We investigate theoretically Rabi-like splitting and Fano resonance in absorption spectra of quantum dots (QDs) based on a hybrid QD-semiconducting nanowire/superconductor (SNW/SC) device mediated by Majorana fermions (MFs). Under the condition of pump on-resonance and off-resonance, the absorption spectrum experiences the conversion from Fano resonance to Rabi-like splitting in different parametric regimes. In addition, the Fano resonances are accompanied by the rapid normal phase dispersion, which will indicate the coherent optical propagation. The results indicate that the group velocity index is tunable with controlling the interaction between the QD and MFs, which can reach the conversion between the fast- and slow-light. Fano resonance will be another method to detect MFs and our research may indicate prospective applications in quantum information processing based on the hybrid QD-SNW/SC devices.

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