Distinguishing between Direct and Parametric Driving in Nanomechanics Using a Vibrating Carbon Nanotube

Parametric driving is a powerful route to amplification and nonlinear control in nanomechanical resonators, but its signatures can be ambiguous because standard dc electrical readout does not directly reveal the frequency of motion. Here we resolve this ambiguity by measuring the motional frequency of a vibrating carbon nanotube independently of the drive frequency. We operate the nanotube as an electromechanical mixer and detect microwave sidebands using a low-noise superconducting amplifier. This frequency-resolved readout distinguishes direct motion of the first overtone from parametric motion of the fundamental, even when the corresponding drive frequencies nearly coincide. The two mechanisms are further separated by their drive-power dependence. Beyond conventional parametric resonance at 2f_0, we observe responses to driving at 3f_0 and 4f_0, consistent with high-order parametric excitation associated with nonlinear stiffness terms. The data repository contains all data, figures, and code used for creating the figures used in "Distinguishing between Direct and Parametric Driving in Nanomechanics Using a Vibrating Carbon Nanotube". Software Used: Python Illustrator OriginPro