  We investigate the sensing capacity of non-equilibrium dynamics in quantum
systems exhibiting Bloch oscillations. By focusing on resource efficiency of
the probe, quantified by quantum Fisher information, we find different scaling
behaviors in two different phases, namely localized and extended. Our results
provide a quantitative ansatz for quantum Fisher information in terms of time,
probe size, and the number of excitations. In the long-time regime, the quantum
Fisher information is a quadratic function of time, touching the Heisenberg
limit. The system size scaling drastically depends on the phase changing from
super-Heisenberg scaling in the extended phase to size-independent behavior in
the localized phase. Furthermore, increasing the number of excitations always
enhances the precision of the probe, although, in the interacting systems the
enhancement becomes less eminent than the non-interacting probes, which is due
to induced localization by interaction between excitations.
