Quantum many-body system based on phonons and donors in silicon

Cold atoms in optical lattices have become an indispensable tool for the study of many-body physics. Here, we introduce a novel many-body quantum system based on phonons with potentially useful properties. Theoretical results will be presented on the possibility of interacting systems based on phonitons, hybrid composite objects of a matter excitation and a cavity phonon. We discuss experimentally accessible regimes in silicon phoniton systems involving Mott insulator and superfluid phases. We consider experimental tools to probe these many-body states and give explicit designs for devices where they can be observed.