Dynamics of two quantized vortices belonging to different components of binary Bose-Einstein condensates in a circular box potential

TL;DR

This paper investigates the complex dynamics of two quantized vortices in two-component Bose-Einstein condensates within a circular box potential, revealing how their interactions depend on initial conditions and circulation signs.

Contribution

It provides a detailed analysis of vortex interactions in binary condensates, highlighting the effects of intercomponent interactions and initial vortex configurations on their dynamics.

Findings

Vortices can rotate around each other if they have the same circulation sign.

Vortices with opposite circulations initially move together and overlap during evolution.

Interaction with image vortices influences vortex behavior even with repulsive intrinsic interactions.

Abstract

This study aims to research on dynamics of two quantized vortices in miscible two-component Bose--Einstein condensates, trapped by a circular box potential by using the Gross--Pitaevskii equation. We consider a situation in which two vortices belong to different components and they are initially close. Their dynamics are significantly different from those of a vortex pair in a single-component condensate. When two vortices are initially co-located, they are split by dynamical instability or remain co-located depending on their intercomponent interaction. If the two split vortices have the same sign of circulation, they rotate around each other. Then, the angular velocity can be given as a function of the distance between two vortices, which is understood through the equations of motion and their interaction. If the circulations of two close vortices have different signs, however, they move in the same direction initially, then overlap during the dynamics. This subsequent overlap can be categorized into two types based on the initial distance between them. The mechanism of this overlapping can be understood from the interaction between the vortex and its image vortex, which makes the two vortices close to each other even if the intrinsic interaction between them is repulsive.