A quantum mechanical superposition of a long-lived, localized phonon and a matter excitation is described. We identify a realization in strained silicon: a low-lying donor transition (P or Li) driven solely by acoustic phonons at wavelengths where high-$Q$ phonon cavities can be built. This phonon-matter resonance is shown to enter the strongly coupled regime where the “vacuum” Rabi frequency exceeds the spontaneous phonon emission into noncavity modes, phonon leakage from the cavity, and phonon anharmonicity and scattering. We introduce a micropillar distributed Bragg reflector $\mathrm{Si}/\mathrm{Ge}$ cavity, where $Q\simeq {10}^5–{10}^6$ and mode volumes $\mathcal{V}\lesssim 25{\lambda }^3$ are reachable. These results indicate that single or many-body devices based on these systems are experimentally realizable.

• Received 14 July 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.235502