Simulating many-body lattice systems on a single nano-mechanical resonator

We show that lattice systems, such as the Bose-Hubbard model, can be simulated on a single nano- or micro-mechanical resonator, by exploiting its many modes. The on-site Hamiltonians are engineered by coupling the mechanical modes to the modes of a pair of optical or stripline resonators, and the connections between the lattice sites are engineered in a similar way. The lattice network structure is encoded in the frequency components of the fields driving the resonators. This three-resonator configuration also allows universal quantum computing on the nano-resonator.