Rotational stability in nanorotor and spin contrast in one-loop interferometry in the Stern-Gerlach setup

The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats the rotation in the co-frame of the nanorotor in the presence of external fields. Besides rotation, we will further investigate how to create large spatial superpositions in the inhomogeneous external magnetic field, such as in the case of the Stern-Gerlach apparatus. The spin-embedded nanorotors play a crucial role in creating matter-wave interferometers through their spin and external magnetic field interaction Hamiltonian. We aim to provide a holistic interpretation of the dynamics of three Euler angles, their quantum evolution, and the nanorotor's spatial motion in a Stern-Gerlach-type setup where we will consider one-full-loop interferometry. We will then study how the quantum evolution of all the Euler angles leads to a spin coherence loss upon interference and what manifests the Einstein-de Haas effect in an external magnetic field. In particular, we show that by imparting rotation along the direction of the magnetic field, we can stabilise the nanorotor's libration mode. We will also extend our analysis to a case where the initial state of the libration mode is thermal and discuss the contrast loss due to interference of the nanorotor upon one-loop completion.