Ground-state cooling of a nanomechanical oscillator with N spins

It is typical of modern quantum technologies employing nanomechanical oscillators to demand few mechanical quantum excitations, for instance, to prolong coherence times of a particular task or to engineer a specific nonclassical state. For this reason, we devote the present work to exhibiting how to bring an initially thermalized nanomechanical oscillator to near its ground state. Particularly, we focus on extending the novel results of D. D. B. Rao et al. [Phys. Rev. Lett. 117, 077203 (2016)], where a mechanical object can be heated up, squeezed, or cooled down to near its ground state through conditioned single-spin measurements. In our work, we study a similar iterative spin-mechanical system when N spins interact with the mechanical oscillator. Here, we have also found that the postselection procedure acts as a discarding process; i.e., we steer the mechanics to the ground state by dynamically filtering its vibrational modes. We show that when considering symmetric collective spin postselection, the inclusion of N spins in the quantum dynamics is highly beneficial-in particular, decreasing the total number of iterations to achieve the ground state, with a success rate of probability comparable with the one obtained from the single-spin case.