Fig. 1. (a) Schematic diagram of the relevant transitions in cavity-EIT system. A single Sr87 four-level atom is trapped inside a high-finesse optical cavity. The bias field B parallels the cavity axis, which defines the quantization axis and generates a Zeeman splitting ℏΔ between the magnetic sublevels |3⟩ and |4⟩ of P13. The cavity is driven by a weak σ-polarized laser field (given by the superposition of σ+ and σ− polarizations), and the atom is pumped by a π-polarized classical control field orthogonal to the cavity axis. (b) Typical energy spectrum for optical Stark shift mediated cavity-EIT. The dressed-state splitting δ1,− (the red dashed line), δ1,0 (the black line), and δ1,+ (the blue dotted line) as a function of the optical Stark shift U0 for (c) Ω/g=0.01 and (d) Ω/g=2.1, respectively.

Fig. 2. (a) Second-order correlation function g(2)(0) and (b) cavity transmission Ta as functions of cavity-light detuning Δc for U0/g=0 and 1. (c) g(2)(0) and (d) Ta as functions of Δc and optical Stark shift U0. The white dashed line shows the corresponding dressed-state splitting for the three branches of the energy spectrum. The colors with blue–red gradient shading indicate the values of log[g(2)(0)] in (c) and Ta in (d).

Fig. 3. (a) g(2)(0) and (b) Ta as functions of Δc with Ω/g=2 for U0/g=0 and 1.6. The solid blocks mark the minimum value of g(2)(0) for U0/g=1.6 and the corresponding Ta. (c) Log[g(2)(0)] and (d) Ta as functions of Δc and Ω. The white dashed line shows the corresponding dressed-state splitting for the three branches of the energy spectrum. (e) The optimal gopt(2)(0) and (f) the corresponding cavity transmission Topt as functions of Ω. In (c) and (d), the other parameter is fixed at U0/g=1.6.

Fig. 4. (a) Contour plots of log[g(2)(0)] and (b) cavity transmission as functions of Δc and U0. The white dashed line shows the dressed-state splitting for the three branches of the energy spectrum. (c) The optimal gopt(2)(0) and (d) the corresponding Topt [the red curve] as functions of U0, with the light pink area exhibiting the strong PB regime and the corresponding Ta, respectively. The black curve in (d) shows the corresponding occupancy probability of atomic excited state |3⟩. Here, the classical control field is fixed at the optimal value with Ω/g=2.1.

Fig. 5. (a) Contour plots of log[g(2)(0)] for the earlier proposals in Refs. [57–60" target="_self" style="display: inline;">–60] on the U0−Ω parameter plane with Δc/g=0. (b) The optimal gopt(2)(0) in the presence of Stark shift U0a^†a^σ^11 (dashed line) with Ω/g=2.1 and U0a^†a^σ^22 (solid line) with Ω/g=0.44 as a function of U0, respectively. The light pink area exhibiting the strong PB regime with g(2)(0)<0.01 is a guide for the eye.