Dynamics of vortex quadrupoles in nonrotating trapped Bose-Einstein condensate

TL;DR

This paper investigates the dynamics of vortex quadrupoles in trapped 2D Bose-Einstein condensates, identifying three regimes of behavior and mechanisms of vortex interactions, with implications for understanding superfluid phenomena.

Contribution

It provides a detailed analysis of vortex quadrupole dynamics, including regime classification and mechanisms, applicable to both mean-field and quantum fluctuation systems.

Findings

Three distinct dynamical regimes identified: recombination, exchange, and annihilation.

Charge flipping and vortex disappearance occur via an intermediate soliton ring state.

Parameter ranges for regimes and phase diagram of vortex positions are established.

Abstract

Dynamics of vortex clusters is essential for understanding diverse superfluid phenomena. In this paper, we examine the dynamics of vortex quadrupoles in a trapped two-dimensional (2D) Bose-Einstein condensate. We find that the movement of these vortex-clusters fall into three distinct regimes which are fully described by the radial positions of the vortices in a 2D isotropic harmonic trap, or by the major radius (minor radius) of the elliptical equipotential lines decided by the vortex positions in a 2D anisotropic harmonic trap. In the "recombination" and "exchange" regimes the quadrupole structure maintains, while the vortices annihilate each other permanently in the "annihilation" regime. We find that the mechanism of the charge flipping in the "exchange" regime and the disappearance of the quadrupole structure in the "annihilation" regime are both through an intermediate state where two vortex dipoles connected through a soliton ring. We give the parameter ranges for these three regimes in coordinate space for a specific initial configuration and phase diagram of the vortex positions with respect to the Thomas-Fermi radius of the condensate. We show that the results are also applicable to systems with quantum fluctuations for the short-time evolution.