Enhanced sensing of a weak Stark field under the influence of Aubry-André-Harper criticality

The localization transition can be exploited as a resource for achieving quantum-enhanced sensitivity in parameter estimation. We demonstrate that by employing different classes of localization inducing potentials, one can significantly enhance the precision of parameter estimation. Specifically, we focus on the precision measurement of the Stark strength parameter encoded in the low- and high-energy eigenstates of a one-dimensional fermionic lattice under the influence of Aubry-André-Harper localization-delocalization transition. For the ground state, we consider the single-particle system, in addition to the system at half filling. Our work reveals that Quantum Fisher Information (QFI) offers superior scaling with respect to the system size compared to the pure Stark case, leading to a better parameter estimation. However, experimental measurement of the QFI based on fidelity in a multibody system is a significant challenge. To address this, we suggest experimentally relevant operators that can be utilized to achieve precision surpassing the Heisenberg Limit (HL) or can even saturate the QFI scaling. These operators, relevant for practical experimental setups, provide a feasible pathway to harness the advantages offered by the localization-delocalization transition by exploiting two distinct localizing potentials for quantum-enhanced parameter estimation.