Exact measurement of the second-order correlation function $g^{\left(2\right)}\left(t\right)$ 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, the Mandel $Q$ factor is directly related to $g^{\left(2\right)}\left(0\right)$. For a large mean photon number in the mode, the deviation of $g^{\left(2\right)}\left(0\right)$ from unity is so small that even a tiny error in measuring $g^{\left(2\right)}\left(0\right)$ would result in an inaccurate Mandel $Q$. In this work, we address the detector-dead-time effect on $g^{\left(2\right)}\left(0\right)$ of stationary sub-Poissonian light. It is then found that detector dead time can induce a serious error in $g^{\left(2\right)}\left(0\right)$ and thus in Mandel $Q$ in those cases even in a two-detector configuration. Utilizing the cavity-QED microlaser, a well-established sub-Poissonian light source, we measured $g^{\left(2\right)}\left(0\right)$ with two different types of photodetectors with different dead times. 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 $g^{\left(2\right)}\left(0\right)$ as a function of the dead time.

• Received 28 March 2015

DOI:https://doi.org/10.1103/PhysRevA.92.023830