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(2)0.16em0exnm for position and 8(2)4.pt0exzN0.16em0ex0.16em0exs for momentum observables, superresolving variations on timescales 100 ns. The implications of our findings contribute to enhancing quantum control and metrological applications.