Ultrasensitive single-ion electrometry in a magnetic field gradient.

Hyperfine energy levels in trapped ions offer long-lived spin states. In addition, the motion of these charged particles couples strongly to electric field perturbations. These characteristics make trapped ions attractive platforms for the quantum sensing of electric fields. However, the spin states do not exhibit a strong intrinsic coupling to electric fields, lim iting the achievable sensitivity. Here, we amplify the coupling between electric field perturbations and the spin states by using a static magnetic field gradient. Displacements of the trapped ion resulting from the applied electric field perturbations are thereby mapped to an instantaneous change in the energy-level splitting of the internal spin states. This gradient-mediated coupling of the electric field to the spin enables the use of well-established magnetometry protocols for electrometry, making it possible to achieve extremely sensitive measurements of d.c. and a.c. electric fields. We also employ a rotating-frame relaxometry technique and demonstrate the use of our quantum sensor as an electric field noise spectrum analyser. Finally, we describe a set of hardware modifications that are capable of achieving a further improvement in sensitivity by up to six orders of magnitude.