High-gain quantum free-electron laser: Emergence and exponential gain

We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum FEL in the high-gain mode and avoids the experimental challenges of an x-ray FEL oscillator. Moreover, we study the intensity fluctuations of the emitted radiation, which turn out to be super-Poissonian.