Delay-Time Statistics and Inhomogeneous Line Broadening in Superfluorescence

A probability distribution $W\left(t\right)\mathrm{}$ for the delay time $t$ of superfluorescent pulses is defined in terms of a functional integral, which is evaluated exactly. Although the linearized early-stage dynamics is used, full agreement is obtained with previous numerical and experimental results for the variance of $t$ and, more generally, for the shape of $W\left(t\right)\mathrm{}$. The effect of inhomogeneous broadening of the atomic levels, showing that decrease of the dephasing time ${T_2}^{*}$ leads to substantial increase of the mean and variance of $t$, is also analyzed.