Solitons In Bose-Einstein Condensates Research Articles

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.

Autoresonant generation of solitons in Bose-Einstein condensates by modulation of the interaction strength.

The autoresonant approach to generation of solitary structures in Bose-Einstein condensates by chirped frequency space-time modulation of the interaction strength is proposed. Both a spatially periodic case and a finite-size trap are studied numerically within a Gross-Pitaevskii equation. Weakly nonlinear theory of the process is developed in the spatially periodic case using Whitham's averaged variational principle. The theory also describes the threshold phenomenon setting the lowest bound on the amplitude of modulations of the interaction strength for autoresonant excitation.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose–Einstein condensate

Manipulating nonlinear excitations, including solitons and vortices, is an essential topic in quantum many-body physics. A new progress in this direction is a protocol proposed in [Phys. Rev. Res. 2 043256 (2020)] to produce dark solitons in a one-dimensional atomic Bose–Einstein condensate (BEC) by quenching inter-atomic interaction. Motivated by this work, we generalize the protocol to a two-dimensional BEC and investigate the generic scenario of its post-quench dynamics. For an isotropic disk trap with a hard-wall boundary, we find that successive inward-moving ring dark solitons (RDSs) can be induced from the edge, and the number of RDSs can be controlled by tuning the ratio of the after- and before-quench interaction strength across different critical values. The role of the quench played on the profiles of the density, phase, and sound velocity is also investigated. Due to the snake instability, the RDSs then become vortex–antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction. By tuning the geometry of the box traps, demonstrated as polygonal ones, more subtle dynamics of solitons and vortices are enabled. Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in near future cold-atom experiments.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure. The characteristics of these breathing structures can be described by breathing frequency Ω, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a 12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a 12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

One-dimensional Townes solitons in dual-core systems with localized coupling.

The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons. It is based on a dual-core waveguide with quintic self-focusing and fused (localized) coupling between the cores. The respective system of coupled nonlinear Schrödinger equationsgives rise to exact solutions for full families of symmetric and asymmetric solitons, which are produced by the supercritical SSB bifurcation (i.e., the symmetry-breaking phase transition of the second kind). Stability boundaries of asymmetric solitons are identified by dint of numerical methods. Unstable solitons spontaneously transform into robust moderately asymmetric breathers or strongly asymmetric states with small intrinsic oscillations. The setup can be used in the design of photonic devices operating in coupling and switching regimes.

Soliton collisions in spin–orbit coupled spin-1 Bose–Einstein condensates

We investigate analytically the effects of spin–orbit coupling (SOC) for the dynamics of soliton collisions in spin-1 Bose–Einstein condensates (BECs). Applying the non-standard Hirota’s bilinear method, we derive some exact one- and two-soliton solutions for the one-dimensional system of a spin–orbit coupled spin-1 BEC, which clearly shows how the dynamics of the solitons in spinor BECs can be engineered by SOC. Under SOC, the soliton collisions of ferromagnetic-polar type, ferromagnetic-ferromagnetic type and polar-polar type are discussed in details. Comparisons for the soliton states between the systems with and without SOC are displayed, a remarkable phenomenon is that the SOC can lead to the split of a soliton.

Rydberg-dressed solitons in Bose-Einstein condensates with parity-time symmetry

Generating stable bright solitons in free space has been a long-standing goal in the study of matter waves in Bose-Einstein condensates (BECs). Rydberg-induced matter wave demonstrates an excellent effect in balancing the repulsive and attractive interactions between remote atoms. Parity-time (PT) symmetric lattices have been widely studied in controlling the flow of matter waves. In this study, we theoretically investigated the localization of nonlinear matter waves in the PT-symmetric Rydberg atomic BECs system. The numerical simulation method was used to obtain the stationary solutions of the wave function by solving the Gross-Pitaevskii equation (GPE) of the Rydberg-dressed BECs system. Fundamental, higher-order solitons and vortical ones were uncovered, and their stabilities were evaluated through linear-stability analysis and direct simulation with perturbation. Furthermore, the collision of solitons exhibited a quasi-elastic feature.

