Strong photon antibunching of symmetric and antisymmetric modes in weakly nonlinear photonic molecules

We study the photon statistics of symmetric and antisymmetric modes in a photonic molecule consisting of two linearly coupled nonlinear cavity modes. Our calculations show that strong photon antibunching of both symmetric and antisymmetric modes can be obtained even when the nonlinearity in the photonic molecule is weak. The strong antibunching effect results from the destructive interference between different paths for two-photon excitation. Moreover, we find that the optimal frequency detunings for strong photon antibunching in the symmetric and antisymmetric modes are linearly dependent on the coupling strength between the cavity modes in the photonic molecule. This implies that the photonic molecules can be used to generate tunable single-photon sources by tuning the values of the coupling strength between the cavity modes with weak nonlinearity.

Figure 1

Schematic diagram of the setup for the detection of photon antibunching effects of symmetric and antisymmetric modes in a photonic molecule consisting of two tunnel-coupled nonlinear microtoroids. ${\kappa }_{\exp }$ is the loss rate for detection.

Figure 2

Logarithmic plot (of base 10) of the equal-time second-order correlation functions $g_{\pm }^{\left(2\right)}\left(0\right)$ as functions of the detuning $\Delta$ and the nonlinear interaction strength $U/\kappa$ for the coupling strength $J=20\kappa$ and Rabi frequency $\varepsilon =0.01\kappa$.

Figure 3

The equal-time second-order correlation functions $g_{\pm }^{\left(2\right)}\left(0\right)$ plotted as functions of the detuning $\Delta /\kappa$ for nonlinear interaction strength (a) $U/\kappa =0.0125$ and (b) $U/\kappa =-0.0125$. The parameters are $J=20\kappa$ and $\varepsilon =0.01\kappa$.

Figure 4

The equal-time second-order correlation functions $g_{\pm }^{\left(2\right)}\left(0\right)$ as functions of nonlinear interaction strength $U$ normalized to ${\kappa }^2/J$ with Rabi frequency $\varepsilon =0.01\kappa$: black solid line, $g_{+}^{\left(2\right)}\left(0\right)$ for $\Delta =-J=-20\kappa$; red dashed line, $g_{-}^{\left(2\right)}\left(0\right)$ for $\Delta =J=20\kappa$.

Figure 5

Logarithmic plot (of base 10) of the equal-time second-order correlation function $g_{+}^{\left(2\right)}\left(0\right)$ as a function of nonlinear interaction strength $U/\kappa$ and coupling strength $J/\kappa$ for $\Delta =-J$ and $\varepsilon =0.01\kappa$.

Figure 6

The equal-time second-order correlation function $g_{+}^{\left(2\right)}\left(0\right)$ as a function of the detuning $\Delta /\kappa$ for different values of the coupling strength $J$ with nonlinear interaction strength $U/\kappa =\kappa /\left(4J\right)$ and Rabi frequency $\varepsilon =0.01\kappa$: black solid line, $J=30\kappa$; red dashed line, $J=20\kappa$; blue short dashed line, $J=10\kappa$.

Figure 7

(a) The second-order correlation functions $g_{+}^{\left(2\right)}\left(\tau \right)$ as a function of the time delay $\tau$. (b) $g_{+}^{\left(2\right)}\left(\tau \right)$ as a function of the normalized time delay $\tau /[2\pi /(2J\left)\right]$. The parameters are $\Delta =-5\kappa$, $J=5\kappa$, $U=0.05\kappa$, $\varepsilon =0.01\kappa$, and $\kappa =2\pi \times 100$ MHz.

Figure 8

Energy-level diagram showing the zero-, one-, and two-photon states (horizontal black short lines) and the transition paths leading to the quantum interference responsible for the strong antibunching (color lines with arrows). $|n_{+},n_{-}\rangle$ represents the Fock state with $n_{+}$ photons in the symmetric mode and $n_{-}$ photons in the antisymmetric mode.