Levitated dielectric particles in vacuum provide a versatile platform to study and control the dynamics of micro- and nanoscale resonators, owing to their high isolation from environmental noise and low decoherence rates. In this thesis, we explore the coupling between internal spin and mechanical rotation - known as spin-rotation coupling - in such systems. This coupling is manifested in the Einstein-de Haas and Barnett effects, which describe how changes in spin or magnetization induce mechanical rotation and vice versa. Due to the reduced moment of inertia of nano- and microscale particles, these effects can play a dominant role and are central to the dynamics studied here. We theoretically investigate spin-rotation coupling in two distinct levitated platforms, encompassing both collective magnetization and single-spin dynamics in the presence of static magnetic fields. First, we develop a theoretical framework for the quantum dynamics of a nanodiamond with a single nitrogen-vacancy (NV) center, electrically suspended in a Paul trap. While the nanodiamond itself is not magnetically ordered, the NV center's spin couples directly to the particle’s rotation. We show that this coupling can exceed the characteristic frequencies of the system, enabling access to the so-called ultrastrong coupling regime. Furthermore, we demonstrate how the embedded spin influences the rotation of gyroscopically stabilized rotors. The strong spin-rotation signatures make the system attractive for probing spin-rotation coupling, and open the door to superposition experiments with massive objects, for which we propose potential experimental protocols. Second, to investigate the optical signatures of spin-mechanical interactions in a magnetically ordered system, we consider a levitated Faraday-active dielectric microsphere driven by a laser field. This hybrid platform, where light, magnetization, and rotation are intertwined, combines levitated optomechanics and cavity optomagnonics. We find that the optically driven magnetization dynamics induces angular oscillations of the particle, and show that the optical response carries clear signatures of this spin-rotation interplay, making light a sensitive probe of magneto-mechanical dynamics.
Vanessa Wachter (Wed,) studied this question.