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We theoretically investigate the pure dephasing dynamics of two staticimpurity qubits embedded within a common environment of ultracold fermionicatoms, which are confined to one spatial dimension. Our goal is to understandhow bath-mediated interactions between impurities affect their performance asnonequilibrium quantum thermometers. By solving the dynamics exactly using afunctional determinant approach, we show that the impurities become correlatedvia retarded interactions of the Ruderman-Kittel-Kasuya-Yosida type. Moreover,we demonstrate that these correlations can provide a metrological advantage,enhancing the sensitivity of the two-qubit thermometer beyond that of twoindependent impurities. This enhancement is most prominent in the limit of lowtemperature and weak collisional coupling between the impurities and the gas.We show that this precision advantage can be exploited using standard Ramseyinterferometry, with no need to prepare correlated initial states nor toindividually manipulate or measure the impurities. We also quantitativelyassess the impact of ignoring these correlations when constructing atemperature estimate, finding that acceptable precision can still be achievedfrom a simplified model of independent impurities. Our results demonstrate therich nonequilibrium physics of impurities dephasing in a common Fermi gas, andmay help to provide better temperature estimates at ultralow temperatures.

Thermometry by correlated dephasing of impurities in a 1D Fermi gas