Quantum fluctuations of position of a mirror in vacuum
Résumé
A mirror scattering vacuum fields is submitted to a quantum fluctuating radiation pressure. It also experiences a motional force, related to force fluctuations through fluctuation-dissipation relations. The resulting position fluctuations of the coupled mirror are related to the dissipative part of the mechanical admittance. We compute the time dependent position commutator, which makes apparent the difference between the low-frequency and high-frequency masses, and the anticommutator noise spectrum, which describes the ultimate sensitivity in a length measurement using mirrors.