Nonequilibrium Transport in a Superfluid Josephson Junction Chain: Is There Negative Differential Conductivity?

TL;DR

This paper models far-from-equilibrium quantum transport in a 1D Bose-Einstein condensate Josephson junction chain, showing that negative differential conductivity is not valid outside weak coupling, and highlights the importance of quantum fluctuations.

Contribution

The study develops a unitary c-field model that accurately reproduces experimental results without fitting parameters and analyzes the role of quantum fluctuations in the transport dynamics.

Findings

The model matches experimental refilling dynamics across all tunnel couplings.

Negative differential conductivity is invalid outside the weak coupling regime.

Quantum fluctuations significantly influence filling and phase variations.

Abstract

We consider the far-from-equilibrium quantum transport dynamics in a 1D Josephson junction chain of multi-mode Bose-Einstein condensates. We develop a theoretical model to examine the experiment of R. Labouvie et al. [Phys. Rev. Lett. 115, 050601 (2015)], wherein the phenomenon of negative differential conductivity (NDC) was reported in the refilling dynamics of an initially depleted site within the chain. We demonstrate that a unitary c-field description can quantitatively reproduce the experimental results over the full range of tunnel couplings, and requires no fitted parameters. With a view towards atomtronic implementations, we further demonstrate that the filling is strongly dependent on spatial phase variations stemming from quantum fluctuations. Our findings suggest that the interpretation of the device in terms of NDC is invalid outside of the weak coupling regime. Within this restricted regime, the device exhibits a hybrid behaviour of NDC and the AC Josephson effect. A simplified circuit model of the device will require an approach tailored to atomtronics that incorporates quantum fluctuations.