Graphene-nanodiamond membranes for atomic-impact sensing: design and fluorescence readout limits

Hybrid nanomaterial platforms that combine mechanically compliant two-dimensional membranes with optically active quantum emitters offer an attractive route towards ultrasensitive particle detection. Here, we investigate a sensor concept based on a graphene membrane suspended over a nanoscale aperture and functionalised with fluorescent nanodiamonds. The impact of an incoming atom transfers momentum to the membrane and excites an out-of-plane mechanical motion, which is transduced into an optical signal through the nanodiamond fluorescence. We develop a quantitative upper-bound model linking atomic momentum transfer, the mechanical response of the nanodiamond-loaded membrane, and the resulting optical transduction. Design maps for the mechanical resonance frequency and collision-induced oscillation amplitude reveal single-impact displacements in the femtometre-to-sub-picometre range for helium atoms. Even under favourable mechanical, collision, and optical conditions, the corresponding relative fluorescence modulation remains below 10^-6 throughout the investigated parameter space and reaches only a few 10^-7 under the most favourable conditions. Combined with photon-counting statistics, these results show that direct fluorescence-intensity detection of individual atomic impacts is impractical in the considered configuration. Importantly, the analysis identifies optical displacement transduction, rather than the absence of a mechanical response, as the principal limitation. The predicted absolute displacements approach the scale accessible to state-of-the-art graphene optomechanical measurements, making interferometric or cavity-based displacement readout a more promising direction, although single-impact detectability remains dependent on bandwidth and noise. Our results establish quantitative feasibility bounds for graphene-nanodiamond atomic-impact sensors and identify the readout mechanism as the central design parameter for future hybrid nano-mechanical sensing architectures.