e. two peaks are at Δ pr=±1.2 GHz as shown in Figure 3. The physical origin of this result is due to mechanically induced coherent population oscillation (MICPO), which makes quantum interference between the resonator and the beat of the two optical fields via the QD when the probe-pump detuning is equal to the resonator frequency [58]. DOT1 inhibitor Turning on the QD-MF coupling,

in addition to two sharp peaks located at ±1.2 GHz, the other two sideband peaks induced by the QD-MF coupling appear at Δ pr=±0.5 GHz simultaneously. Figure 3 The optical Kerr coefficient as a function of the probe detuning Δ pr for η =0 . 06. The other parameters used are the same as Figure 2. To illustrate the advantage of the NR in our system, we adjust the detuning Δ MF=-0.5 GHz to Δ MF=-1.2 GHz, in this case, the location of

the two RAD001 sideband peaks induced by the QD-MF coupling coincides with the two sharp peaks induced by the vibration of NR, so the NR is resonant with the coupled QD-MF Smoothened inhibitor system and makes the coherent interaction of QD-MF more strong. Figure 4 gives the result of the optical Kerr coefficient as a function of probe detuning with or without the QD-NR coupling for the QD-MF coupling g=0.03 GHz. The blue and red curves correspond to η=0 and η=0.06, respectively. It is obvious that the role of NR is to narrow and to increase the optical Kerr effect. In this case, the NR as a phonon cavity will enhance the sensitivity for detecting MFs. Figure 4 Optical Kerr coefficient as a function of probe detuning Δ pr with η =0 and η =0 . 06. g=0.03 GHz and Δ MF=-1.2 GHz. The other parameters used are the same as Figure 2. Conclusion

We have proposed a nonlinear optical method to detect the existence of Majorana fermions in semiconductor nanowire/superconductor hybrid structure via a single quantum dot coupled to a nanomechanical resonator. The optical Kerr effect may provide another supplement for detecting Majorana fermions. Due to the nanomechanical resonator, the nonlinear optical effect becomes much more significant and then enhances Ribose-5-phosphate isomerase the detectable sensitivity of Majorana fermions. Finally, we hope that our proposed scheme can be realized experimentally in the future. Acknowledgements The authors gratefully acknowledge support from the National Natural Science Foundation of China (No. 10974133 and No. 11274230). References 1. Nayak C, Simon SH, Stern A, Freedman M, Das SS: Non-Abelian anyons and topological quantum computation . Rev Mod Phys 2008, 80:1083.CrossRef 2. Beenakker CWJ: Search for Majorana fermions in superconductors . Annu Rev Condens Matter Phys 2013, 4:113.CrossRef 3. Stanescu TD, Tewari S: Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment . J Phys Condens Matter 2013, 25:233201.CrossRef 4. Diehl S, Rico E, Baranov MA, Zoller P: Topology by dissipation in atomic quantum wires . Nat Phys 2011, 7:971.CrossRef 5.