  Quantum fluctuations give rise to Casimir forces between two parallel
conducting plates, the magnitude of which increases monotonically as the
separation decreases. By introducing nanoscale gratings to the surfaces, recent
advances have opened opportunities for controlling the Casimir force in complex
geometries. Here, we measure the Casimir force between two rectangular gratings
in regimes not accessible before. Using an on-chip detection platform, we
achieve accurate alignment between the two gratings so that they interpenetrate
as the separation is reduced. Just before interpenetration occurs, the measured
Casimir force is found to have a geometry dependence that is much stronger than
previous experiments, with deviations from the proximity force approximation
reaching a factor of ~500. After the gratings interpenetrate each other, the
Casimir force becomes non-zero and independent of displacement. This work shows
that the presence of gratings can strongly modify the Casimir force to control
the interaction between nanomechanical components.
