Force Sensing with an Optomechanical Self-Oscillator

Ultra-high-frequency nanomechanical resonators (${f}_{m}g300$ MHz) can increase our capacity to study fast physical phenomena, for example by measuring forces. Their extreme stiffness is also a chance to access molecular forces in the subpicometer low amplitude of motion limit, but it makes them hard to drive and control. Here we analyze a method to optomechanically sense a force field with an ultra-high-frequency and stiff mechanical resonator, where back-action optical forces set the resonator into a self-sustained stable oscillator trajectory. After elucidating the experimental conditions to obtain optimal resolution, we carry out controlled experiments where the oscillator senses an optical force generated by a secondary laser. We analyze and model our results, and illustrate the concrete advantage of the method in the measurement of such a weak force, which would otherwise remain undetected by the undriven probe. We establish the thermodynamical limits of the approach, and finally connect it to the class of feedback-controlled problems, clarifying its assets and limitations.