Fig. 1. Schematic of a chiral QE-microresonator system. A two-level QE is coupled to a whispering-gallery mode microresonator in a chiral way to form the QE-microresonator system. A waveguide is side coupled to the microresonator as input and output ports. A scatterer on the microresonator is considered to introduce backscattering. The arrows represent the propagating direction of a single photon for an input to port 1 (green) or port 2 (red).

Fig. 2. Transmission spectra of a waveguide coupled with a microresonator. The blue solid, red dashed, and green dotted curves are calculated by the TM, ME, and SPT methods, respectively. The settings in the following figures are the same: (a) in the absence of backscattering, (b) and (c) in presence of the backscattering with strengths h = κ_in and h = 10κ_in, respectively. See Sec. 3 for other parameters.

Fig. 3. Transmission spectra for a chiral QE-microresonator system without considering the backscattering: (a)–(c) Γ = 0.1γ, Γ = γ, and Γ = 100γ, respectively.

Fig. 4. Transmission spectra for a chiral QE-microresonator system with the QE and the scatterer: (a) Γ = 100γ, h = κ_in and (b) Γ = 100γ, h = 10κ_in.

Fig. 5. (a) Transmission spectra for different driving amplitudes α_in (corresponding to different pump powers), where the blue solid curve is calculated by the TM method, and the green dash-dotted curve (the red dashed curve, the purple dotted curve) is calculated by the ME method, with ${\alpha }_{\mathrm{in}}/\sqrt{{\kappa }_{\mathrm{tol}}}=0.1$ (${\alpha }_{\mathrm{in}}/\sqrt{{\kappa }_{\mathrm{tol}}}=0.5$, ${\alpha }_{\mathrm{in}}/\sqrt{{\kappa }_{\mathrm{tol}}}=1$). (b) Transmission spectra as a function of α_in at different decay rates, where Γ = γ (the blue solid curve) and Γ = 100γ (the red dash-dotted curve) correspond to weak and strong coupling, respectively. Other parameters are κ_ex = κ_in = 0.5κ_tol, γ/κ_tol = 1 × 10⁻⁴, g/κ_tol = 1, and h = κ_in.