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Gradient fields can effectively suppress particle tunneling in a lattice andlocalize the wave function at all energy scales, a phenomenon known as Starklocalization. Here, we show that Stark systems can be used as a probe for theprecise measurement of gradient fields, particularly in the weak-field regimewhere most sensors do not operate optimally. In the extended phase, Starkprobes achieve super-Heisenberg precision, which is well beyond most of theknown quantum sensing schemes. In the localized phase, the precision drops in auniversal way showing fast convergence to the thermodynamic limit. Forsingle-particle probes, we show that quantum-enhanced sensitivity, withsuper-Heisenberg precision, can be achieved through a simple positionmeasurement for all the eigenstates across the entire spectrum. For suchprobes, we have identified several critical exponents of the Stark localizationtransition and established their relationship. Thermal fluctuations, whoseuniversal behavior is identified, reduce the precision from super-Heisenberg toHeisenberg, still outperforming classical sensors. Multiparticle interactingprobes also achieve super-Heisenberg scaling in their extended phase, whichshows even further enhancement near the transition point. Quantum-enhancedsensitivity is still achievable even when state preparation time is included inresource analysis.

Stark localization as a resource for weak-field sensing with super-Heisenberg precision