Quantum Mechanical Limits to Inertial Mass Sensing by Nanomechanical Systems

TL;DR

This paper investigates the fundamental quantum limits on the sensitivity of nanomechanical systems for inertial mass sensing, highlighting how quantum fluctuations and cavity noise set ultimate detection bounds.

Contribution

It introduces a quantum mechanical analysis of nanomechanical mass sensors, revealing limits imposed by zero-point fluctuations and cavity noise, and compares free and optomechanical configurations.

Findings

Quantum zero-point fluctuations limit mass sensitivity to about an electron mass.

Quantum cantilever sensitivity is independent of resonant frequency at low temperatures.

Optomechanical setup improves temperature dependence of mass sensitivity, reaching about a quarter of a Dalton at zero temperature.

Abstract

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.