Nonlinearity-enhanced quantum sensing in Stark probes

Stark systems in which a linear gradient field is applied across a many-body system have recently been proposed for quantum sensing. Here, we explore sensing capacity of Stark probes, in both single-particle and many-body interacting systems, for estimating nonlinear forms of the gradient fields. Our analysis reveals that, this estimation can achieve super-Heisenberg scaling precision that grows linearly by increasing the nonlinearity. Specifically, we find a universal algebraic relation between the scaling of the precision and the degree of the nonlinearity. This universal behavior remains valid in both single-particle and many-body interacting probes and reflects itself in the properties of the phase transition from an extended to a localized phase, obtained through establishing a comprehensive finite-size scaling analysis. Considering a parabolic gradient potential composed of both linear and nonlinear fields, we used multi-parameter estimation methodology to estimate the components of the gradient potential. The phase diagram of the system is determined in terms of both linear and nonlinear gradient fields showing how the nonlocalized phase turns into a localized one as the Stark fields increase. The sensing precision of both linear and nonlinear Stark fields follows the same universal algebraic relation that was found for the case of single parameter sensing. We demonstrate that simple and experimentally available measurements can reach the theoretical precision bounds. Finally, we show that quantum enhanced sensitivity is still achievable even when we incorporate the preparation time of the probe into our resource analysis.