  An optically levitated nonspherical nanoparticle can exhibit both librational
and translational vibrations due to orientational and translational
confinements of the optical tweezer, respectively. Usually, the frequency of
its librational mode in a linearly-polarized optical tweezer is much larger
than the frequency of its translational mode. Because of the frequency
mismatch, the intrinsic coupling between librational and translational modes is
very weak in vacuum. Here we propose a scheme to couple its librational and
center-of-mass modes with an optical cavity mode. By adiabatically eliminating
the cavity mode, the beam splitter Hamiltonian between librational and
center-of-mass modes can be realized. We find that high-fidelity quantum state
transfer between the librational and translational modes can be achieved with
practical parameters. Our work may find applications in sympathetic cooling of
multiple modes and quantum information processing.
