Interferometric phenomenologies in a nanoelectromechanical interaction

In this paper, we investigate a nanomechanically induced transparency (NIT) effect that arises from the coupling of a nanoelectromechanical system (NEM) 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 focused 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. In addition, the intriguing effect of coupling between the two phononic modes, switching the response to exhibit the Fano-profile spectra at the output. NEM-Ion interaction in the present nanoelectromechanical system paves the way for future studies of interferometric phenomena in nanoscale architectures, with promising prospects for experimental implementation.