Thermomechanical noise limits on parametric sensing with nanomechanical resonators

Measuring and monitoring the dynamic parameters of a nanomechanical resonator, in particular the resonance frequency, has received significant attention recently, in part due to the possibility of very sensitive, fast and precise mass sensing. Added mass can include chemisorbed or physisorbed metals or organic molecules, and if sufficiently high sensitivity, dynamic range and detector speed can be achieved, they could have applications in, e. g., proteomics. Here, I investigate some of the fundamental limits to mass sensing in such resonators, discussing the limits imposed by thermomechanical noise on both the linear operating regime of a simple harmonic oscillator, and the equivalent limits on nonlinear parametric amplifiers used as parametric sensors. The model system is a cantilevered flexural resonator, but the results apply equally well (in most cases) to doubly clamped or torsional resonant structures as well.