Strongly coupled fermionic probe for nonequilibrium thermometry

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 \(t^*\), which we characterize, in contrast to the solution \(t^* \rightarrow 0\) 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.