The Josephson junction as a quantum engine

TL;DR

This paper models the Josephson junction as a quantum engine using a Markovian master equation, explaining its current-voltage behavior, self-oscillations, and radiation, with implications for quantum thermodynamics.

Contribution

It introduces a novel quantum engine perspective of the Josephson junction, providing a dynamical model that captures key experimental features and explains self-oscillations and radiation phenomena.

Findings

The model reproduces the current-voltage characteristic and hysteresis.

It predicts self-oscillation at frequency 2eV/ħ.

It explains the generation of monochromatic radiation and harmonics.

Abstract

We treat the Cooper pairs in the superconducting electrodes of a Josephson junction (JJ) as an open system, coupled via Andreev scattering to external baths of electrons. The disequilibrium between the baths generates the direct-current bias applied to the JJ. In the weak-coupling limit we obtain a Markovian master equation that provides a simple dynamical description consistent with the main features of the JJ, including the form of the current-voltage characteristic, its hysteresis, and the appearance under periodic voltage driving of discrete Shapiro steps. For small dissipation, our model also exhibits a self-oscillation of the JJ's electrical dipole with frequency $\Omega = 2 e V / \hbar$ around mean voltage $V$. This self-oscillation, associated with "hidden attractors" of the nonlinear equations of motion, explains the observed production of monochromatic radiation with frequency $\Omega$ and its harmonics. We argue that this picture of the JJ as a quantum engine resolves open questions about the Josephson effect as an irreversible process and could open new perspectives in quantum thermodynamics and in the theory of dynamical systems.