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.
(Submitted on 23 Feb 2013)