N -Phonon Bundle Emission via the Stokes Process

We demonstrate theoretically the bundle emission of $n$ strongly correlated phonons in an acoustic cavity QED system. The mechanism relies on Stokes resonances that generate super-Rabi oscillations between states with a large difference in their number of excitations, which, combined with dissipation, transfer coherently pure $n$-phonon states outside of the cavity. This process works with close to perfect purity over a wide range of parameters and is tunable optically with well-resolved operation conditions. This broadens the realm of quantum phononics, with potential applications for on-chip quantum information processing, quantum metrology, and engineering of new types of quantum devices, such as optically heralded $n$-phonon guns.