Collapses and revivals of exciton emission in a semiconductor microcavity: Detuning and phase-space filling effects

We investigate exciton emission of a quantum well embedded in a semiconductor microcavity. The analytical expressions of the light intensity for the cases of the excitonic number state and the coherent state are presented by using secular approximation. Our results show that the effective exciton-exciton interaction leads to the appearance of collapse and revival of the light intensity. The revival time is twice compared the coherent state case with that of the number state. The dissipation of the exciton-polariton lowers the revival amplitude but does not alter the revival time. The influences of the detuning and the phase-space filling are studied. We find that the effect of higher-order exciton-photon interaction can be removed by adjusting the detuning.

Figure 1

Light intensity for the number state case as a function of time $t$. Time is in units of $1∕\gamma$ and light intensity is in arbitrary units. The parameters are $g=1000\gamma$, $A=0.01g$, $B=0$, and $\delta =0$. Starting from the top: (a) $N=2$, without dissipation; (b) $N=2$, $\gamma =1$; (c) $N=11$, without dissipation; (d) $N=11$, $\gamma =1$.

Figure 2

Light intensity for the number state case as a function of time $t$, obtained from Eq. (15). Time is in units of $1∕\gamma$ and light intensity is in arbitrary units. Other parameters are $g=1000\gamma$, $A=0.01g$, and $N=10$. Starting from the top: (a) $\delta =0.2g$, $B=0$; (b) $\delta =0.2g$, $B=0.3A$; (c) $\delta =0.4g$, $B=0.3$; (d) $\delta =0.6g$, $B=0.3A$.

Figure 3

Light intensity for the coherent state case as a function of time $t$. Time is in units of $1∕\gamma$ and light intensity is in arbitrary units. Other parameters are $g=1000\gamma$, $A=0.01g$, $B=0$, and $\delta =0$. From top to bottom: (a) $⟨N⟩=2$, without dissipation; (b) $⟨N⟩=2$, $\gamma =1$; (c) $⟨N⟩=11$, without dissipation; (d) $⟨N⟩=11$, $\gamma =1$.