Dissipation-assisted preparation of steady spin-squeezed states of SiV centers

We propose an efficient scheme for generating spin-squeezed states at steady state in a spin-mechanical hybrid system, where an ensemble of SiV centers is coupled to a strongly damped nanomechanical resonator. We show that there exists a collective steady state in the system, which is exactly formed by the collective spin states plus the zero excitation state of the mechanical mode. The generation of the steady spin-squeezed state is based on a dissipative quantum dynamical process in which the mechanical dissipation plays a positive role but without destroying the target state. We demonstrate that the spin-squeezed steady state can be deterministically prepared via dissipative means, with the optimal spin squeezing up to $4/N$ in the ideal case, where $N$ is the number of spins. This work provides a promising platform for quantum information processing and quantum metrology.