Ultra-sensitive measurement of mechanical displacements with photonic gears.

Accurately measuring mechanical displacements is essential for a vast portion of current technologies. Several optical techniques accomplish this task, allowing for non-contact sensing even below the diffraction limit. Structured light can be a resource for enhanced sensing purposes as for instance in the "photonic gears". This technique enables a boost of the sensitivity in roll angle measurements thanks to a bidirectional mapping between the polarization state and a properly tailored vectorial mode of a paraxial light beam. Similarly, ultra-sensitive measurements of a transverse displacement can be performed by mapping it into the polarization rotation of a laser beam. By exploiting this technique, dubbed "linear photonic gears", we measured, in ordinary ambient conditions, the relative shift between two objects with a resolution of $400 {pm}$. We argue that a resolution of $50 {pm}$ should be achievable with existing state-of-the-art technologies. Our single-optical-path scheme is intrinsically stable and it could be implemented as a compact sensor, using cost effective integrated optics.