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Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes

Enforcing discipline on nanomechanical vibration

When one strongly shakes a pendulum close to its resonance frequency, it eventually locks to the shaking, i.e. tightly follows the applied force. Here we investigate such phenomena for two orthogonal vibrations of a nanomechanical string resonator which is five hundred times smaller than a human hair and embedded in an all integrated electrical circuit. Because the mechanical string is not a purely harmonic oscillator we discover nanomechanical analogs of nonlinear optical effects and demonstrate nanomechanical frequency multiplexing. When the two modes are pumped above a certain threshold, they are enforced to vibrate in unison at the half of the pump frequency. This disciplined vibration is referred to as two-mode injection locking, a state of large mechanical amplitude, which is extremely stable against external perturbations as for example noise. These experimental results grant nanoelectromechanical systems access to the investigation of nonlinear effects which have previously been demonstrated in nonlinear optical and electrical systems, and open up the path towards parametric control in multimode nanoelectromechanics.

Maximilian J. Seitner, Mehdi Abdi, Alessandro Ridolfo, Michael J. Hartmann, and Eva M. Weig
Phys. Rev. Lett. 118, 254301 (2017)