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Physical Review A

Delay-time statistics in superfluorescence for large Fresnel numbers

Jan Mostowski, Božena Sobolewska

Published Oct 1, 1983• 13 citations
Publisher

Abstract

A probability distribution for the delay time of superfluorescent pulses is calculated as a function of the Fresnel number from the solution of the linearized Maxwell-Bloch equations in three dimensions.
DOI
10.1103/physreva.28.2573

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We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ensuremath{\ge} 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.
Measurements are reported of the quantum fluctuations in superfluorescence delay times. The fluctuations depend strongly on the Fresnel number FFF of the sample. For $F\ensuremath{\approx}1$ fair agreement with recent theories is obtained, while for larger FFF the fluctuations are smaller. A qualitative explanation for this FFF dependence is proposed. No correlation has been found between the delay times of pulses emitted from opposite ends of the same sample.
A probability distribution W(t)W(t)W(t) for the delay time ttt 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 ttt and, more generally, for the shape of W(t)W(t)W(t). The effect of inhomogeneous broadening of the atomic levels, showing that decrease of the dephasing time T2∗{{T}_{2}}^{*}T2​∗ leads to substantial increase of the mean and variance of ttt, is also analyzed.