Low-temperature thermometry can be enhanced by strong coupling

TL;DR

This paper demonstrates that strong coupling between a quantum probe and a cold sample can significantly improve the precision of low-temperature measurements, with potential applications in nanoscale quantum thermometry.

Contribution

It provides an analytical model showing how strong probe-sample coupling enhances low-temperature thermometry and suggests engineering the spectral density for further improvements.

Findings

Thermometric precision increases with stronger coupling.

Variance of quadrature yields near-minimal statistical uncertainty.

Spectral density engineering can further enhance performance.

Abstract

We consider the problem of estimating the temperature $ T $ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their non-perturbative interaction. We argue that this is advantageous for low temperature thermometry, as we show in our model that: (i) The thermometric precision at low $ T $ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.