Dynamics of trapped interacting vortices in Bose-Einstein condensates: Role of breathing degree of freedom

TL;DR

This paper explores how the breathing width degree of freedom influences vortex dynamics in trapped Bose-Einstein condensates, revealing oscillations and chaos through a variational approach and Hamiltonian formalism.

Contribution

It introduces a variational method incorporating vortex core breathing modes, uncovering their impact on vortex interactions and chaotic behavior in BECs.

Findings

Rapid radial breathing oscillations observed

Breathing mode induces chaos in vortex dynamics

Derived charge-dependent inter-vortex interactions

Abstract

With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose-Einstein condensates in 2 dimensions under the strong repulsive cubic nonlinearity. As for the trial function, we choose a product of two vortex functions assuming a pair interaction and employ the amplitude form of each vortex function in the Pad\'e approximation which accommodates a hallmark of the vortex core. We have obtained Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of Gross-Pitaevskii equation. In higher-energy states of 2 vortex systems, the breathing width degree of freedom plays role of a kicking in the kicked rotator and generates chaos with a structure of sea-urchin needles. Byproduct of the present variational approach includes: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.