Precision thermometry and the quantum speed limit

TL;DR

This paper investigates the limits of quantum thermometry, revealing how system properties like energy gaps influence temperature estimation precision and exploring the role of dynamics and anharmonicity.

Contribution

It introduces a framework linking energy gaps to optimal temperature estimation and analyzes how system spectra and dynamics affect thermometry precision.

Findings

Energy gap determines a single optimal temperature for harmonic systems

Precision scales quadratically with the temperature for these systems

Anharmonicity and degeneracy can significantly improve thermometry accuracy

Abstract

We assess precision thermometry for an arbitrary single quantum system. For a $d$-dimensional harmonic system we show that the gap sets a single temperature that can be optimally estimated. Furthermore, we establish a simple linear relationship between the gap and this temperature, and show that the precision exhibits a quadratic relationship. We extend our analysis to explore systems with arbitrary spectra, showing that exploiting anharmonicity and degeneracy can greatly enhance the precision of thermometry. Finally, we critically assess the dynamical features of two thermometry protocols for a two level system. By calculating the quantum speed limit we find that, despite the gap fixing a preferred temperature to probe, there is no evidence of this emerging in the dynamical features.