Fig. 1. Scheme diagrams. (a) This hybrid device consists of two parts, a chiral switch for emitting photon pulse and an optical microcavity embedded with a single NV center, both of which are connected with an optical nanofiber. The outputs are delivered to the optical microcavity through nanofiber. A single NV center, driven by a dichromatic microwave field, is planted in the optical microcavity, which will also interact with the optical modes near-resonantly. (b) Level diagram of the NV center ground triplet state and excited state, and the feasible transition channels. The brown and blue solid arrows indicate the dichromatic microwave driving fields (with frequencies ω1 and ω2, and Rabi frequencies Ω1 and Ω2) applied between the state |ms=0⟩ and the state |ms=∓1⟩. The red solid arrows indicate the optical transition between the state |ms=0⟩ and the excited state |e⟩, which is induced by σ+ modes.

Fig. 2. For Case (I), the dynamical evolution of the fidelity, (a) and (b) with the initial state |1⟩p|−1⟩, and (c) and (d) with the initial state |1⟩p|+1⟩, in which (a) and (c) correspond to the dynamical fidelity versus the coupling strength g, with the coefficients g∈[5Ω,10Ω], Δ≃25Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω; (b) and (d) correspond to the dynamical fidelity versus the detuning Δ, with the coefficients Δ∈[25Ω,50Ω], g=5Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω.

Fig. 3. For Case (II), the dynamical evolution of the fidelity, with the initial state |−1⟩ and the coefficients Δ≃25Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω, in which the solid gray line with the hollow square shows the fidelity of |0⟩, the solid blue line with the open circle shows the fidelity of |−1⟩, and the solid red line with the hollow diamond shows the fidelity of |+1⟩.

Fig. 4. For Case (I), (a) and (b) the dynamical fidelity of state transitions |1⟩p|±1⟩→|1⟩p|±1⟩ versus the dispersion δΩ∈[−0.2Ω,0.2Ω], with the coefficients g≃5Ω, Δ≃25Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω, while for Case (II), (c) and (d) the dynamical fidelity of states |−1⟩ and |0⟩ during the process of state transitions |−1⟩ ↔ |+1⟩, versus the dispersion δΩ∈[−0.2Ω,0.2Ω], with the coefficients Δ≃25Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω.

Fig. 5. The estimation of the average fidelity for this whole C-NOT operation process versus the dispersion rate δΩ/Ω∈[−0.2,0.2], in which, the black line with the open square means the average fidelity of the controlled spin-invariant operation, the red line with the open circle means the average fidelity of the controlled spin-flip operation, the blue line with the open up triangle means the whole average fidelity of this C-NOT operation, and the violet line with open down triangle means the whole average fidelity of the C-NOT operation accompanied with the realistic chiral switch efficiency (estimated as ∼0.9). The parameters are assumed as Δ≃25Ω, κ≃0.1Ω, γe≃Ω, and γg≃0.001Ω.