Quantum statistical properties of an FEL amplifier

We discuss the problem of photon quantum statistics of a single particle free-electron laser (FEL) amplifier in the small-signal cold beam regime to first order in the electron quantum recoil. The initial radiation wave is an arbitrary coherent state. We show that Glauber coherence is not preserved by the FEL interaction if the initial coherent state is not the vacuum, even if we neglect the electron quantum recoil (absence of gain). We evaluate the first two moments of the final photon distribution and find sub- (super)-Poissonian photon statistics for a negative (positive) resonance parameter.