Optimal sensing of momentum kicks with a feedback-controlled nanomechanical resonator

External disturbances exciting a mechanical resonator can be exploited to gain information on the environment. Many of these interactions manifest as momentum kicks, such as the recoil of residual gas, radioactive decay, or even hypothetical interactions with dark matter. These disturbances are often rare enough that they can be resolved as singular events rather than cumulated as force noise. While high-Q resonators with low masses are particularly sensitive to such momentum kicks, they will strongly excite the resonator, leading to nonlinear effects that deteriorate sensing performance. Hence, this paper utilizes optimal estimation methods to extract individual momentum kicks from measured stochastic trajectories of a mechanical resonator kept in the linear regime through feedback control. The developed scheme is illustrated and tested experimentally using a prestressed silicon nitride trampoline resonator. Apart from enhancing a wide range of sensing scenarios mentioned above, our results indicate the feasibility of novel single-molecule mass spectrometry approaches.