Criticality-Enhanced Precision in Phase Thermometry

TL;DR

This paper demonstrates that critical behavior in a 2D Ising lattice significantly enhances the precision of non-invasive quantum thermometry, surpassing mean-field predictions and enabling better investigation of finite many-body systems.

Contribution

It introduces a method for phase-enhanced quantum thermometry using non-Markovian dephasing, revealing critical scaling beyond mean-field models.

Findings

Critical enhancement of quantum Fisher information near phase transitions

Comparison of numerical results with analytic models showing limitations of mean-field theory

Potential for phase metrology to probe critical behavior in finite systems

Abstract

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study non-invasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the non-Markovian dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behaviour of finite many-body systems beyond the validity of mean-field models.