Entanglement and quantum superposition induced by a single photon

We predict the occurrence of single-photon-induced entanglement and quantum superposition in a hybrid quantum model, introducing an optomechanical coupling into the Rabi model. Originally, it comes from the photon-dependent quantum property of ground state featured by the proposed hybrid model. It associates with a single-photon-induced quantum phase transition, and is immune to the $A^2$ term of the spin-field interaction. Moreover, the obtained quantum superposition state is actual a squeezed cat state, which can give a significant precision enhancement in quantum metrology. This work offers an approach to manipulate entanglement and quantum superposition with a single photon, which might has potential applications in the engineering of new single-photon quantum devices, and also fundamentally broaden the regime of cavity QED.