Observation of Space-Dependent Rotational Doppler Shifts with a Single Ion Probe

We measured the rotational Doppler effect, which arises in structured vortex-type light beams, on a single ion. The Doppler effect experienced by vortex beams behaves very differently from the standard Doppler effect associated with a non-structured (approximately plane) wave. First, in the standard Doppler effect, the beam is sensitive to the velocity of the object in the direction of the beam’s travel, but not transversally. For example, a speed radar, which operates based on the Doppler effect, can detect the velocity of a car approaching (or receding), but not if the car were driving in circles around the radar. Conversely, if one uses a structured vortex-type beam, it becomes possible to detect the motion of an object moving transversely to the direction of propagation of the sensing beam.

To demonstrate the existence of this effect, we used a laser beam structured in the form of a vortex, which we focused onto a trapped ion to measure its velocity. By controlling the ion’s velocity and position, we observed three distinct features of this rotational Doppler effect. First, as described, it detects motion transverse to the direction of propagation of the beam. Second, the sensitivity to motion increases dramatically as one approaches the center of the beam. Third, the sensitivity is independent of the beam's focus size and depends only on the distance from the center.

The observation of these three unique features confirms the rotational Doppler effect and paves the way for designing new experiments in which we can use this effect for motion sensing. It also opens the door to the observation of a related, even more counterintuitive and yet unobserved effect: Berry's super-kicks, a momentum kick from a light beam that exceeds ℏk.