Perturbative algorithm for rotational decoherence

Recent advances in levitated optomechanics provide new perspectives for the use of rotational degrees freedom development quantum technologies as well testing fundamental physics. As translational case, their use, especially regime, is limited by environmental noises, characterization which order to assess, control, and minimize effect, particular decoherence. Here, we present a general perturbative approach compute decoherence system superposition its freedom. The specific cases dipole-dipole quadrupole-quadrupole interactions are solved explicitly, show that decohere on time scale can be longer than one.