Individual quantum probes for optimal thermometry

TL;DR

This paper demonstrates that the most effective quantum thermometer is a two-level atom with a degenerate excited state, and it explores optimal strategies for temperature estimation with partial thermalization.

Contribution

It identifies the optimal quantum probe for thermometry and develops protocols for partial thermalization scenarios, emphasizing the importance of energy spectrum optimization.

Findings

Maximal thermal sensitivity achieved by a two-level atom with degenerate excited state.

Proposed sequential protocol improves estimation when full thermalization is not reached.

Sensitivity increases with the number of energy levels, highlighting the importance of spectrum optimization.

Abstract

The unknown temperature of a sample may be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.