Mind the Gap: Anti-Critical Quantum Metrology

TL;DR

This paper introduces an anti-critical quantum metrology scheme where quantum-enhanced measurement precision is achieved without the slow dynamics typical of critical points, using the quantum Rabi model as an example.

Contribution

It demonstrates that quantum-enhanced sensitivity can occur with increasing energy gaps, avoiding critical slowing down and enabling faster, more practical quantum metrology protocols.

Findings

Quantum-enhanced sensitivity can emerge with increasing energy gaps.

The quantum Rabi model illustrates a route to metrological advantage without critical slowing down.

Precision can remain quantum-enhanced despite shorter evolution times.

Abstract

Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.