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

Abstract

Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function of a single particle at all energy scales, a phenomenon known as Stark localization. The energy-dependent Stark localization transition point, i.e. mobility edge, tends to a transition at infinitesimal fields as the system size increases, closely resembling the Anderson localization without disorder. Here, we show that the single-particle Stark probe not only achieves quantum-enhanced sensitivity for weak-field sensing but also allows for strong super-Heisenberg scaling across its entire spectrum. This quantum-enhanced sensitivity, which is well-beyond most of the known quantum sensing schemes, stretches from the extended phase and goes beyond the transition point and can be achieved by a simple position measurement. Moreover, through extensive finite-size scaling analysis, we have identified several critical exponents of the Stark localization transition and established their relationship. Interestingly, at finite temperatures, the achievable precision reduces to Heisenberg scaling, which is still well beyond the capability of classical sensors. We have also identified a universal behavior for Stark probes at thermal equilibrium with respect to their temperature and system size.