  Coherent scattering of an elliptically polarised tweezer into a cavity mode
provides a promising platform for cooling levitated nanoparticles into their
combined rotational and translational quantum regime [Phys. Rev. Lett. 126,
163603 (2021)]. This article presents the theory of how aspherical
nanoparticles are affected by elliptically polarised laser beams, how two
orthogonal cavity modes enable rotational and translational cooling, and how
the resulting power spectra contain signatures of rotational non-linearities.
We provide analytic expressions for the resulting trapping frequencies,
opto-mechanical coupling strengths, cooling rates, and steady-state occupations
and we study their dependence on the tweezer ellipticity.
