# Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation

## TL;DR

This paper investigates the non-equilibrium dynamics of superfluid currents in a Bose-Hubbard ring during the superfluid to Mott insulator transition, revealing persistent oscillations linked to defect formation and spectral gap properties.

## Contribution

It introduces a combined variational and tensor network approach to analyze persistent currents and defect dynamics during the transition in a ring-shaped Bose-Hubbard model.

## Key findings

- Persistent superfluid current oscillations inside the Mott phase.
- Oscillation amplitude correlates with residual energy and defect creation.
- Oscillation frequency matches the spectral gap in the Mott phase.

## Abstract

We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition towards the Mott-insulating phase. By means of a combination of the Time-Dependent Variational Principle and a Tree-Tensor Network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the amplitude of such oscillations is connected to the residual energy, characterizing the creation of defects while crossing the quantum critical point, while their frequency matches the spectral gap in the Mott insulating phase. Our predictions can be verified in future atomtronics experiments with neutral atoms in ring shaped traps. We believe that the proposed setup provides an interesting but simple platform to study the non-equilibrium quantum dynamics of persistent currents experimentally.