Majorana bound states induced transparency and slow light enhanced by mechanical resonators in a hybrid quantum system

We present a hybrid quantum system comprising a coupled Majorana-quantum dot-mechanical resonator (Majorana-QD-MR), wherein a two-level QD is simultaneously coupled to both a MR and a Majorana nanowire loop. The latter is a hybrid semiconducting/superconducting nanowire system that hosts two Majorana bound states (MBSs) at its ends. This hybrid system incorporates four distinct coupling mechanisms: QD-MBS coupling, QD-MBS coupling without overlap between the two MBSs, QD-MBS coupling with overlap between the two MBSs, and QD-MR coupling. These couplings collectively determine the optical response of the two-level QD. We investigate the absorption spectra of the two-level QD under conditions of pump resonance and pump detuning. Our findings reveal that MBS-induced transparency with symmetrical splitting is accompanied by rapid dispersion, leading to fast or slow light propagation. Notably, in the case of detuning, double MBS-induced transparency characterized by two asymmetrical Fano-like resonances emerges in the absorption spectra, facilitating transitions between fast and slow light. The introduction of a MR, acting as a phonon cavity, not only enhances the optical response of the QD but also results in a more significant slow and fast light effect generated by the MBSs.