Symmetry breaking of large-amplitude parametric oscillations in few-layer-graphene nanomechanical resonators

Graphene nanomechanical resonators are well suited for the study of parametric oscillations. Their large frequency tunability and their pronounced nonlinearities enable an efficient modulation of their resonant frequencies. Here, we present measurements of the response of few-layer-graphene nanomechanical resonators, each driven by a large parametric pump at frequency $2\ensuremath{\omega}$ and a weak external drive at $\ensuremath{\omega}$, where $\ensuremath{\omega}$ is set near the mechanical resonant frequency ${\ensuremath{\omega}}_{0}$. The pump actuates the resonator beyond the threshold for large-amplitude parametric oscillations, while the drive breaks the symmetry between the parametric phase states. By increasing and decreasing a gate voltage to detune ${\ensuremath{\omega}}_{0}$ in the presence of the pump and the drive, we observe a double hysteresis in the response. The double hysteresis reveals the existence of two possible large-amplitude vibrational states whose phase difference is nearly $\ensuremath{\pi}$ radians. We deterministically prepare the resonator in either one of these states by cycling the gate voltage. We measure the stationary occupation probabilities of the two states in the presence of a white Gaussian force noise, and find that they strongly depend on the amplitude and on the phase of the external drive. The phase states of parametric oscillations with broken amplitude symmetry can be mapped to biased bimodal degrees of freedom, such as Ising spins in an external magnetic field. Therefore, they hold promise as units of binary information.