Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers

Ultrafast changes in the statistical properties of light emission are studied for quantum-dot micropillar lasers. Using pulsed excitation with varying power, we follow the time evolution of the second-order correlation function $g^{\left(2\right)}\left(t,\tau =0\right)$ reflecting two-photon coincidences and compare it to that of the output intensity. The previously impossible time resolution of a few picoseconds gives insight into the dynamical transition between thermal and coherent light emission. The $g^{\left(2\right)}$ results allow us to isolate the spontaneous and stimulated-emission contributions within an emission pulse, not accessible via the emission-intensity dynamics. Results of a microscopic theory confirm the experimental findings.

Figure 1

Integrated intensity of the $6\mu \text{m}$ pillar’s fundamental mode under nonresonant pulsed excitation. Above threshold, saturation effects become apparent. Filled squares mark the data sets shown in Fig. 2.

Figure 2

(Color online) Time evolution of second-order photon-correlation function $g^{\left(2\right)}\left(t,0\right)$ (symbols) compared to the normalized output intensity (solid lines) for the $6\mu \text{m}$ pillar fundamental mode. Black and red dotted lines denote the limiting cases of $g^{\left(2\right)}\left(t,0\right)$ for coherent and thermal light, respectively. The power density for pulsed excitation increases from top to bottom. $t_{\text{peak}}$ corresponds to the maximum of the emission intensity for each pump power.

Figure 3

(Color online) Upper panel: relative fractions of coherent and thermal emission at a fixed $g^{\left(2\right)}\left(t,0\right)$ as given by a two-mode model (solid lines) compared to the ideal case for infinitely small sampling time (dashed lines). Small deviations occur at high thermal fractions. Lower panel: effect of jitter on the measured $g^{\left(2\right)}\left(t,0\right)$ for a coherent light pulse depending on the ratio $r$ of the mean photon count rates at the pulse positions connected by the jitter and the relative frequency $p$ of jitter occurrence. While frequent jitter (solid red line) has the same effects for pulse positions with high and low intensity, rare events (dotted black line) only affect regions with low mean photon count rate (high $r$).

Figure 4

(Color online) Calculated input-output curve (inset) and time evolution of the mean photon number (dashed lines) and the second-order correlation function (solid lines) for selected values of the time-integrated pump rate indicated by the color-coded dots on the input-output curve. All curves are calculated for a pump-pulse width of 68 ps. The following parameters were used: number of resonant QDs: 140, cavity loss rate 2 $\kappa :0.09{\text{ps}}^{-1}$, spontaneous lifetime: 4.3 ps, scattering rates into (out of) the lasing transition: $11.7{\text{ps}}^{-1}\left(23.3{\text{ps}}^{-1}\right)$, light-matter coupling constant $g:0.22{\text{ps}}^{-1}$, loss rate to nonlasing modes: ${\Gamma }_{nl}=0.22{\text{ps}}^{-1}$, and constant dephasing: $\Gamma =8.5{\text{ps}}^{-1}$. Comparison with extended calculations including an inhomogeneously broadened ensemble gives very similar results with the present calculations using a homogeneous ensemble subject to considerable dephasing.