  We investigate confinement-induced resonances in atom-ion quantum mixtures
confined in hybrid traps. Specifically, we consider an ion confined in a
time-dependent radio-frequency Paul trap with linear geometry, while the atom
is constrained to move into a quasi-one-dimensional optical waveguide within
the ion trap. We evaluate the impact of the ion intrinsic micromotion on the
resonance position. Thus, we solve the atom-ion dynamics semiclassically,
namely the atom dynamics is governed by the three-dimensional time-dependent
Schr\"odinger equation, whereas the ion motion is described by the classical
Hamilton equations. We find that the energy of the ion provided by the
oscillating radiofrequency fields can affect the resonance position
substantially. Notwithstanding, the peculiar phenomenology of those resonances
regarding perfect transmission and reflection is still observable. These
findings indicate that the intrinsic micromotion of the ion is not detrimental
for the occurrence of the resonance and that its position can be controlled by
the radiofrequency fields. This provides an additional mean for tuning atom-ion
interactions in low spatial dimensions. The study represents an important
advancement in the scattering physics of compound atomic quantum systems in
time-dependent traps.
