Figure 3: Schematic of the procedure to compensate a stray electric field E_S.

Our scheme is based on exploiting the a.c. Stark shift induced by a tightly focused dipole laser beam (green) as well as the related modulation of the fluorescence rate of the ion exposed to a detection beam (not shown). The latter is tuned close to the unshifted transition and of nearly constant intensity on the scale of relevant displacements. (a) The dipole beam is first characterized and centred on the ion (black sphere) at maximal confinement (ω_y=2π × (307±0.1) kHz). This is done by displacing the beam along a chosen axis (here y axis) with micrometre screws (see step 1 in the main text) and piezo actuators (see step 2 in the main text and Fig. 4) respectively, as indicated by the double-headed arrow at the bottom. (b) The confinement is switched to its minimal value (ω_y=2π × (27.3±0.1) kHz) and the ion (blue sphere) shifts into the new equilibrium position at lower intensity of the dipole laser beam. Thus, with its transition closer to resonance with the detection beam, this leads to increased fluorescence. (c) The ion is moved to its original position in a with the compensation field E_C induced by potentials applied to compensation electrodes along the y axis (see steps 3 and 4 in the main text and Fig. 5).