  Doppler cooling is a widely used technique to laser cool atoms and
nanoparticles exploiting the Doppler shift involved in translational
transformations. The rotational Doppler effect arising from rotational
coordinate transformations should similarly enable optical manipulations of the
rotational degrees of freedom in rotating nanosystems. Here, we show that
rotational Doppler cooling and heating (RDC and RDH) effects embody rich and
unexplored physics, such as a strong dependence on particle morphology. For
geometrically confined particles, such as a nanorod that can represent diatomic
molecules, RDC and RDH follow similar rules as their translational Doppler
counterpart, where cooling and heating are always observed at red- or
blue-detuned laser frequencies, respectively. Surprisingly, nanosystems that
can be modeled as a solid particle shows a strikingly different response, where
RDH appears in a frequency regime close to their resonances, while a detuned
frequency produces cooling of rotation. We also predict that the RDH effect can
lead to unprecedented spontaneous chiral symmetry breaking, whereby an achiral
particle under linearly polarized illumination starts spontaneously rotating,
rendering it nontrivial compared to the translational Doppler effect. Our
results open up new exciting possibilities to control the rotational motion of
molecules and nanoparticles.
