Collisional dynamics of multiple dark solitons in a toroidal Bose-Einstein condensate: Quasiparticle picture

Abstract

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.

arXiv comment13 pages, 8 figures

References in corpus (23)

• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap
• Hysteresis in a quantized, superfluid atomtronic circuit
• Motion of dark solitons in trapped Bose-Einstein condensates
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity
• Collisions of matter-wave solitons
• Experimental realization of Josephson junctions for an Atom SQUID
• Atomtronics: ultracold atom analogs of electronic devices
• Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
• Bose-Einstein condensates with vortices in rotating traps
• Landau dynamics of a grey soliton in a trapped condensate
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Motion of a Solitonic Vortex in the BEC-BCS Crossover
• Dissipative dynamics of a kink state in a Bose-condensed gas
• Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
• Resistive flow in a weakly interacting Bose-Einstein condensate
• Probing the circulation of ring-shaped Bose-Einstein condensates
• Producing superfluid circulation states using phase imprinting
• Sound Propagation in Elongated Bose-Einstein Condensed Clouds
• Engineering Dark Solitary waves in Ring-Trap Bose-Einstein condensates
• Dark soliton collisions in a toroidal Bose-Einstein condensate
• Quantum gray solitons in confining potentials