Correction to the detector-dead-time effect on the second-order correlation of stationary sub-Poissonian light in a two-detector configuration

Exact measurement of the second-order correlation function $g^{(2)}(t)$ of a light source is essential when investigating the photon statistics and the light generation process of the source. For a stationary single-mode light source, Mandel Q factor is directly related to $g^{(2)}(t)$. For a large mean photon number in the mode, the deviation of $g^{(2)}(t)$ from unity is so small that even a tiny error in measuring $g^{(2)}(t)$ would result in an inaccurate Mandel Q. In this work, we have found that detector dead time can induce a serious error in $g^{(2)}(t)$ and thus in Mandel Q in those cases even in a two-detector configuration. Our finding contradicts the conventional understanding that detector dead time would not affect $g^{(2)}(t)$ in two-detector configurations. Utilizing the cavity-QED microlaser, a well-established sub-Poissonian light source, we measured $g^{(2)}(t)$ with two different types of photodetectors with different dead time. We also introduced prolonged dead time by intentionally deleting the photodetection events following a preceding one within a specified time interval. We found that the observed Q of the cavity-QED microlaser was underestimated by 19% with respect to the dead-time-free Q when its mean photon number was about 600. We derived an analytic formula which well explains the behavior of the $g^{(2)}(t)$ as a function of the dead time.