We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable interest
as special cases allow for quantum nondemolition measurements of the mechanical resonators energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function and second order optomechanical coupling. By measuring the dependence of the linear and nonlinear signal transduction -- as well as the mechanical frequency shift -- on laser detuning from optical resonance, we provide estimates of the contributions from the linear and quadratic optomechanical couplings.
High-frequency atomic force microscopy has enabled extraordinary new science through large bandwidth, high speed measurements of atomic and molecular structures. However, traditional optical detection schemes restrict the dimensions, and therefore th
e frequency, of the cantilever - ultimately setting a limit to the time resolution of experiments. Here we demonstrate optomechanical detection of low-mass, high-frequency nanomechanical cantilevers (up to 20 MHz) that surpass these limits, anticipating their use for single-molecule force measurements. These cantilevers achieve 2 fm / sqrt(Hz) displacement noise floors, and force sensitivity down to 132 aN / sqrt(Hz). Furthermore, the ability to resolve both in-plane and out-of-plane motion of our cantilevers opens the door for ultrasensitive multidimensional force spectroscopy, and optomechanical interactions, such as tuning of the cantilever frequency in situ, provide new opportunities in high-speed, high-resolution experiments.
