Delay-time statistics and inhomogeneous line broadening in superfluorescence

A probability distribution W(t) 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(t). The effect of inhomogeneous broadening of the atomic levels, showing that decrease of the dephasing time T2* leads to substantial increase of the mean and variance of t, is also analyzed