Optomechanics with cavity vacuum fluctuations: Self-alignment and collective rotation mediated by Casimir torque

We theoretically consider an ensemble of quantum dimers placed inside an optical cavity. We predict two effects. First, an exchange of angular momentum between the dimers mediated by the emission and reabsorption of the cavity photons leads to the alignment of dimers. Second, the optical angular momentum of the vacuum state of the chiral cavity is transferred to the ensemble of dimers, which leads to the synchronous rotation of the dimers at certain levels of light-matter coupling strength.