Polariton quantum blockade in a photonic dot

We investigate the quantum nonlinear dynamics of a resonantly excited photonic quantum dot embedding a quantum well in the strong exciton-photon coupling regime. Within a master equation approach, we study the polariton blockade effect due to polariton-polariton interactions as a function of the photonic dot geometry, spectral linewidths and energy detuning between quantum well exciton and confined photon mode. The second order coherence function $g^{\left(2\right)}(t,t^{\prime })$ and the photon antibunching are calculated for both continuous wave and pulsed excitations.

Figure 1

(Color online) Intra-cavity second-order coherence function $g^{\left(2\right)}\left(0\right)$ vs pump detuning $\hslash {\omega }_p-\hslash {\omega }_{LP}^{\mathit{\text{dot}}}$ (meV) for three different cavity-exciton detunings. Solid, dashed, dotted-dashed line: $\hslash ({\omega }_C^{\mathit{\text{dot}}}-{\omega }_X)=5$, 0, $-5\mathrm{meV}$. Parameters: $\hslash {\omega }_{nl}=0.4\mathrm{meV}$, $\hslash {\gamma }_X=\hslash {\gamma }_C=0.1\mathrm{meV}$, $\hslash {\Omega }_R=2.5\mathrm{meV}$ and continuous wave excitation field $\hslash {\mathcal{F}}_0={10}^{-2}\mathrm{meV}$.

Figure 2

(Color online) Second-order coherence function $g^{\left(2\right)}\left(0\right)$ for the photon (circles) and exciton (triangles) as a function of the normalized nonlinear coefficient ${\omega }_{nl}∕\gamma$ for three different values of $\delta =\hslash ({\omega }_C^{\mathit{\text{dot}}}-{\omega }_X)$. Parameters: $\hslash {\gamma }_X=\hslash {\gamma }_C=0.1\mathrm{meV}$ and ${\omega }_{LP}^{\mathit{\text{dot}}}={\omega }_p$.

Figure 3

(Color online) (a) Second-order coherence function $g_{\mathit{phot}}^{\left(2\right)}\left(0\right)$ (solid line) and intracavity photon population (dotted line) inside the dot as a function of pump power in the continuous wave regime. (b) Second-order coherence function $g_{\mathit{phot}}^{\left(2\right)}(t,t^{\prime })$ at a fixed $t^{\prime }$ as a function of time for two different pump powers. Parameters: $\delta =\hslash ({\omega }_C^{\mathit{\text{dot}}}-{\omega }_X)=5\mathrm{meV}$, $\hslash {\omega }_{nl}=1\mathrm{meV}$, $\hslash {\gamma }_X=\hslash {\gamma }_C=0.1\mathrm{meV}$.

Figure 4

(Color online) (a) Second-order correlation function $G_{\mathit{phot}}^{\left(2\right)}(t,t^{\prime })$ for $t^{\prime }=6\mathrm{ps}$ under the excitation of a train of Gaussian pulses (pulse duration of $5\mathrm{ps}$) separated from each other by $60\mathrm{ps}$. The normalized area is indicated for each peak. (b) Corresponding intra-cavity photon population $N_{\mathit{ph}}\left(t\right)$. Dotted line: Shape of the pump amplitude ${\mathcal{F}}_0\left(t\right)$. Parameters: $\hslash ({\omega }_C^{\mathit{\text{dot}}}-{\omega }_X)=5\mathrm{meV}$, $\hslash ({\omega }_p-{\omega }_{LP}^{\mathit{\text{dot}}})=-0.05\mathrm{meV}$, $\hslash {\omega }_{nl}=1.1\mathrm{meV}$, ${\mid {\mathcal{F}}_0\mid }^2∕{\gamma }^2=0.09$, $\hslash {\gamma }_X=\hslash {\gamma }_C=0.1\mathrm{meV}$, so $1∕\gamma =6.6\mathrm{ps}$.