Arrays of coupled cavity quantum phonodynamical systems in silicon are considered. We study physical systems that can exhibit, e.g., Mott insulator states of phonons due to a strong phonon-phonon interaction (which is mediated by the impurity-cavity-phonon coupling). Our results indicate that quantum many-body phonon systems are achievable both in on-chip nanomechanical systems in silicon and DBR phonon cavity heterostructures in silicon-germanium. Experimental procedures to detect these states and temperature considerations are given. Cavity-phoniton systems enable large phonon-phonon interactions while single phonons offer long wavelengths for forming extended quantum states; they may have some advantage in forming truly quantum many-body mechanical states as compared to other optomechanical systems.

Toward engineered quantum many-body phonon systems

Schematic of a strain-matched silicon superlattice heterostructure (acoustic DBR with layers of Si(x)Ge(1−x)/Si(y)Ge(1−y)) containing donors is shown (left). A two-dimensional phononic crystal structure with acceptors placed at the cavity sites is also shown (right).