The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a non-linear coupling term exhibits much higher measurement precisions due to its first order like phase transition at \emph{finite} frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.
@article{arxiv.2206.08410,
title = {Critical Quantum Metrology in the Non-Linear Quantum Rabi Model},
author = {Zu-Jian Ying and Simone Felicetti and Gang Liu and Daniel Braak},
journal= {arXiv preprint arXiv:2206.08410},
year = {2022}
}