Circulation Statistics and Migdal Area Rule Beyond the Kibble-Zurek Mechanism in a Newborn Bose-Einstein Condensate

TL;DR

This paper investigates vortex circulation statistics in a newly formed Bose-Einstein condensate, verifying the Migdal area rule and exploring the universal breakdown and power-law scalings beyond the Kibble-Zurek mechanism.

Contribution

It demonstrates the validity and limits of the Migdal area rule in quantum turbulence and uncovers universal power-law behaviors in circulation statistics beyond KZM predictions.

Findings

Migdal area rule holds for small loops but breaks down for larger loops.

Circulation moments exhibit power-law scaling with quench time.

Universal behavior governed by KZM dynamics is observed in vortex statistics.

Abstract

The Kibble-Zurek mechanism (KZM) predicts that a newly formed superfluid prepared by a finite-time thermal quench is populated with vortices. The universality of vortex number statistics, beyond KZM, enables the characterization of circulation statistics within any region of area $A$ enclosed by a loop $C$. Migdal's minimal area rule of classical turbulence predicts that the probability density function of circulation around a closed contour is independent of the contour's shape. We verify the Migdal area rule for small loops with respect to the distance between the vortex and antivortex pairs and further characterize its universal breakdown for bigger loops. We further uncovered the nonequilibrium universality dictated by the KZM dynamics, which results in power-law scalings of the moments of the circulation statistics as a function of the quench time.