Irregular spin angular momentum transfer from light to small birefringent particles

The transfer of spin angular momentum from photons to small particles is a key experiment of quantum physics. The particles rotate clockwise or counterclockwise depending on the polarization of the light beam which holds them in an optical trap. We show that even perfectly disk shaped particles will in general not rotate with a constant angular speed. The particles will periodically accelerate and decelerate their rotational motion due to a varying spin angular momentum transfer from the light. Using the Poincaré sphere we derive the equation of motion of a birefringent plate and verify the results by measuring the time dependent rotation of small crystals of $\text{Hg}\left(\text{I}\right)$ iodide and 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) in the trap of polarized optical tweezers. For small ellipticities of the polarized light in the tweezers the plate stops in a fixed orientation relative to the axes of the light ellipse. We discuss the origin of this halt and propose an application of small birefringent plates as self-adjusting optical retarders in micro-optics.