Entanglement of a Laguerre-Gaussian cavity mode with a rotating mirror

It is known that the exchange of linear momentum between an optical cavity field mode and a vibrating mirror can entangle them together [1]. We consider here the rotational analog of this situation and show that radiation torque can entangle a Laguerre-Gaussian cavity field mode with a rotating mirror [2]. We present the arrangement used to generate the entanglement and study its robustness against temperature, showing that it persists up to $100K$ for experimentally accessible parameters. We further study the dependence of the entanglement with angular momentum and the detuning from the cavity resonance. Finally we observe a strong correlation between the behavior of the entanglement at low temperature and the mean number of thermal phonons at the mirror rotation frequency, a consequence of the black-body law for the phonons. \newline \newline [1] D. Vitali \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 030405 (2007). \newline [2] M. Bhattacharya, P. -L. Giscard, P. Meystre, Phys. Rev. A \textbf{77}, 013827 (2008).