Nanomechanical quantum many-body phonon-qubit systems for quantum simulators

We investigate nanomechanical systems consisting of arrays of coupled phonon cavities each including an impurity qubit in silicon. These experimentally feasible architectures can exhibit quantum many-body phase transitions, e.g. Mott insulator and superfluid states, due to a strong phonon-phonon interaction, and are suitable in the pursuit of quantum simulators. We investigate driven dissipative non-equilibrium systems at zero and non-zero temperatures. These quantum many-body phonon systems can be implemented using either on-chip nano mechanical systems in silicon or DBR heterostructures in silicon-germanium. We examine the experimental procedures to detect these states and show that temperature and driving field (write/read-out) play a critical role in achieving these phonon superfluid and insulator states. These many-body cavity phonon/qubit systems with strong phonon-phonon interactions can be used in forming truly quantum many-body mechanical states for quantum simulators as well as to complement other nano/optomechanical systems.