Robust scheme for high-fidelity generation of mesoscopic entangled cat state

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We here study a hybrid quantum system of one solid-state electronic spin coupled to a mechanical resonator (MR) using the crystal strain, with the purpose of engineering the mesoscopic spin-phonon entangled cat state. The feature of this work to be mentioned is that it proposes a different and feasible method to achieve the entanglement, especially with the higher fidelity. This scheme mainly contains two steps, namely the coherent population trapping (CPT) initialization and large-detuning evolution (LDE). By taking all of the adverse decoherence factors into our considerations, the numerical simulations indicate that its fidelity can reach more than 0.995 (or 0.999) when the spin-mechanical coupling strength is 10 (or 100) times larger than spin dephasing and mechanical resonator dissipation rate, respectively. Because of the cooperation of CPT and LDE, this proposal also exhibits a considerable robustness for engineering the entangled cat state, and which may be considered as a general attempt that may be suitable for different systems.