Enhanced unconventional photon-blockade effect in one- and two-qubit cavities interacting with nonclassical light

The antibunching effect generated in a cavity containing first a single two-level atomic system and then two identical atoms is explored for off-resonant interactions, in strong- and weak-coupling regimes. The cavity is driven by coherent and squeezed sources. Using the second-order correlation function analytically derived in the weak-excitation regime, we show that squeezed light achieves and improves strong antibunching, leading to a photon blockade. This enhancement is due to a destructive quantum interference mechanism induced by the nonclassical light, creating a supplementary transition pathway. The best effect is obtained for equal frequency detunings in the strong-coupling regime. More interestingly, our investigation reveals that the two-atom-cavity system can further improve the antibunching effect compared to the single-atom cavity. It turns out that the additional couplings appearing in the cavity due to the implementation of the two atoms, combined with the squeezed light, could substantially enhance the photon-blockade effect.

Figure 1

(a) Scheme of a two-level system trapped in a single-mode cavity. The cavity is coherently pumped by a laser of amplitude $\varepsilon$. A second-order nonlinear crystal is attached to the cavity in such a way that the generated squeezed photons interact with the two-level system. (b) Transition paths for different photon states induced by coherent and squeezed sources.

Figure 2

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted at total resonance (${\mathrm{\Delta }}_a={\mathrm{\Delta }}_c=0$) as a function of the normalized coupling strength $g/\kappa$ for $\varepsilon /\kappa =0.01, \gamma =\kappa /2$, and three values of the squeezed light amplitude $\lambda$.

Figure 3

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted versus normalized detuning ${\mathrm{\Delta }}_a/\kappa$ (${\mathrm{\Delta }}_c=0$) for $\gamma =\kappa /2, \varepsilon /\kappa =0.01$, and three values of the squeezed light strength $\lambda$ are considered in (a) the weak-coupling regime $g/\kappa =0.45$ and (b) the strong-coupling regime $g/\kappa =10$.

Figure 4

Optimal PB conditions for (a) squeezed light amplitude ${\lambda }_{3,4}$ and (b) detunings ${\mathrm{\Delta }}_{a,3,4}$ plotted as a function of the coupling strength $g/\kappa$ for $\gamma =\kappa /2$ and $\varepsilon /\kappa =0.01$.

Figure 5

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted as a function of the normalized detuning ${\mathrm{\Delta }}_c/\kappa$ (${\mathrm{\Delta }}_a=0$) for $\gamma =\kappa /2, \varepsilon /\kappa =0.01$, and three values of $\lambda$ in (a) the weak-coupling regime $g/\kappa =0.45$ and (b) the strong-coupling regime $g/\kappa =10$.

Figure 6

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted versus the normalized detuning $\mathrm{\Delta }/\kappa$ for $\gamma =\kappa /2, \varepsilon /\kappa =0.01$, and several values of $\lambda$ in (a) the weak-coupling regime $g/\kappa =0.45$ and (b) the strong-coupling regime $g/\kappa =10$.

Figure 7

Transition pathways in the two-atom cavity system in the presence of squeezed light. The antisymmetric Dicke states $|-,0\rangle$ and $|-,1\rangle$ are dark states, decoupled from the other states of the system.

Figure 8

Plots of the second-order correlation function $g^{\left(2\right)}\left(0\right)$ at total resonance (${\mathrm{\Delta }}_a={\mathrm{\Delta }}_c=0$) as a function of the normalized squeezed light strength $\lambda /\kappa$ for the two systems considered for the parameters $\varepsilon /\kappa =0.01$ and $\gamma =\kappa /2$ in (a) the weak-coupling regime case ($g=0.5\kappa$) and (b) the strong-coupling regime ($g=10\kappa$).

Figure 9

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted versus of the normalized strength of squeezed light $\lambda /\kappa$ for the two systems (${\mathrm{\Delta }}_c=0$ and ${\mathrm{\Delta }}_a=-0.5\kappa$) for the parameters $\varepsilon /\kappa =0.01$ and $\gamma =\kappa /2$ in (a) the weak-coupling regime ($g=0.5\kappa$) and (b) the strong-coupling regime ($g=10\kappa$).

Figure 10

Plots of the second-order correlation function $g^{\left(2\right)}\left(0\right)$ against the normalized strength of squeezed light $\lambda /\kappa$ for the two systems (${\mathrm{\Delta }}_a=0$ and ${\mathrm{\Delta }}_c=-0.5\kappa$) for parameters $\varepsilon /\kappa =0.01$ and $\gamma =\kappa /2$ in (a) the weak-coupling case ($g=0.5\kappa$) and (b) the strong-coupling case ($g=10\kappa$).

Figure 11

Optimal PB conditions for (a) squeezed light amplitude ${\lambda }_{1,2}$ and (b) detunings ${\mathrm{\Delta }}_{c,1,2}$ plotted as a function of the coupling strength $g/\kappa$ for the two systems, with $\gamma =\kappa /2$ and $\varepsilon /\kappa =0.01$.

Figure 12

Second-order correlation function $g^{\left(2\right)}\left(0\right)$ plotted versus normalized amplitude of squeezed light $\lambda /\kappa$ for the two systems (${\mathrm{\Delta }}_a={\mathrm{\Delta }}_c=\mathrm{\Delta }=-10\kappa$) for the parameters $\varepsilon /\kappa =0.01$ and $\gamma =\kappa /2$ in (a) the weak-coupling regime ($g=0.5\kappa$), (b) the strong-coupling regime ($g=10\kappa$), and (c) the strong-coupling regime ($g=10.3\kappa$).

Figure 13

(a)–(c) Density plots of the second-order correlation function $g^{\left(2\right)}\left(0\right)$ versus the normalized detunings ${\mathrm{\Delta }}_a/\kappa$ and ${\mathrm{\Delta }}_c/\kappa$ for $\gamma =\kappa /2, \varepsilon /\kappa =0.01$, and various values of squeezed light strength $\lambda$ for weak coupling given by $g/\kappa =0.45$: (a) $\lambda =0$, (b) $\lambda ={10}^{-4}\kappa$, and (c) $\lambda =5\times {10}^{-4}\kappa$. (d), (e), and (f) Cross sections of (a), (b), and (c), respectively, along ${\mathrm{\Delta }}_a$.