Fig. 1. Sketch of the two-qubit cavity QED system with different cavity mode frequency ωc and qubit resonant frequency ωa. A pump field Ωp couples the qubit ground state |g⟩ and excited state |e⟩ with the angular frequency ωp. γ and κ denote the qubit decay rate and the cavity decay rate, respectively. Here, DDI represents the dipole–dipole interaction when two qubits are close enough.

Fig. 2. (a), (b) The anharmonic ladder-type energy structure and the destructive interference pathways for the ELA-based and QDI-induced PBs, respectively. In (a), the absorption of a second photon of the pump field will be blocked due to the large energy mismatch if the pump field is tuned to the state Ψ1(±) as denoted by the blue and red arrows, respectively. In (b), two interference pathways from state |+,0⟩ to state |+,1⟩ are indicated by the yellow and green arrows, respectively. (c) The equal-time second-order correlation function g(2)(0) (solid curve) and mean photon number ⟨a†a⟩ (dashed curve) as a function of the normalized detuning Δa/κ. Here, we chose J=0, Δc=−30κ, g=5κ, γ=κ, and Ωp=0.1κ.

Fig. 3. Logarithmic plots of (a) the second-order correlation function g(2)(0) and (b) the mean photon number ⟨a†a⟩ as functions of the normalized detuning Δa/κ with the DDI strength J=0 (black curves), g (blue curves), and 3.5g (red curves), respectively. The green dashed line indicates the condition Δc=−2Δa. Other system parameters are the same as those used in Fig. 2(c).

Fig. 4. Logarithmic plots of (a) the second-order correlation function g(2)(0) and (b) the mean photon number ⟨a†a⟩ as functions of the DDI strength J/g and detuning Δa/κ by setting Δc=−2Δa and g=5κ. Other system parameters are the same as those used in Fig. 3. The dashed curves denote the optimal condition g2=−Δa(Δa−J).

Fig. 5. Logarithmic plots of (a) the second-order correlation function g(2)(0) and (b) the mean photon number ⟨a†a⟩ against the detuning Δa/κ and coupling strength g/κ with Δc=−2Δa and J=2g. The white dashed line corresponds to the condition g=Δa, while the black solid curves denote g(2)(0)=0.01.

Fig. 6. (a) The second-order correlation function log10[g(2)(0)] versus the normalized pump field Rabi frequency Ωp/κ with spontaneous decay rate γ/2π=0.1κ (red solid curves), 0.5κ (black dashed curves), and κ (blue dotted curves), respectively. (b) The plot of the photon number in Fock states with Ωp=0.2κ. Here, the system parameters are given by g=2κ, and J=Δc=−2Δa=2g.

Fig. 7. Logarithmic plot of (a) the equal-time second-order correlation function g(2)(0) and (b) the mean photon number ⟨a†a⟩ as functions of the normalized atomic detuning Δc/κ and the cavity detuning Δa/κ. The white dashed–dotted curves denote the condition of the ELA-based PB [i.e., Eq. (6)], and the white dashed lines denote the condition of the QDI-induced PB [i.e., Eq. (10)]. The system parameters are given by Ωp=0.1κ, g=5κ, and γ=κ.

Fig. 8. Logarithmic plot of (a) the equal-time second-order correlation function g(2)(0) and (b) the mean photon number ⟨a†a⟩ as functions of Δc/κ and Δa/κ with J=2g. The white dashed–dotted curves denote the condition of the ELA-based PB [i.e., Eq. (13)], and the white dashed lines denote the condition of the QDI-induced PB [i.e., Δc=−2Δa].