Strongly coupled fermionic probe for nonequilibrium thermometry

Abstract

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>t</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> , which we characterize, in contrast to the solution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>t</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mn>0</mml:mn> </mml:math> 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.