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Register a new userInelastic Collisions of Solitary Waves in Anisotropic Bose-Einstein Condensates: Sling-Shot Events and Expanding Collision Bubbles
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We study experimentally and theoretically the dynamics of apparent dark soliton stripes in an elongated Bose-Einstein condensate. We show that for the trapping strengths corresponding to our experimental setup, the transverse confinement along one of the tight directions is not strong enough to arrest the formation of solitonic vortices or vortex rings. These solitonic vortices and vortex rings, when integrated along the transverse direction, appear as dark soliton stripes along the longitudinal direction thereby hiding their true character. The latter significantly modifies the interaction dynamics during collision events and can lead to apparent examples of inelasticity and what may appear experimentally even as a merger of two dark soliton stripes. We explain this feature by means of the interaction of two solitonic vortices leading to a sling shot event with one of the solitonic vortices being ejected at a relatively large speed. Furthermore we observe expanding collision bubbles which consist of repeated inelastic collisions of a dark soliton stripe pair with an {it increasing} time interval between collisions.
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We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multi-dimensional space of the chemical potentials. The Bogolyubov-de Gennes (BdG) spectra analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical $SU(n)$-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.
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We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities $ell =0$ (fundamental solitons), $ell =1$, and $ell =2$. The fundamental solitons and vortices with $ell =1$ exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with $ell =2$ are stable solely in the isotropic model.
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