Continuous mode cooling and phonon routers for phononic quantum networks

We study the implementation of quantum state transfer protocols in phonon networks, where, in analogy to optical networks, quantum information is transmitted through propagating phonons in extended mechanical resonator arrays or phonon waveguides. We describe how the problem of a non-vanishing thermal occupation of the phononic quantum channel can be overcome by implementing optomechanical multi- and continuous mode cooling schemes to create a 'cold' frequency window for transmitting quantum states. In addition, we discuss the implementation of phonon circulators and switchable phonon routers, which rely only on strong coherent optomechanical interactions and do not require strong magnetic fields or specific materials. Both techniques can be applied and adapted to various physical implementations, where phonons coupled to spin-or charge-based qubits are used for on-chip networking applications.