Multi-spin probes for thermometry in the strong-coupling regime

TL;DR

This paper investigates how strong coupling between multi-spin probes and a sample affects thermometric sensitivity, revealing enhanced precision at low temperatures beyond weak-coupling limits using quantum Fisher information.

Contribution

It extends thermometry analysis into the strong-coupling regime, demonstrating increased sensitivity with multiple spins and identifying optimal interaction energies for improved temperature estimation.

Findings

Single-spin sensitivity decreases at intermediate coupling but improves at high coupling in low-temperature regimes.

Multi-spin probes can surpass weak-coupling limits with optimal interaction energies.

Enhanced sensitivity can be achieved even with suboptimal measurement strategies.

Abstract

We study the sensitivity of thermometric probes that are composed of $N$ spins coupled to a sample prepared at temperature $T$. Our analysis extends beyond the weak-coupling limit into the strong sample-probe coupling regime. In particular, sample-induced interactions between each of the spins are generated via strong coupling effects and are not fine-tuned amongst each body composing the probe. By employing the reaction-coordinate mapping to evaluate the non-canonical equilibrium state of the probe at finite coupling, we compute the thermometric sensitivity via the quantum Fisher information through the equilibrium state itself. We find that for single-spin probes $(N = 1)$, temperature sensitivity decreases in the regime of weak-to-intermediate coupling strength, however, as the coupling increases we observe much higher sensitivity of the probe in the low-temperature regime. Furthermore, as long as $N > 1$, there exist optimal values of the sample-probe interaction energy that allow one to attain enhanced thermometric sensitivity when compared to the maximum achieved precision obtained from thermal Gibbs states at weak coupling, particularly in the regime of low temperature. Finally, we show that this enhanced sensitivity may be observed from suboptimal measurements.