  We present an experiment investigating the rotational Doppler effect using a
single trapped ion excited by two copropagating vortex laser beams. The setup
isolates the azimuthal gradients of the fields, eliminating longitudinal and
curvature effects. We provide a detailed characterization of the phenomenon by
deterministically positioning a single ion across the beams, achieving a signal
which depends on the angular velocity of the ion and the difference of optical
orbital angular momentum between the two beams. The interpretation of the
measurements is supported by numerical simulations and by a simplified
analytical model. Our results reveal key properties of the rotational Doppler
effect, showing that it increases approaching the center of the beam and that
it is independent of the waist of the beam. This offers insights into the
feasibility of super-kicks or super-Doppler shifts for sensing and manipulating
atomic motion transverse to the beams' propagation direction.
