Enhancement of the two-photon blockade in a strong-coupling qubit-cavity system

The output incoherent spectrum and the photon blockade for the two-photon near-resonant excitation are numerically investigated by using the modified theories which are valid for an arbitrary degree of the qubit-cavity interaction. Owing to the effects of strong coupling of the system, the relaxation coefficients of the system are very sensitive to the coupling strength between the qubit and the cavity mode, which results in the redistribution of the populations and the appearance of the population inversion between the ground state and the first excited state, and it is demonstrated by the intensity of the output incoherent spectrum. The redistribution of the populations leads to one cascaded decay channel being weakened and the other possibly being enhanced significantly. Moreover, by adjusting the detuning between the qubit and the cavity mode, the phenomenon of the intercrossing in the energy levels appears. Through choosing the proper two-photon near-resonant excitation of the external classical driving field, the strong-coupling qubit-cavity system effectively causes one cascaded decay channel to realize the two-photon blockade. It is shown that the two-photon blockade can be further enhanced by one cascaded decay channel.

Figure 1

Energy ladders of the numerical results of the Rabi model without the RWA in Eq. (7) and truncation model for the two-photon near-resonant excitation $({\omega }_d\simeq E_{30}/2)$ from $|{\psi }_0\rangle$ to $|{\psi }_3\rangle$. (a) The four-state truncation model without the intercrossing of the energy levels between $|{\psi }_3\rangle$ and $|{\psi }_2\rangle$ when $\Delta =0$. (b) The three-state truncation model with the intercrossing of the energy levels between $|{\psi }_3\rangle$ and $|{\psi }_2\rangle$ when $g=0.3$. (All parameters are measured in units of ${\omega }_0$; that is, we set ${\omega }_0=1$ throughout these figures.)

Figure 2

The relaxation coefficients ${\Gamma }_{nm}$ including the qubit and the cavity mode as a function of the interaction strength $g$ for the four-state truncation model when $\Delta =0$. Here ${\gamma }_0={\kappa }_0={10}^{-3}$.

Figure 3

Comparisons of the stationary populations in the eigenstates with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation and the four-state truncation model when $\Delta =0$. Here $\Omega =6\times {10}^{-2}$, and the other parameters are the same as in Fig. 2.

Figure 4

Comparisons of the stationary populations in the eigenstates with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation and the four-state truncation model when $\Delta =0$. Here $g=0.3$, and the other parameters are the same as in Fig. 2.

Figure 5

Incoherent emission characteristics with (solid curve) and without (dotted curve) the effects of the CRTs for the four-state truncation when $\Delta =0$. Here $\Omega =6\times {10}^{-2}$, $g=0.3$, and other parameters are the same as in Fig. 2.

Figure 6

Second-order correlation functions with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation and the four-state truncation model when $\Delta =0$. (a) $\Omega =1\times {10}^{-3}$; (b) $\Omega =1\times {10}^{-2}$; (c) $\Omega =6\times {10}^{-2}$. Here $g=0.01$, and other parameters are the same as in Fig. 2.

Figure 7

Second-order correlation functions with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation and the four-state truncation model when $\Delta =0$. (a) $\Omega =1\times {10}^{-3}$; (b) $\Omega =1\times {10}^{-2}$; (c) $\Omega =6\times {10}^{-2}$. Here $g=0.3$, and other parameters are the same as in Fig. 2.

Figure 8

Second-order correlation functions with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation when $\Delta =0$. (a) The second-order correlation function for the $|{\psi }_3\rangle \to |{\psi }_1\rangle \to |{\psi }_0\rangle$ transition. (b) The second-order correlation function for the $|{\psi }_3\rangle \to |{\psi }_2\rangle \to |{\psi }_0\rangle$ transition. Here $g=0.3$, $\Omega =6\times {10}^{-2}$, and other parameters are the same as in Fig. 2.

Figure 9

Second-order correlation functions with (solid curves) and without (dotted curves) the effects of the CRTs for the two-photon near-resonant excitation and the three-state truncation model when $\Delta =0.4$. (a) $g=0.3$; (b) $g=0.5$. Here $\Omega =2\times {10}^{-2}$ and ${\gamma }_0={\kappa }_0={10}^{-3}$.