Correlated decoherence and thermometry with mobile impurities in a one-dimensional Fermi gas

We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localization as the impurity-gas interaction strength is increased. We then study the nonequilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behavior associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment, and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of nontrivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and they can help to provide more precise temperature estimates of ultracold fermionic mixtures.