Critical quantum thermometry and its feasibility in spin systems

TL;DR

This paper investigates the potential of quantum critical systems for precise temperature sensing, demonstrating how quantum Fisher information scales near critical points in spin systems like Bose-Einstein condensates and Heisenberg chains.

Contribution

It introduces a finite-size scaling framework for quantum Fisher information in critical systems and analyzes its implications for quantum thermometry in experimentally-realizable spin models.

Findings

QFI exhibits finite-size scaling near critical points.

Certain observables nearly saturate the QFI at criticality.

Feasibility of quantum thermometry in spin systems is confirmed.

Abstract

In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the sensitivity in the temperature estimation, and apply a finite-size scaling framework to link this sensitivity to critical exponents of the system around critical points. We numerically calculate the QFI around the critical points for two experimentally-realizable systems: the spin-1 Bose-Einstein condensate and the spin-chain Heisenberg XX model in the presence of an external magnetic field. Our results confirm finite-size scaling properties of the QFI. Furthermore, we discuss experimentally-accessible observables that (nearly) saturate the QFI at the critical points for these two systems.