Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

TL;DR

This paper introduces an improved critical quantum metrology protocol that quenches beyond the critical point in superradiant systems, achieving exponential quantum Fisher information growth and practical advantages over existing methods.

Contribution

It presents a novel protocol for critical quantum metrology that surpasses previous approaches by quenching beyond the critical point, leading to exponential information gain.

Findings

Exponential increase of quantum Fisher information over time.

Protocol saturation of the Cramér-Rao bound via homodyne detection.

Potential for exponential enhancement with atom number in cavity systems.

Abstract

We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cram\'er-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms $N$ in the cavity, even in the absence of $N$-body coupling terms.