Quantum Mechanical Limits to Inertial Mass Sensing by Nanomechanical Systems

We determine the quantum mechanical limits to inertial mass-sensing based on nanomechanical systems. We first consider a harmonically oscillating cantilever whose vibration frequency is changed by mass accretion at its surface. We show that its zero-point fluctuations limit the mass sensitivity, for attainable parameters, to about an electron mass. In contrast to the case of a classical cantilever, we find the mass sensitivity of the quantum mechanical cantilever is independent of its resonant frequency in a certain parameter regime at low temperatures. We then consider an optomechanical setup in which the cantilever is reflective and forms one end of a laser-driven Fabry-P\'erot cavity. For a resonator finesse of 5 the mass sensitivity at T=0 is limited by cavity noise to about a quarter of a Dalton, but this setup has a more favorable temperature dependency at finite temperature, compared to the free cantilever.