On-chip cavity quantum phonodynamics with an acceptor qubit in silicon

We describe a chip-based, solid-state analog of cavity-QED utilizing acoustic phonons instead of photons. We show how long-lived and tunable acceptor impurity states in silicon nanomechanical cavities can play the role of a matter nonlinearity for coherent phonons just as, e. g., the Josephson qubit plays in circuit QED. Both strong coupling (number of Rabi oscillations less than or similar to 100) and strong dispersive coupling (0.1-2 MHz) regimes can be reached in cavities in the 1-20-GHz range, enabling the control of single phonons, phonon-phonon interactions, dispersive phonon readout of the acceptor qubit, and compatibility with other optomechanical components such as phonon-photon translators. We predict explicit experimental signatures of the acceptor-cavity system.