Nonclassical correlation between optical and microwave photons in a hybrid electro-optomechanical system

•Correlate optical and microwave photons in a hybrid electro-optomechanical system.•Nonclassical correlated photon pairs are generated in the weak coupling condition.•The cross-correlation function strongly violates the Cauchy–Schwarz inequality.•Combine the advantages of optical photons, microwave photons, and phonons.

A scheme to correlate optical and microwave photons is proposed in a hybrid electro-optomechanical system, where mechanical resonator is coupled to both optical and microwave fields. Analytical and numerical simulation results show that the cross-correlation function between Stokes and anti-Stokes photons strongly violates the Cauchy–Schwarz inequality, which confirms the nonclassical correlation between the optical and microwave photons. It is worth noting that the nonclassical photon pairs with vast different wavelengths, which may be useful for quantum communication, are generated under the experimentally accessible weak coupling limit rather than single-photon strong coupling regime. In addition, the protocol provides a possible route to combine the respective advantages of optical photons, microwave photons, and phonons in a hybrid electro-optomechanical system.