Entangled three-particle states and phonon pairs in an optomechanical system with quadratic mechanical-displacement coupling

We study the generation of three-particle (one photon plus two phonons) states and phonon pairs in a cavity-waveguide system where the optomechanical coupling is quadratic in the mechanical displacement. Both the three-particle state and the phonon pair exhibit quantum entanglement in the continuous frequency domain, and the entanglement can be controlled by adjusting the pump-pulse spectral width. By introducing a phantom waveguide, we can analyze the impact of intrinsic cavity losses on the quantum-state generation, and we find that the cavity losses can actually enhance the entanglement in the successfully generated three-particle state or phonon pair.