Interaction of chiral solitons in a Bose-Einstein Condensate under density-dependent gauge potential

The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.

Nonlinear Fourier analysis of matter-wave soliton interferometry

The bright solitons in quasi-1D atomic Bose-Einstein condensates are good candidates for constructing matter-wave interferometers with high sensitivity and long phase-accumulation times. Such interferometers at the mean-field level can be theoretically studied within the framework of quasi-1D Gross-Pitaevskii (GP) equation with narrow repulsive potential barriers. In this paper we present a basic proposal of using the nonlinear Fourier transform (NFT), also known as the inverse scattering transform, as an effective tool to analyze the soliton contents for those interferometers, which thanks to the nearly integrable nature of the GP equation when the normalized atom number fraction near the barrier is small. Based on typical cases, we show that the soliton components can be accurately detected from the output wave fields of the interferometers by computing the NFT spectra.

Two-dimensional bright soliton in exciton-polariton condensate

In non-conservative nonlinear systems, the basic physical mechanics of soliton generation is that the kinetic energy and nonlinear terms of the system, as well as the gain and dissipation terms reach a double dynamic balance. How to generate stable free high-dimensional solitons in such a system is currently a challenging topic in soliton theory. In this article, we propose a theoretical scheme for realizing two-dimensional free bright solitons in exciton-polariton Bose-Einstein condensates, which proposes a physical mechanism for generating stable two-dimensional free space bright solitons through time periodic modulation interactions and a dual balance between gain and dissipation. In this end, firstly, we obtain the dynamic equations of two-dimensional bright soliton parameters through the Lagrange variational method, and obtain its dynamically stable parameter space. Secondly, the evolution of the generalized dissipative Gross-Pitaveskii equation is numerically simulated to verify the stability of two-dimensional bright solitons. Finally, we add Gaussian noise to simulate a real experimental environment and find that two-dimensional bright solitons are also stable within the observable time range of the experiment. Our experimental scheme opens the door to the study of bright solitons in high-dimensional free space in non-conservative systems.

Exact analytical soliton solutions of N-component coupled nonlinear Schrödinger equationswith arbitrary nonlinear parameters.

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not hold in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in N-component coupled nonlinear Schrödinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameter regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

Observing phase jumps of solitons in Bose-Einstein condensates

The phase difference of the macroscopic wave function is a unique structure of the soliton in an atomic Bose--Einstein condensate (BEC). However, experiments on ultracold atoms so far have observed the valley of the density profile to study the dynamics of solitons. We propose a method to observe the phase difference of a soliton in a BEC by using an interference technique with Raman and rf pulses. We introduce a phase jump factor, which is an indicator to measure the phase difference between two points. It is demonstrated by using the projected Gross--Pitaevskii equation that an interference density ratio, the density ratio of two-component BECs after the Raman and rf pulses, reproduces the phase jump factor well. This technique will become an alternative method to study the decay and breakdown of a phase imprinted soliton in atomic BECs.

Dynamics of a pair of overlapping polar bright solitons in spin-1 Bose-Einstein condensates

We analyze the dynamics of both population and spin densities, emerging from the spatial overlap between two distinct polar bright solitons in Spin-1 Spinor Condensates. The dynamics of overlapping solitons in scalar condensates exhibits soliton fusion, atomic switching from one soliton to another and repulsive dynamics depending on the extent of overlap and the relative phase between the solitons. The scalar case also helps us understand the dynamics of the vector solitons. In the spinor case, non-trivial dynamics emerge in spatial and spin degrees of freedom. In the absence of spin changing collisions, we observe Josephson-like oscillations in the population dynamics of each spin component. In this case, the population dynamics is independent of the relative phase, but the dynamics of the spin-density vector depends on it. The latter also witnesses the appearance of oscillating domain walls. The pair of overlapping polar solitons emerge as four ferromagnetic solitons irrespective of the initial phase difference for identical spin-dependent and spin-independent interaction strengths. But the dynamics of final solitons depends explicitly on the relative phase. Depending on the ratio of spin-dependent and spin-independent interaction strengths, a pair of oscillatons can also emerge as the final state. Then, increasing the extent of overlap may lead to the simultaneous formation of both a stationary ferromagnetic soltion and a pair of oscillatons depending on the relative phase.

