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 |>+ei|> encoded in two 40Ca+ ions stored at different locations. Due to the linear Zeeman effect, the relative phase 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 S1/2 ground state and in the D5/2 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 of around 300~fT, sensitivities down to 12~pT / Hz, and spatial resolutions down to 10~nm. For optimizing the information gain while maintaining a high dynamic range, we implement an algorithm for Bayesian frequency estimation.
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