Dynamical Transition of Quantum Vortex-Pair Annihilation in a Bose-Einstein Condensate

TL;DR

This paper investigates the vortex annihilation process in a 2D Bose-Einstein condensate, revealing a dynamical transition from four-body to three-body vortex interactions influenced by initial vortex density and sound wave energy.

Contribution

It uncovers a dynamical transition in vortex annihilation processes in BECs, dependent on vortex density and sound wave energy, advancing understanding of quantum vortex dissipation mechanisms.

Findings

Existence of a transition from four-body to three-body vortex annihilation.

Transition depends on initial vortex density and sound wave energy.

Shift of transition point with increased confinement along the third dimension.

Abstract

Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, besides the vortex drift-out process from the boundary, vortex-antivortex pair can annihilate in the bulk, but controversy remains on the number of vortices involved in the annihilation process. We find there exists a dynamical transition from four-body to three-body vortex annihilation processes with the time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical transition depends on the initial vortex pair density, and occurs when the sound waves generated in the vortex annihilation process surpass a critical energy. With the confinement along the third direction is relaxed in a quasi-2D BEC, the critical sound wave energy decreases due to the 3D vortex line curve and reconnection, shifting the dynamical transition to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.