The precise measurement of low temperatures is a challenging, important, and fundamental task for quantum science. In particular, in situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here, we demonstrate that the temperature of a noninteracting Fermi gas can be accurately inferred from the nonequilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity.

• Received 13 April 2020
• Accepted 27 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.080402

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society