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