Phase encoding in parametric nanomechanical resonator via annealing

Nanomechanical resonators driven parametrically enable binary information encoding based on the control of their two possible vibrational phases. We present a protocol to flip the parametric phase in a graphene nanomechanical resonator via annealing, offering a novel approach to nanomechanical logic. The core of our methodology involves driving the resonator with a parametric excitation near twice its resonant frequency and applying an external drive to break the symmetry of the dynamical double-well potential of the bistable states. By introducing white force noise to anneal the resonator, its vibrational phase settles into the state with the lower potential. The phase can be deterministically prepared in one of two states, differing by approximately π radians, by controlling the phase of direct drive and annealing. The demonstrated protocol offers a promising approach for nanomechanical logic with potential advantages in efficiency, error resilience, and scalability.