Phase-Stable Traveling Waves Stroboscopically Matched for Super-Resolved Observation of Trapped-Ion Dynamics

In quantum technologies, it is essential to understand and exploit the interplay of light and matter. We introduce an approach, creating and maintaining the coherence of four oscillators: a global microwave reference field, a polarization-gradient traveling-wave pattern of light, and the spin and motional states of a single trapped ion. The features of our method are showcased by probing the 140-nm periodic light pattern and stroboscopically tracing dynamical variations in position and momentum observables with noise floors of $1.8(2)$nm and $8(2)$zN$\mu$s, respectively. The implications of our findings contribute to enhancing quantum control and metrological applications.