Entanglement-Based dc Magnetometry with Separated Ions*

Abstract

We demonstrate sensing of inhomogeneous dc magnetic fields by employing entangled trapped ions, which are shuttled in a segmented Paul trap. As sensor states, we use Bell states of the type |↑↓⟩+e^{iφ}|↓↑⟩ encoded in two ^{40}Ca^{+} ions stored at different locations. The linear Zeeman effect leads to the accumulation of a relative phase φ, which serves for measuring the magnetic-field difference between the constituent locations. Common-mode magnetic-field fluctuations are rejected by the entangled sensor state, which gives rise to excellent sensitivity without employing dynamical decoupling and therefore enables accurate dc sensing. Consecutive measurements on sensor states encoded in the S_{1/2} ground state and in the 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 mm, with accuracies down to 300 fT and sensitivities down to 12 pT/sqrt[Hz]. Our sensing scheme features spatial resolutions in the 20-nm range. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.