Delay-time statistics of superfluorescent pulses

Abstract

We discuss the delay-time statistics of superfluorescent pulses by introducing the concept of a passage time at which the field intensity reaches a specified value. Such passage times can be estimated accurately from the early-stage linear dynamics of the radiating system. The distribution function for the passage times, we show, can be expressed as a functional integral over the random zero point fluctuations of the atomic polarization. The functional integral can be evaluated exactly and reduced to an elementary closed form. Our theory applies both to the sharp and the broadened atomic line. The results we obtain agree with experimental data and numerical calculations already in existence for the unbroadened line. For the broadened line we predict substantial changes of the mean value and the variance of the passage time as the width of the atomic line increases. We also investigate the influence of the shape of the spectral distribution of atomic frequencies and show that the delay statistics depend significantly on the way in which the spectral density decreases in the wings of the atomic line.