Multiparameter critical quantum metrology with impurity probes

TL;DR

This paper investigates the use of the two-impurity Kondo model for critical quantum metrology, demonstrating enhanced sensitivity near phase transitions and proposing control strategies to mitigate parameter uncertainty effects.

Contribution

It introduces the two-impurity Kondo model as a new paradigm for critical quantum metrology and analyzes multiparameter estimation at finite temperature.

Findings

Enhanced sensitivity near criticality evidenced by diverging QFI and QSNR.

Singularity in the QFI matrix due to parameter uncertainty can be removed with control fields.

Degradation in measurement sensitivity is linked to parameter correlation.

Abstract

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin-1/2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo (2IK) model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular -- even though the parameters to be estimated are independent -- resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.