Phase-stable traveling waves stroboscopically matched for superresolved 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. Our method employs a UV light pattern capable of achieving a gigahertz-modulation bandwidth, here demonstrated in the megahertz regime, allowing for stroboscopic tracking of dynamic changes in phase space. We achieve noise floors of $1.8\left(2\right)\text{nm}$ for position and $8\left(2\right)\text{zN}\mu s$ for momentum observables, superresolving variations on timescales $\lesssim 100$ ns. The implications of our findings contribute to enhancing quantum control and metrological applications.