Collisional dynamics of multiple dark solitons in a toroidal Bose–Einstein condensate: quasiparticle picture

JEZEK, DORA M.; CATALDO, HORACIO M.

EUROPEAN PHYSICAL JOURNAL D

SPRINGER

Año: 2018 vol. 72

1434-6060

We study the collisional dynamics of multiple dark solitons in a Bose-Einstein condensate confined by a  toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence of solitonic vortices. Analytical expressions for the initial order parameters with imprinted phases are utilized to generate different initial arrays of solitons, for which the time-dependent  Gross-Pitaevskii equation is numerically solved. Given that the soliton velocity is conserved due to the lack of  dissipation, we are able to apply a simple quasiparticle  description  of the soliton dynamics. In fact, the  trajectory equations are written in terms of the  velocities and the angular shifts produced at each collision, in analogy to the infinite one-dimensional system. To calculate the angular shifts, we directly extract them from the trajectories  given by the Gross-Pitaevskii simulations and, on the other hand, we show that  accurate values can be analytically obtained  by adapting a formula valid for the  infinite one-dimensional system that involves the healing length, which in our inhomogeneous system  must be evaluated  in terms of the sound velocity along the azimuthal direction. We further  show that  very good estimates of such a sound velocity can be directly determined by using the ground state density profile  and the values of the imprinted phases. We discuss the possible implementation of the system here proposed using the current experimental techniques.