Strongly coupled fermionic probe for nonequilibrium thermometry

Abstract

We characterise the measurement sensitivity, quantified by the Quantum Fisher Information (QFI), of a single-fermionic thermometric probe strongly coupled to the sample of interest, a fermionic bath, at temperature $T$. For nonequilibrium protocols, in which the probe is measured before reaching equilibrium with the sample, we find new behaviour of the measurement sensitivity arising due to non-Markovian dynamics. First, we show that the QFI displays a highly non-monotonic behaviour in time, in contrast to the Markovian case where it grows monotonically until equilibrium, so that non-Markovian revivals can be exploited to reach a higher QFI. Second, the QFI rate is maximised at a finite interrogation time $t^{\ast }$, which we characterize, in contrast to the solution $t^{\ast }\to 0$ known in the Markovian limit [Quantum 6, 869 (2022)]. Finally, we consider probes make up of few fermions and discuss different collective enhancements in the measurement precision.

changed some citations. This version is very similar to the one published in NJP

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