliton. If the two- and the three-body interaction are both repulsive,the width and the amplitude of the dark soliton decrease with the strength of the three-body interaction increasing. Especially, if the strength of the three-body interaction is large, which is on the order of that of the two-body interaction, the condensat collapse takes place.

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.

Dynamics of ring dark solitons in Bose–Einstein condensates and nonlinear optics

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schrödinger or Gross–Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.

Vortices and ring dark solitons in nonlinear amplifying waveguides

We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being \emph{stable} against azimuthal perturbations.

Dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction

We investigate both analytically and numerically the dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction. The analytic solutions for the ring dark soliton are derived by using a transformation method. A shallow ring dark soliton is stable when the ring is slightly distorted, while for large deformation of the ring, vortex pairs appear and demonstrate different dynamical behaviors: the vortex pairs transform into dark lumplike solitons and revert to ring dark solitons periodically. Moreover, our results show that the dynamical evolution of the ring dark soliton can be dramatically affected by the Feshbach resonance, and the lifetime of the ring dark soliton can be greatly extended, which offers a useful method for observing ring dark solitons in future experiments.

Spatial weak-light ring dark solitons in an electromagnetically induced transparency medium

By using multiple-scale method，we analytically study the nonlinear dynamical properties of an electromagnetically induced transparency medium with three-level atoms and a strong coupling light field. It is shown that a weak probe light beam can form spatial weak-light dark solitons. When it propagates along axial direction，the dark soliton will transforms into a steady spatial weak-light ring dark soliton，which results from the balance of the interplay between beam diffraction and refractive nonlinearity.

Dynamical properties of ring dark soliton in quasi-two dimensional Bose-Einstein condensates

By developing the multiple-scale method，we study analytically the dynamical properties of soliton in a quasi-two-dimensional Bose-Einstein condensate. For the repulsive inter-atomic interaction，a unstable dark soliton can be found in the condensate，which would evolve into ring dark soliton with small amplitude. Especially，it is shown that the ring dark soliton has dynamic stability.