Probe thermometry with continuous measurements

TL;DR

This paper investigates continuous probe thermometry using a two-level system, demonstrating real-time temperature estimation with Bayesian and adaptive strategies, and analyzing effects of noise in bosonic and fermionic environments.

Contribution

It introduces a comprehensive Bayesian framework for continuous thermometry with a two-level probe, including adaptive strategies and noise impact analysis.

Findings

Adaptive strategies significantly improve precision.

Noise affects short-time measurements more in adaptive methods.

Framework applicable to other environmental parameter estimations.

Abstract

Temperature estimation plays a vital role across natural sciences. A standard approach is provided by probe thermometry, where a probe is brought into contact with the sample and examined after a certain amount of time has passed. In many situations however, continuously monitoring the probe may be preferred. Here, we consider a minimal model, where the probe is provided by a two-level system coupled to a thermal reservoir. Monitoring thermally activated transitions enables real-time estimation of temperature with increasing accuracy over time. Within this framework we comprehensively investigate thermometry in both bosonic and fermionic environments employing a Bayesian approach. Furthermore, we explore adaptive strategies and find a significant improvement on the precision. Additionally, we examine the impact of noise and find that adaptive strategies may suffer more than non-adaptive ones for short observation times. While our main focus is on thermometry, our results are easily extended to the estimation of other environmental parameters, such as chemical potentials and transition rates.