Quantum critical metrology

TL;DR

This paper demonstrates that quantum critical points in many-body systems can be exploited for enhanced quantum metrology, achieving precision beyond standard limits through quantum critical squeezing.

Contribution

It introduces the concept of quantum critical squeezing in many-body systems, showing its potential for improved quantum metrology near quantum phase transitions.

Findings

Quantum criticality enables squeezing of one spin component.

Scaling of estimation precision exceeds standard quantum limit in 2D and 3D.

Quantum critical squeezing approaches the quantum Fisher information bound.

Abstract

Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that, under equilibrium conditions, the management of quantum noise becomes extremely flexible around the quantum critical point of a quantum many-body system: this is due to the critical divergence of quantum fluctuations of the order parameter, which, via Heisenberg's inequalities, may lead to the critical suppression of the fluctuations in conjugate observables. Taking the quantum Ising model as the paradigmatic incarnation of quantum phase transitions, we show that it exhibits quantum critical squeezing of one spin component, providing a scaling for the precision of interferometric parameter estimation which, in dimensions $d \geq 2$, lies in between the standard quantum limit and the Heisenberg limit. Quantum critical squeezing saturates the maximum metrological gain allowed by the quantum Fisher information in $d=\infty$ (or with infinite-range interactions) at all temperatures, and it approaches closely the bound in a broad range of temperatures in $d=2$ and 3. This demonstrates the immediate metrological potential of equilibrium many-body states close to quantum criticality, which are accessible \emph{e.g.} to atomic quantum simulators via elementary adiabatic protocols.