Multiphoton processes and higher resonances in the quantum regime of the free-electron laser

Despite exhibiting novel radiation features, the operation of the proposed quantum free-electron laser would have the drawback that the number of emitted photons is limited by one per electron, significantly reducing the output power of such a device. We show that relying on different resonances of the initial momentum of the electrons increases the number of emitted photons, but also increases the required length of the undulator impeding an experimental realization. Moreover, we investigate how multiphoton processes influence the dynamics in the deep quantum regime.