# Quantum properties of a strongly driven Josephson junction

## TL;DR

This paper investigates the quantum behavior of a strongly driven Josephson junction, revealing complex dynamics beyond classical models and highlighting the influence of quantum fluctuations on its nonlinear properties.

## Contribution

It provides a detailed quantum analysis of a driven Josephson junction, extending beyond the Duffing approximation and exploring classical-quantum correspondence in nonlinear regimes.

## Key findings

- Identification of parameter regions where Duffing approximation is valid
- Analysis of quantum fluctuations affecting junction parameters
- Study of quantum effects on dynamics near classical fixed points

## Abstract

A Josephson junction embedded in a dissipative circuit can be externally driven to induce nonlinear dynamics of its phase. Classically, under sufficiently strong driving and weak damping, dynamic multi-stability emerges associated with dynamical bifurcations so that the often used modeling as a Duffing oscillator, which can exhibit bi-stability at the most, is insufficient. The present work analyzes in this regime corresponding quantum properties by mapping the problem onto a highly-nonlinear quasi-energy operator in a rotating frame. This allows us to identify in detail parameter regions where simplifications such as the Duffing approximation are valid, to explore classical-quantum correspondences, and to study how quantum fluctuations impact the effective junction parameters as well as the dynamics around higher amplitude classical fixed points.