Sub-micron positioning of trapped ions with respect to the absolute center of a standing-wave cavity field

Abstract

We demonstrate that it is possible, with sub-micron precision, to locate the absolute center of a Fabry–Pérot resonator oriented along the radiofrequency-field-free axis of a linear Paul trap through the application of two simultaneously resonating optical fields. In particular, we apply a probe field, which is near-resonant with an electronic transition of trapped ions, simultaneously with an off-resonant strong field acting as a periodic AC Stark-shifting potential. Through the resulting spatially modulated fluorescence signal, we can find the cavity center of an 11.7-mm-long symmetric Fabry–Pérot cavity with a precision of ±135 nm, which is smaller than the periodicity of the individual standing-wave fields. This can, e.g., be used to position the minimum of the axial trap potential with respect to the center of the cavity at any location along the cavity mode.