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Register a new userRotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction
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We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of repulsive contact interaction does not prevent the existence of those solutions, but allows to control their rotation. We conjecture that self-trapped azimuthons are generic for condensates with attractive nonlocal interaction.
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In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.
Solitons play a fundamental role in dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional uniform Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin dynamics of solitons is governed by a nonlinear Bloch equation. The spin dynamics influences the orbital motion of the solitons leading to the spin-orbit effects in the dynamics of the macroscopic quantum objects (mean-field solitons). The latter perform oscillations with a frequency determined by the SOC, Raman coupling, and intrinsic nonlinearity. These findings reveal unique features of solitons affected by the SOC, which is confirmed by analytical considerations and numerical simulations of the underlying Gross-Pitaevskii equations.
We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with topological charge up to S = 6 (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with S). The largest nonlinearity-localization radius admitting the stabilization of the higher-order vortices is estimated analytically and accurately identified in a numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, S > 1, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.
We introduce an effectively one-dimensional (1D) model of a bosonic gas of particles carrying collinear dipole moments which are induced by an external polarizing field with the strength periodically modulated along the coordinate, which gives rise to an effective nonlocal nonlinear lattice in the condensate. The existence, shape and stability of bright solitons, appearing in this model, are investigated by means of the variational approximation and numerical methods. The mobility of solitons and interactions between them are studied too.
We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions and multiple-dark-bright soliton complexes in atomic t wo-component Bose-Einstein condensates. We study analytically the interactions b etween two-dark-bright solitons in a homogeneous condensate and, then, extend ou r considerations to the presence of the trap. An effective equation of motion is derived for the dark-bright soliton center and the existence and stability of stationary two-dark-bright soliton states is illustrated (with the bright components being either in- or out-of-phase). The equation of motion provides the characteristic oscillation frequencies of the solitons, in good agreement with the eigenfrequencies of the anomalous modes of the system.
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