Stability and chaos of a driven nano-electromechanical Josephson junction

TL;DR

This paper investigates the complex dynamics, including stability and chaos, of a mechanically oscillating superconducting island in a Josephson junction, revealing how electromechanical coupling influences its motion under different conditions.

Contribution

It introduces a model describing the electromechanical behavior of a driven nano-electromechanical Josephson junction, highlighting the transition from stable to chaotic dynamics due to bias voltage.

Findings

At zero bias, the system exhibits bistable solutions depending on superconducting phases.

Under bias voltage, the system shows quasi-periodic and chaotic behavior.

The mechanical motion can be described by a modified Duffing equation with time-dependent coefficients.

Abstract

We consider the motion of and Josephson current through a mechanically oscillating superconducting island asymmetrically embedded in a Josephson junction. The electromechanical coupling is provided by distance dependent tunneling rates between the electrodes and the island. The system asymmetry, resulting from the geometrical configuration, leads, for weak coupling, to an equation of the mechanical motion that reduces to the well-known Duffing equation. At zero bias voltage the island motion is determined by the homogenous Duffing equation that opens up two separate regions of solutions depending on the superconducting phases. The island either moves under influence of an anharmonic single well potential, or is governed by a double well potential that allows for off-center oscillations. Under applied bias voltage the island equation of motion turns into a modified Duffing equation, with time dependent coefficients, that demonstrate both quasi periodic and chaotic behavior.