  Casimir torque -- a rotational motion caused by the minimization of the
zero-point energy -- is a problem that attracts significant theoretical and
experimental interest. Recently, it has been realized using liquid crystal
phases and natural anisotropic substrates. However, for natural materials, the
torque reaches substantial values only at van der Waals distances of ~10 nm.
Here, we employ Casimir self-assembly using templated gold nanostructures of
triangular symmetry for the purpose of rotational self-alignment at truly
Casimir distances (100 -- 200 nm separation). The joint action of repulsive
electrostatic and attractive Casimir potentials leads to the formation of a
stable quantum trap, giving rise to a tunable Fabry-Perot microcavity. This
cavity self aligns both laterally and rotationally to maximize the overlap area
between the templated and floating triangular flakes. The rotational
self-alignment is remarkably sensitive to the equilibrium distance between the
two triangles as well as their area, which opens possibilities for active
control through manipulating the electrostatic screening. Our self-assembled
and self-aligned Casimir microcavities could find future use as a versatile and
tunable platform for nanophotonic, polaritonic, and optomechanical
applications.
