Measuring a single atom's position with extreme sub-wavelength resolution and force measurements in the yoctonewton range

The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing a near-resonant radio frequency field of wavelength 2.37 cm and a static magnetic field gradient of 19 T/m, the spatial location of the ion is determined with an unprecedented wavelength-relative resolution of 5 × 10⁻⁹, corresponding to an absolute precision of 0.12 nm. Measurements of an electrostatic force on a single ion demonstrate a sensitivity of 2.2 × 10⁻²³ ~N/√Hz. The real-time measurement of an atom's position complements the well-established technique of scanning near-field radio frequency transmission microscopy and opens up a novel route to using this method with path breaking spatial and force resolution.