Fig. 1. Schematic diagram of a hybrid atom–optomechanical system interacting with an optical waveguide. The hybrid system consists of an optomechanical cavity and a VTA, and the single-photon travels along the arrow direction in the one-dimensional optical waveguide.

Fig. 2. Single-photon transmission spectra for different atom–cavity detunings. (a)–(e) Δac1=0, and Δac2≠0. (f)–(j) Δac1≠0, and Δac2≠0. Other parameters: g0=0, λ1=λ2=0.05, γ2=γ3=0, Γ=0.1. All of the parameters are in units of Ω.

Fig. 3. Single-photon transmission spectra for different optomechanical coupling strengths. Other parameters: λ1=λ2=0.05, Δac1=0, Δac2=0.1, γ2=γ3=0, and Γ=0.1. All of the parameters are in units of Ω.

Fig. 4. Single-photon transmission spectra for various interaction strengths between the hybrid atom–optomechanical system and the waveguide. Other parameters: g0=0.4, λ1=λ2=0.05, Δac1=0, Δac2=0.1, γ2=γ3=0. All of the parameters are in units of Ω.

Fig. 5. Single-photon transmission spectra for various coupling strengths between the cavity and the VTA. Other parameters: g0=0.4, Δac1=0, Δac2=0.1, γ2=γ3=0, and Γ=0.1. All of the parameters are in units of Ω.

Fig. 6. (Color online) Single-photon transmission and reflection spectra in atomic dissipation and non-dissipation cases for various coupling strengths between the cavity and the VTA. (a) γ2=γ3=0. (b)–(f) γ2=γ3=0.001. Other parameters: g0=0.4, Δac1=0, Δac2=0.1, and Γ=0.1. All of the parameters are in units of Ω.

Fig. 7. (Color online) Sum of transmission and reflection probabilities of the single photon in atomic dissipation for various coupling strengths between the cavity and the three-level atom. Other parameters: g0=0.4, Δac1=0, Δac2=0.1, Γ=0.1. All of the parameters are in units of Ω.