Propagation effects in the quantum description of collective recoil lasing

The free electron laser and collective atomic recoil laser (CARL) are examples of collective recoil lasing, where exponential amplification of a radiation field occurs simultaneously with self-bunching of an ensemble of particles (electrons in the case of the FEL and atoms in the case of the CARL). In this paper, we discuss quantum and propagation effects using a model where the particle dynamics are described quantum-mechanically in terms of a matter-wave field, which evolves self-consistently with the radiation field. The model shows that the scattered radiation evolves superradiantly both in the case where the particle ensemble is short compared to the cooperation length of the system, and where the ensemble is long compared to the cooperation length. In both short and long pulse cases there exist a classical and quantum regime of superradiant emission. For short samples in both quantum and classical regimes the superradiant pulse has a low peak intensity and is said to exhibit 'weak' superradiance. For long pulses in both quantum and classical regimes of evolution, the dynamics at the rear edge of the sample is dominated by propagation. This produces a 'strong' superradiant pulse with much higher peak intensity than that predicted by 'mean-field' or 'steady-state' models in which propagation effects are neglected.