Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a weakly nonlinear cavity

We study the photon-photon correlation properties of two-photon transport in a one-dimensional waveguide coupled to a nonlinear cavity via a real-space approach. It is shown that the intrinsic dissipation of the nonlinear cavity has an important effect upon the correlation of the transported photons. More importantly, strongly correlated photons can be obtained in the transmitted photons even when the nonlinear interaction strength is weak in the cavity. The strong photon-photon correlation is induced by the Fano resonance involving destructive interference between the plane wave and bound state for two-photon transport.

Figure 1

Schematic diagram of a 1D waveguide coupled to a cavity with a Kerr-type nonlinear medium. Photons injected into the waveguide from the left side are scattered by the nonlinear cavity, so the photons are reflected or transmitted in the waveguide.

Figure 2

(a), (b) ${\eta }_t$ and (c) ${\eta }_r$ plotted as functions of relative coordinate $\kappa x$ for different values of the coupling constant $\Gamma /\kappa$; (d) ${\eta }_{rt}$ plotted as a function of center-of-mass coordinate $\kappa x_c$ for different values of $\Gamma /\kappa$. The other parameters are ${\Delta }_1={\Delta }_2={\Delta }_a=0$, $U/\kappa =10$.

Figure 3

${\eta }_t$ plotted as a function of $\Gamma /\kappa$ for $x=0$. The other parameters are the same as in Fig. 2.

Figure 4

(a), (b) ${\eta }_t$ and (c) ${\eta }_r$ plotted as functions of $U/\kappa$ for different values of $\Gamma /\kappa$ with $x=0$; (d) ${\eta }_{rt}$ plotted as a function of $U/\kappa$ for different values of $\Gamma /\kappa$ with $x_c=0$. Here, ${\Delta }_1={\Delta }_2={\Delta }_a=0$.

Figure 5

(a) ${\eta }_t$ and ${\eta }_r$, (b) $|t(x_1,x_2){|}^2$ and $|r(x_1,x_2){|}^2$, and (c) ${log}_{10}\left[\right|t(x_1,x_2){|}^2]$, ${log}_{10}\left[\right|t_p(x_1,x_2){|}^2]$, and ${log}_{10}\left[\right|t_b(x_1,x_2){|}^2]$ plotted as functions of the detuning ${\Delta }_a/\kappa$ for $x=0$; (d) ${\eta }_t$ as a function of relative coordinate $\kappa x$ for ${\Delta }_a=\kappa /2$. The other parameters are $\Gamma =100\kappa$, $U=\kappa /100$, and ${\Delta }_1={\Delta }_2=0$.

Figure 6

(a) ${log}_{10}\left({\eta }_t\right)$ plotted as a function of $U/\kappa$ and $\Gamma /\kappa$; (b) ${log}_{10}\left({\eta }_t\right)$ plotted as a function of $U/\kappa$ for different values of $\Gamma /\kappa$. The detunings ${\Delta }_a=\kappa /2$, ${\Delta }_1={\Delta }_2=0$, and $x=0$.