A ring of BEC pools as a trap for persistent flow

TL;DR

This paper investigates how the winding number of a Bose-Einstein condensate in a Josephson junction array evolves during a phase transition, revealing a crossover from Kibble-Zurek scaling to a slow-quench regime where phase rearrangements dominate.

Contribution

It uncovers a new regime in slow quenches where wavefunction phase rearrangements suppress winding number fluctuations, contrasting with traditional Kibble-Zurek predictions.

Findings

Winding numbers decrease with quench time following KZM in fast quenches.

In very slow quenches, winding number variance saturates due to phase rearrangements.

Wavefunction becomes too cold to overcome potential barriers, halting winding number growth.

Abstract

Mott insulator - superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. Resulting winding numbers $W$ of the condensate wavefunction decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches Bose-Hubbard dynamics rearranges wavefunction phase so that its random walk cools, $\bar{W^2}$ decreases and eventually the wavefunction becomes too cold to overcome potential barriers separating different $W$. Thus, in contrast with KZM, in very slow quenches $\bar{W^2}$ is set by random walk with "critical" step size, independently of $\tau_Q$.