Interfering pathways for photon blockade in cavity QED with one and two qubits

We theoretically study the quantum-interference-induced photon blockade and antiblockade phenomenon in an atom-cavity QED system, where the destructive [constructive] interference between two different transition pathways prohibits [enhances] two-photon excitation. To begin with, we study a single-atom–cavity QED system where the atom or cavity is driven by a coherent pump field. We show that the cavity-driven case will lead to the quantum-interference-induced photon blockade under a specific condition, but such an interference-induced photon blockade cannot be realized in the atom-driven case. This is an important consequence of the pathways possible for the two types of drives. Then, we investigate the two-atom case, and find that an additional transition pathway appears in the atom-driven case. We show that this additional transition pathway results in the quantum-interference-induced photon blockade only when the atomic resonant frequency is different from the cavity mode frequency otherwise antiblockade occurs. Moreover, in this case, the condition for realizing the interference-induced photon blockade is independent of the system's intrinsic parameters, which can be used to generate antibunched photons in both weak and strong coupling regimes.

Figure 1

(a) Sketch of a two-level atom with resonant frequency ${\omega }_a$ trapped in a single-mode cavity. The red (purple) arrow corresponds to the atom (cavity) drive with driving strength $\eta$. For atomic drive the atom is driven from the side. $|g\rangle$ ($|e\rangle$) is the ground (excited) state of the atom. $\gamma$ and $\kappa$ are the atomic and cavity decay rates, respectively. Panels (b) and (c) show the transition pathways in an atom- and cavity-driven cases, respectively. Here yellow arrows represent the atom-cavity coupling with strength $g$. $|\alpha ,n\rangle (\alpha =g,e)$ is the product state of atomic state $|\alpha \rangle$ and photon state $|n\rangle$.

Figure 2

The equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ versus the normalized coupling strength $g/\kappa$ in (a) cavity-driven and (b) atom-driven systems. In panel (a), we choose $\gamma =\kappa$ (blue dashed curve) and $\gamma =\kappa /2$ (red solid curve), respectively. The driving strength $\eta =0.01\kappa$. In panel (b), we choose $\gamma =\kappa$, but the driving strength is chosen as $\eta =0.01\kappa$ (blue dashed curve), $\eta =0.3\kappa$ (red solid curve) and $\eta =\kappa$ (green dash dotted curve).

Figure 3

(a) Sketch of two two-level atoms trapped in a single-mode cavity. The red (purple) arrow corresponds to the atom (cavity) drive with driving strength $\eta$. Panels (b) and (c) show the transition pathways in cavity- and atom-driven systems, respectively.

Figure 4

The equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ versus the normalized coupling strength $g/\kappa$ in the (a) cavity-driven and (b) atom-driven systems, respectively. The blue dashed curves correspond to the one-atom case, while the red solid curves correspond to the two-atom case. The system parameters are given by ${\mathrm{\Delta }}_a={\mathrm{\Delta }}_c=0$, $\gamma =\kappa$, and $\eta =0.01\kappa$.

Figure 5

(a) Sketch of a two-atom-driven cavity QED system, where two atoms are driven by a coherent field $\eta$ and the atomic resonant frequency ${\omega }_a\ne {\omega }_c$. (b) The corresponding transition pathways show the destructive interference process.

Figure 6

Plots of the equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ (red solid curves) and the probability of detecting state $|C_{+,1}{|}^2$ (blue dashed curves) as a function of the normalized detuning ${\mathrm{\Delta }}_a/\kappa$. Here, we choose $\kappa /2\pi =2.8$ MHz, $\gamma /2\pi =3.0$ MHz, ${\mathrm{\Delta }}_c=20\kappa$, and $\eta =0.5\kappa$ [45]. The coupling strength is given by (a) $g=0.5\kappa$ and (b) $g=5\kappa$.

Figure 7

Equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ versus the cavity detuning ${\mathrm{\Delta }}_c$ and atomic detuning ${\mathrm{\Delta }}_a$. Here, the coupling strength is chosen as (a) $g=0.5\kappa$ and (b) $g=5\kappa$. The white dashed curves represent the traditional PB condition (${\mathrm{\Delta }}_a{\mathrm{\Delta }}_c=2g^2$) and the white dash-dotted curves denote the condition of the interference-induced PB (${\mathrm{\Delta }}_c=-2{\mathrm{\Delta }}_a$). The other parameters are same as those used in Fig. 6.

Figure 8

Plots of the equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ [panel (a)] and the counting rate [panel (b)] as functions of the detuning $\mathrm{\Delta }\equiv {\mathrm{\Delta }}_a=-{\mathrm{\Delta }}_c/2$ and the coupling strength $g$, respectively. The pump field Rabi frequency is $\eta /2\pi =1.4$ MHz and other system parameters are the same as those used in Fig. 6.