  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. Here we
introduce an optical encoding technique, dubbed "linear photonic gears", that
enables ultra-sensitive measurements of transverse displacements by mapping
these into polarization rotations of a laser beam. In ordinary ambient
conditions, we measure 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
integrated optics. We anticipate it may have a strong impact on both research
and industry.
