Second-order correlations in an exciton-polariton Rabi oscillator

We develop the theoretical formalism to calculate second-order correlations in dissipative exciton-polariton system and we propose intensity-intensity correlation experiments to reveal the physics of exciton-light coupling in semiconductor microcavities in the Rabi oscillation regime. We predict a counterintuitive behavior of the correlator between upper and lower polariton branches: Due to the decoherence caused by stochastic exciton-photon conversions this correlator is expected to decrease below 1, while the individual second-order coherence of upper and lower polaritons exhibits nonmonotonous bunching.

Figure 1

The scheme of the two-color intensity-intensity correlation measurement between upper and lower polariton branches. A short pulse of light excites the system and induces polariton Rabi oscillations. Correlations of the intensities of secondary emission harmonics corresponding to upper and lower polariton branches are studied.

Figure 2

Showing the time dependencies of normalized nonzero components of the tensor ${\mathbb{S}}_{\mu \nu }$ after excitation of a photon state at $t=0$. The curves are labeled by indices $\left(\mu \nu \right)$. The parameters are ${\tau }_c/{\tau }_{xc}=0.4, {\tau }_x/{\tau }_{xc}=1.6, {\omega }_R{\tau }_{xc}=10$, and $\mathrm{\Delta }={\gamma }^{\prime }=0$.

Figure 3

The time evolution of the correlators (a) $g_{ul}$, (b) $g_u^{\left(2\right)}$ (solid lines) and $g_l^{\left(2\right)}$ (dashed lines), and (c) $G_{ul}$ for different exciton-photon conversion times, (1) ${\tau }_c/{\tau }_{xc}=0.5$, (2) ${\tau }_c/{\tau }_{xc}=0.1$, and (3) ${\tau }_c/{\tau }_{xc}=0.02$. We note that in the absence of stochastic processes (${\tau }_{xc}^{-1}=0$) all correlators shown in this figure become time independent and stay equal to 1. The other parameters are ${\tau }_x=4{\tau }_c, {\omega }_R{\tau }_c=20, \mathrm{\Delta }{\tau }_c=-5$, and ${\gamma }^{\prime }=0$.

Figure 4

The asymptotic (long time) value of the correlator $G_{ul}$ as a function of detuning for ${\gamma }^{\prime }/{\omega }_R=0$ (curve 1), ${\gamma }^{\prime }/{\omega }_R=0.01$ (curve 2), and ${\gamma }^{\prime }/{\omega }_R=0.02$ (curve 3). The other parameters are $\gamma /{\omega }_R=0.02$ and ${\omega }_R{\tau }_{xc}=200$.