Quantum Robust Stability of a Small Josephson Junction in a Resonant Cavity

TL;DR

This paper investigates the robust stability of a Josephson junction within a resonant cavity using quantum control theory, focusing on the effects of sector-bounded nonlinearities introduced by the cosine Hamiltonian.

Contribution

It applies recent quantum stability results to a Josephson junction system with a non-quadratic cosine Hamiltonian, demonstrating the system's stability analysis.

Findings

Established stability conditions for the Josephson junction system.

Extended quantum stability theory to include cosine sector-bounded nonlinearities.

Validated the approach through theoretical analysis.

Abstract

This paper applies recent results on the robust stability of nonlinear quantum systems to the case of a Josephson junction in a resonant cavity. The Josephson junction is characterized by a Hamiltonian operator which contains a non-quadratic term involving a cosine function. This leads to a sector bounded nonlinearity which enables the previously developed theory to be applied to this system in order to analyze its stability.