  We demonstrate theoretically the bundle emission of $n$ strongly correlated
phonons in an acoustic cavity QED system. The mechanism relies on anti-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.
