Josephson phase diffusion in the SQUID ratchet

TL;DR

This paper investigates Josephson phase diffusion in an asymmetric SQUID under periodic driving and magnetic flux, revealing conditions for normal diffusion, its controllability, and the non-chaotic nature of the underlying dynamics.

Contribution

It demonstrates how phase diffusion in an asymmetric SQUID can be controlled and characterized, highlighting the non-chaotic attractors in the deterministic limit.

Findings

Normal phase diffusion occurs with a small diffusion coefficient.

Diffusion can be significantly enhanced by tuning experimental parameters.

The deterministic regime is non-chaotic with simple attractors.

Abstract

We study diffusion of the Josephson phase in the asymmetric SQUID subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. {\L}uczka, New J. Phys. \textbf{17}, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified \emph{several times} by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially \emph{non-chaotic} and possesses an unexpected simplicity of attractors.