Fig. 4: Saturating the fundamental limit.
From: Achieving the ultimate precision limit with a weakly interacting quantum probe
The maximal value of the QFI (15) (red) for gτ = 0.01 and t = 1 as a function of N (log scale). The optimal QFI follows the weak back-action limit (green) given by Eq. (19) when N(gτ)2 ≪ 1. As N increases the back-action corrects the scaling until N(gτ) > 1, where the QFI approaches the strong limit given by Eq. (21). In the strong back-action regime, the QFI of our scheme is only smaller by a factor of e−1 from the optimal QFI, Nt2, achieved by Ramsey spectroscopy (blue).
