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Journal of Shanxi Datong University

The Dynamics of Vector Soliton in Heteronuclear Two-component Bose-Einstein Condensates

Xueli Feng

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

We have numerically studied the head-on collisions of the bright-bright solitons and bright-dark solitons with different relative phases, based on Gross-Pitaevskii(GP) equation of the quasi-one-dimensional heteronuclear two-component Bose-Einstein condensates. If there is no external potential well, the relative phase zc leads to elastic collision of the bright-bright solitons, but they collide with each other accompanied by some energy transfer for the relative phase π /2. If there is external potential well, they collide periodically with the relative phase π, but with the relative phase π /2, the two solitons combine to one soliton after collision with energy escape. For the bright-dark solitons, their bright-bright solitons in the first component collide periodically with the relative phase 0 or π. The difference of them is that the former has one collision point, the latter two collision points. Furthermore, we have found that the bright-bright solitons are always stable and the bright-dark solitons are unstable by solving its co~esponding Bogoliubov-de Gennes equations.

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We have numerically studied the head-on collisions of the bright-bright solitons and bright-dark solitons with different relative phases, based on Gross-Pitaevskii(GP) equation of the quasi-one-dimensional heteronuclear two-component Bose-Einstein condensates. If there is no external potential well, the relative phase zc leads to elastic collision of the bright-bright solitons, but they collide with each other accompanied by some energy transfer for the relative phase π /2. If there is external potential well, they collide periodically with the relative phase π, but with the relative phase π /2, the two solitons combine to one soliton after collision with energy escape. For the bright-dark solitons, their bright-bright solitons in the first component collide periodically with the relative phase 0 or π. The difference of them is that the former has one collision point, the latter two collision points. Furthermore, we have found that the bright-bright solitons are always stable and the bright-dark solitons are unstable by solving its co~esponding Bogoliubov-de Gennes equations.
We study the phase separation in three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin F=1F=1F=1 ferromagnetic Bose-Einstein condensate upon an increase of the strength of spin-orbit (SO) coupling ${p}_{x}{\mathrm{\ensuremath{\Sigma}}}_{z}$ above a critical value, where px{p}_{x}px​ is the linear momentum and ${\mathrm{\ensuremath{\Sigma}}}_{z}$ is the zzz component of the spin-1 matrix. The bright vector solitons are demonstrated to be mobile and dynamically stable. The collision between two such vector solitons is found to be elastic at all velocities with the conservation of density of each vector soliton. The two colliding vector solitons repel at small separation and at very small colliding velocity, they come close and bounce back with the same velocity without ever encountering each other. This repulsion produced by SO coupling is responsible for the phase separation in a vector soliton for large strengths of SO coupling. The collision dynamics is found to be completely insensitive to the relative phase of the colliding solitons. However, in the absence of SO coupling, at very small velocity, the two colliding vector solitons attract each other and form a vector soliton molecule and the collision dynamics is sensitive to the relative phase as in scalar solitons. The present investigation is carried out through a numerical solution and an analytic variational approximation of the underlying mean-field Gross-Pitaevskii equation.
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the existence of robust DB-soliton molecules, in the form of stationary two- and three-DB-soliton states. Also the equilibrium distance of the constituent solitons and the corresponding oscillation frequencies are found semianalytically, where the latter corresponds to the characteristic anomalous modes' eigenfrequencies that we numerically computed via a so called Bogoliubov-de Gennes (BdG) linearization analysis. Those studies are discussed in Chapter 2. Then, we extend our studies to the dynamics of dark-bright (DB) solitons in binary BECs at finite temperature using a system of two-coupled dissipative GPs. We show that the effect of the bright soliton is to partially stabilize dark solitons against temperature-induced dissipation, thus providing longer lifetimes in Chapter 3. Furthermore, the dark-dark (DD) solitons as a prototypical coherent structure that emerges in two-component BECs are studied and are connected to dark-bright (DB) solitons via SO(2) rotation. We obtained their beating frequency and their frequency of oscillation inside a parabolic trap. They are identified as exact periodic orbits in the Manakov limit of equal inter- and intra- species nonlinearity strengths with and without the trap and we showcase the persistence of such states upon weak deviations from this limit. Also we investigated in detail the effect of the deviation from the Manakov case by considering different from unity scattering length ratios in Chapter 4. Next, we revisited Hamiltonian eigenvalue problems that typically arise in the linearization around a stationary state of a Hamiltonian nonlinear PDE. Also we presented a overview of the known facts for the eigenvalue counts of the corresponding unstable spectra. In particular, we focused on a straightforward plan to implement finite-dimensional techniques for locating this spectrum via the singular points of the meromorphic Krein Matrix and illustrated the value of the approach by considering realistic problems for recently observed experimentally multivortex and multisoliton solutions in atomic Bose-Einstein condensates in Chapter 5. In the two dimensional scenario, we also examine the stability and dynamics of vortices under the effect of dissipation used as a simplified model for the inclusion of the effect of finite temperatures in atomic BECs, which enables an analytical prediction that can be compared directly to numerical results in Chapter 6. In all the above studies, our analytical prediction from the equation of motion are in good agreement with the numerical results from the BdG analysis.
We consider two coupled Gross—Pitaevskii equations describing a two-component Bose—Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.
We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=1)(F=1)(F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the ${m}_{F}=+1,\ensuremath{-}1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasielastic collisions. It is also shown that in the presence of a parabolic trap the bright component(s) is (are) guided by the dark one(s) and, as a result, the small-amplitude vector soliton as a whole performs quasiharmonic oscillations. The oscillation frequency is found as a function of the spin-dependent interaction strength for both small-amplitude and large-amplitude solitons.
We study the interaction of dark-bright solitons in two component Bose-Einstein condensates by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. We show that the coupled Gross-Pitaevskii (GP) equation can be mapped onto the Manakov model. An interesting class of matter wave solitons and their interaction are identified with time independent and periodically modulated trap potentials, which can be experimentally realized in two component condensates. These include periodic collapse and revival of solitons, and snake-like matter wave solitons as well as different kinds of two soliton interactions.
Generation and properties of dark solitons are studied in detail by means of numerical simulation of quasi one-dimensional heteronuclear two-component Bose-Einstein condensates in syntonic potential.Dark solitons are only induced in one of the condensate components by modulational instability with instantaneous conversion of repulsive interspecies interaction to attraction.Solitons pass through each other periodically in syntonic potential.In addition,the number of dark solitons is affiliated with ratio of particle mass and ratio of particles numbers.