By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.
By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.
We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (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.
Spin mixing induced dynamics of spinor solitons in F=1 Bose Einstein condensates
We explore soliton interactions in a homogeneous spinor F=1 Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.
Abstract By adopting a mean-field Gross–Pitaevskii description of spinor polariton Bose–Einstein condensates under nonresonant pumping, we investigate the static and dynamical properties of dark–bright (DB) solitons. We derive the equation of motion for the center of mass of the DB solitons’ center analytically by using the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and the spin degrees of freedom of a polariton Bose–Einstein condensate affects the properties of DB solitons, i.e. DB solitons relax by blending with the background at a finite time. In this case, we also determine the lifetime of the DB solitons. Further numerical solutions of the modified dissipative two-component Gross–Pitaevskii equations are in excellent agreement with the analytical results. In the presence of the Langevin noise, we demonstrate that the DB solitons can still propagate for a long time, which is sufficient for their experimental observations within current facilities.
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we
We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component, and spinor Bose-Einstein condensates. The formation of solitonic entities of the dark-bright type is based on the so-called matter-wave interference of spatially separated condensates. In all three cases, a systematic numerical study is carried out upon considering different variations of each system's parameters both in the absence and in the presence of a harmonic trap. It is found that manipulating the initial separation or the chemical potential of the participating components allows us to tailor the number of nucleated dark-bright states. Particularly, the number of solitons generated increases upon increasing either the initial separation or the chemical potential of the participating components. Similarities and differences of the distinct models considered herein are showcased, while the robustness of the emerging states is illustrated via direct numerical integration, demonstrating their long time propagation. Importantly, for the spinorial system, we unravel the existence of beating dark soliton arrays that are formed due to the spin-mixing dynamics. These states persist in the presence of a parabolic trap, often relevant for associated experimental realizations.
We study the formation of solitons in a uniform quasi-one-dimensional (quasi-1D) spin-orbit (SO) coupled self-repulsive pseudo spin-half and spin-one dipolar Bose-Einstein condensates (BEC), using the mean-field Gross-Pitaevskii equation. The dipolar atoms are taken to be polarized along the quasi-1D x direction. In the pseudo spin-half case, for small SO-coupling, one can have dark-bright and bright-bright solitons. For large SO coupling, the dark-bright and bright-bright solitons may acquire a spatially-periodic modulation in density; for certain values of contact interaction paramerers there is only the normal bright-bright soliton without spatially-periodic modulation in density. In the spin-one anti-ferromagnetic case, for small SO coupling, one can have bright-bright-bright, dark-bright-dark, and bright-dark-bright solitons; and for large SO coupling, the dark-bright-dark and bright-dark-bright solitons are found to have spatially-periodic modulation in density. In the spin-one ferromagnetic case, for both small and large SO coupling, we find only bright-bright-bright solitons. All these solitons, specially those with a dark-soliton component, are dynamically stable as demonstrated by real-time propagation using the converged stationary solution obtained by imaginary-time propagation as the initial state.