  In this paper, we investigate a nanomechanically induced transparency (NIT)
effects that arises from the coupling of a nanoelectromechanical system and a
trapped ion. By confining the ion in mesoscopic traps and capacitively coupling
it with a nanoelectromechanical system suspended as electrodes, the research is
intricately focussed on the implications of including the ion's degrees of
freedom. The Lamb--Dicke approximation is crucial to understanding the effects
of phonon exchange with electronic qubits and revealing transparency phenomena
in this unique coupling. The results underline the importance of the
Lamb--Dicke approximation in modelling the effects of transparency windows in
nanoelectromechanical systems.
