Globalized critical quantum metrology in dynamics of quantum Rabi model by auxiliary nonlinear term

TL;DR

This paper introduces a nonlinear term to the quantum Rabi model, enabling global critical quantum metrology with high precision across all coupling regimes, even under decoherence.

Contribution

It proposes a method to extend the quantum phase transition in the QRM to a continuous regime using an auxiliary nonlinear term, enhancing measurement precision globally.

Findings

Quantum Fisher information diverges across the entire coupling regime.

High measurement precision persists despite decoherence.

The scheme demonstrates a scaling relation with finite frequencies.

Abstract

Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.