Multiparticle entanglement is of great significance for quantum metrology and quantum information processing. We here present an efficient scheme to generate stable multiparticle entanglement in a solid state setup, where an array of silicon-vacancy centers are embedded in a quasi-onedimensional acoustic diamond waveguide. In this scheme, the continuum of phonon modes induces a controllable dissipative coupling among the SiV centers. We show that, by an appropriate choice of the distance between the SiV centers, the dipole-dipole interactions can be switched off due to destructive interferences, thus realizing a Dicke superradiance model. This gives rise to an entangled steady state of SiV centers with high fidelities. The protocol provides a feasible setup for the generation of multiparticle entanglement in a solid state system.

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We propose an efficient scheme for generating spin-squeezed states at steady state in a spinmechanical hybrid system, where an ensemble of SiV centers are 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.

Quantum phononic systems have attracted great attention in quantum science and technology. However, it is quite difficult to realize strong phonon-phonon interactions at the few phonon level in phononic systems, since direct interactions between phonons are generally very weak. Here, the phonon transport properties and the phonon-phonon interactions in a 1D phononic waveguide with embedded silicon-vacancy (SiV) centers are studied. The authors show that, mediated by the SiV centers, strong phonon-phonon interactions can be realized due to coherent interferences of the emitting phonon waves with the incident waves. In particular, the embedded color centers can induce an effective attractive or repulsive interaction in space for phonons, corresponding to phonon bunching or antibunching. Besides, it is found that a single SiV center can capture two resonant phonons simultaneously, forming a phononic bound state in the continuum. Comparing with photon-photon interactions in photonic systems, the phonon-phonon interactions are stronger for relatively slower phonon velocity and the strongly correlated phonon properties are promising for constructing various all-phonon quantum devices in quantum information processing.