Soliton Interferometry with Very Narrow Barriers Obtained from Spatially Dependent Dressed States.

Bright solitons in atomic Bose-Einstein condensates are strong candidates for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. An analog to a beam splitter is then a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but in a typical realization using a blue-detuned optical dipole potential, the width is limited by the laser wavelength. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal configuration.

Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings.

Dynamics of nondegenerate vector solitons in a long-wave-short-wave resonance interaction system.

In this paper, we study the dynamics of an interesting class of vector solitons in the long-wave-short-wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of long wave and two short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multisoliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave component, while a single-humped soliton propagates in the two short-wave components. We establish through a detailed analysis that the nondegenerate multisolitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape-preserving, (ii) shape-altering, and (iii) a shape-changing collision, depending on the choice of the soliton parameters. Here, by shape-altering we mean that the structure of the nondegenerate soliton gets modified slightly during the collision process, whereas if the changes occur appreciably then we call such a collision as shape-changing collision. We distinguish each of the collision scenarios, by deriving a zero phase shift criterion with the help of phase constants. Very importantly, the shape-changing behavior of the nondegenerate vector solitons is observed in the long-wave mode also, along with corresponding changes in the short-wave modes, and this nonlinear phenomenon has not been observed in the already known vector solitons. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics when the long-wave-short-wave resonance interaction is taken into account.

Stability of Spin-Wave Solitons in Bose-Einstein Condensates of Magnons: A Possible Application in Ferromagnetic Films.

In this paper, we theoretically investigate the stability of spin-wave solitons in Bose-Einstein condensates of repulsive magnons, confined by an inhomogeneous external magnetic field described by a Gaussian well. For this purpose, we use the quasi-one-dimensional Gross-Pitaevskii equation to describe the behavior of the condensate. In order to solve the Gross-Pitaevskii equation, we used two different approaches: one analytical (variational method) and another numerical (split-step Crank-Nicolson method). The stability of the solutions and the validation of the numerical results were confirmed, respectively, through the anti-VK criterion and the virial theorem. Furthermore, the simulations described the behavior of physical quantities of interest such as chemical potential, energy per magnon and central density as a function of the nonlinearity of the model (magnon-magnon interactions). The theoretical results provide subsidies for a better understanding of the nonlinear phenomena related to the Bose-Einstein condensates of magnons in ferromagnetic films.

Magnetic solitons in an immiscible two-component Bose-Einstein condensate

We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to dark-bright solitons, other characteristic properties such as maximum velocities, widths, total density depletions, and in-trap oscillations are different. In the low-velocity regime, a magnetic soliton reduces to a traveling pair of magnetic domain walls. Collisional behaviors of the solitons are also briefly discussed. We further demonstrate that these solitonic states can be realized in a quasi-one-dimensional spin-1 ferromagnetic BEC with a weak spin interaction, e.g., a $^{87}\mathrm{Rb}$ BEC.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose–Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross–Pitaevskii equation describing the three-component Bose–Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

Negative mass effects of a spin soliton in Bose-Einstein condensates

We investigate the energy-velocity dispersion relation of spin solitons with arbitrary initial velocities. Based on the dispersion relation, we further characterize the inertial mass of a spin soliton and find two critical velocities to distinguish between the positive mass and negative mass. One critical velocity separates the initial negative and positive masses, and the other denotes the velocity for negative-positive mass transition during an acceleration process. With the aid of the two critical velocities, we further propose two possible ways to observe the pure negative mass effect of a spin soliton. Moreover, the relations between the soliton's width and its velocity are discussed according to the variational results. We report that the soliton width can become narrower with larger moving speed (when a spin soliton possesses positive mass), in sharp contrast to the dark solitons reported before. These results would motivate experiments to observe negative mass effects of solitons in Bose-Einstein condensates.