# Tunneling of persistent currents in coupled ring-shaped Bose-Einstein condensates

## TL;DR

This paper investigates tunneling dynamics of superfluid currents in coupled ring-shaped Bose-Einstein condensates, revealing Josephson oscillations and vortex formations influenced by persistent currents and initial population imbalances.

## Contribution

It introduces a combined analytical and numerical study of tunneling superflows in coupled ring BECs, highlighting effects of persistent currents on Josephson dynamics and vortex formation.

## Key findings

- Josephson oscillations depend on initial population imbalance.
- Persistent currents significantly influence tunneling superflows.
- Formation of Josephson vortices occurs in hybrid states with counter-rotating currents.

## Abstract

Considerable progress in experimental studies of atomic gases in a toroidal geometry has opened up novel prospects for the investigation of fundamental properties of superfluid states and creation of new configurations for atomtronic circuits. In particular, atomic Bose-Einstein condensates loaded in a dual-ring trap suggest a possibility to consider the tunneling dynamics between coupled condensates with different angular momenta. Accordingly, we address the tunneling in a pair of coaxial ring-shaped condensates separated by a horizontal potential barrier. A weak-coupling truncated (finite-mode) Galerkin model and direct numerical simulations of the underlying three-dimensional Gross-Pitaevskii equation are used for the analysis of tunneling superflows driven by an initial imbalance in atomic populations of the rings. The superflows through the Bose-Josephson junction are strongly affected by persistent currents which are present in the rings. Josephson oscillations of the population imbalance and angular momenta in the coupled rings are obtained for co-rotating states and non-rotating ones. On the other hand, the azimuthal structure of the tunneling flow implies formation of Josephson vortices (fluxons) with zero net current through the junction for hybrid states, built of counter-rotating persistent currents in the coupled rings.