Stable metrological precision of quantum sensing in a common classical environment

This study examines a quantum sensor consisting of two qubits modeled in an XXZ Heisenberg spin chain under a homogeneous magnetic field, for use in quantum thermometry and magnetometry. The sensor is subjected to a common classical environment driven by static noise and is in thermal equilibrium with a heat bath. We analyze the impact of spin–spin, Dzyaloshinskii–Moriya, and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions, as well as the static noise characterized by the disorder parameter, on the sensor's time-evolved state. We also assess the influence of magnetic field homogeneity on performance. Employing quantum Fisher information criteria, we determine the sensor's metrological precision. The performance of the proposed sensor in estimating the external magnetic field and temperature in weak and strong field regimes is different over time with temperature variations. In the strong magnetic field regime, static noise reduces the sensitivity of quantum sensing, while in the weak field regime, this effect is negligible. Our sensor achieves optimal sensitivity and precision for temperature and magnetic field estimation in the presence of static noise and in the weak magnetic field and low temperature regime. Finally, we demonstrate that the quantum sensor achieves a stable sensitivity and precision in its performance over time in quantum magnetometry and thermometry, which can be very valuable in quantum sensing. Moreover, we propose some experimental platforms for the realization of our quantum sensor.