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 ∗ → 0 known in the Markovian limit (Pavel Sekatski and Martí Perarnau-Llobet 2022 Quantum 6 869). Finally, we consider probes make up of few fermions and discuss different collective enhancements in the measurement precision.