  We investigate how the coherent spreading of the center of mass wave function
of a particle, such as an atom, molecule or ion, affects the particle's
interaction with fields such as the electromagnetic field or a phonon field, in
view also of possible applications to emerging quantum technologies. To this
end, we develop a suitably generalized Unruh-deWitt model for the interaction
between a delocalizing first quantized particle and a second quantized field.
We study how the coherent spreading of the center of mass wave function of the
particle affects emission and absorption rates and we find, in particular, that
in the case of a supersonic coherent spreading in a medium, there should occur
Cherenkov-like emissions, along with the excitation of the particle.
