Strong Two-Mode Parametric Interaction and Amplification in a Nanomechanical Resonator

We demonstrate a scheme for amplifying nanomechanical motion based on strong parametric interactions between two independent flexural modes of a single nanobeam. A static electric field polarizes a dielectric nanobeam and additional radio-frequency voltage excites the motion of the beam. When the excitation frequency equals the difference of the two resonance frequencies, we observe a mode-splitting feature in the strong-coupling regime. If the excitation frequency overlaps the sum of the two resonance frequencies, the optical signal from the thermal motion of the nanomechanical resonator is amplified by more than 30 dB. We demonstrate that coupling between the odd- and even-numbered oscillatory mode can be realized and a coupled-mode theory is developed from a simple capacitor model to explain our observations. We conclude that the results are thoroughly explained by parametric interactions between two independent nanomechanical modes in thermal motion. This observation of parametric control can be employed in nanomechanical force detection and molecular sensing applications.