Generation of Greenberger-Horne-Zeilinger states for silicon-vacancy centers using a decoherence-free subspace

Generating Greenberger-Horne-Zeilinger (GHZ) states of solid-state spins is of great significance for quantum metrology and quantum error correction. We propose here an efficient scheme for generating high fidelity GHZ states in a solid-state setup where multiple silicon-vacancy (SiV) centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. The lattice distortion gives rise to a strong strain coupling between the orbital degree of freedom of SiV centers and the continuum phonon modes. Due to the permutation symmetry, we can take advantage of the decoherence-free subspace to avoid dissipation. Under the quantum Zeno regime, two control fields are used to achieve a ladderlike coupling structure in decoherence-free subspace along with an off-resonant two-photon Raman transition process. We calculate the pulse sequences for N=4 and at the same time analyze the effect of different collective decay rates. Moreover, we consider the disorder in the imperfect position of SiV centers and the inhomogeneous strain coupling. This paper may provide a feasible protocol for the generation of GHZ states in a solid-state system.