We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As textit{sensor states}, we use Bell states of the type $left|uparrowdownarrowright>+text{e}^{text{i}varphi}left|downarrowuparrowright>$ encoded in two $^{40}$Ca$^+$ ions stored at different locations. Due to the linear Zeeman effect, the relative phase $varphi$ serves to measure the magnetic field difference between the constituent locations, while common-mode fluctuations are rejected. Consecutive measurements on sensor states encoded in the $text{S}_{1/2}$ ground state and in the $text{D}_{5/2}$ metastable state are used to separate an ac Zeeman shift from the linear dc Zeeman effect. We measure magnetic field differences over distances of up to $6.2~text{mm}$, with accuracies of around 300~fT, sensitivities down to $12~text{pT} / sqrt{text{Hz}}$, and spatial resolutions down to $10~text{nm}$. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.
Download