Title: Quantum trapping and rotational self-alignment in triangular Casimir microcavities

Abstract: 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.