Bifurcations and chaos in pulse-train superradiance

Abstract

The superradiant response of a collection of three-level atoms to a train of pump pulses has been investigated numerically. It is assumed that the size of the system is small enough that propagation may be neglected and that the pump is resonant. The atoms are considered to be homogeneously broadened, and all relaxation rates are taken to be equal. The period of the pump pulse train is of the order of the atomic relaxation time, and the width of individual pulses is <4% of the period. Coherence remaining from previous pulses results in qualitative changes in the superradiant pulse train as the pump intensity is increased. Three cases of increasing complexity have been studied: square pump pulses, nondegenerate energy levels; mode-locked pulses, non-degenerate levels; and mode-locked pulses, degenerate levels. The sequence of behavior patterns is somewhat different for different cases. Features of the superradiant output common to the three cases are inversion of the electric field, alternation of positive and negative pulses, and recovery of pulses of one sign after more complicated behavior such as period-doubling, chaos, or intermittency. The effects of varying pump period or pulse shape are found to be less straightforward than that of varying pump intensity. The feasibility of experimental observation is discussed.