Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

TL;DR

This paper demonstrates that the non-linear quantum Rabi model exhibits higher measurement precision than the linear model due to a first order phase transition at finite frequency, enabling improved quantum metrology applications.

Contribution

It introduces a non-linear extension of the quantum Rabi model showing enhanced criticality and measurement precision, avoiding the slowing-down near critical points of the linear model.

Findings

Non-linear QRM exhibits higher measurement precision.

First order phase transition occurs at finite frequency.

System can be used as a fluxmeter or magnetometer.

Abstract

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.