Short range inter-vortex interaction and interacting dynamics of half-quantized vortices in two-component Bose-Einstein condensates

TL;DR

This paper investigates the interactions and dynamics of half-quantized vortices in two-component Bose-Einstein condensates, combining analytical approximations and numerical simulations to understand their behavior.

Contribution

It introduces a detailed analysis of vortex interactions using the Pade approximation and derives equations of motion, enhancing understanding of vortex dynamics in multi-component condensates.

Findings

Different vortex trajectories depend on circulation signs and density coupling.

The initial vortex velocities are well-explained by the point vortex model.

Long-term vortex behavior requires models beyond the current approximation.

Abstract

We study the interaction and dynamics of two half-quantized vortices in two-component Bose- Einstein condensates. Using the Pade approximation for the vortex core profile, we calculate the intervortex potential, whose asymptotic form for a large distance has been derived by Eto et al. [Phys. Rev. A, 83, 063603 (2011)]. Through numerical simulations of the two-dimensional Gross-Pitaevskii equations, we reveal different kinds of dynamical trajectories of the vortices depending on the combinations of signs of circulations and the intercomponent density coupling. Under the adiabatic limit, we derive the equations of motion for the vortex coordinates, in which the motion is caused by the balance between Magnus force and the intervortex forces. The initial velocity of the vortex motion can be explained quantitatively by this point vortex approximation, but under- standing the long-time behavior of the dynamics needs more consideration beyond our model.