Generating quantum entanglement of phonons assisted by hybrid systems

As a result of study on surface acoustic waves (SAWs), we propose protocols for generating the quantum entanglement on phonons. In the protocol of phonon–photon entanglement generation, the hybrid system is composed of a surface acoustic wave resonator (SAWR), a superconducting resonator (SR) and a nitrogen-vacancy-center ensemble (NVE). For the generation of three phonon modes entanglement, the SAWRs are coupled to the corresponding NVEs, while the NVEs interact with the same SR. Both protocols exploit the resonant interaction and the dispersive coupling. By considering the decoherence of the corresponding systems, the fidelities of the phonon–photon entanglement and three phonon modes entanglement reach 99.35% and 91.01%, respectively. Generalizing the approaches, we also present the protocol of multiple phonon modes entanglement.