A free-electron laser (FEL), shown in Fig. 1, is the prime example of a 'Classical Laser' [1], that is we do not need quantum mechanics to understand its operation. However, there also exists a regime of the FEL dynamics, the so-called Quantum FEL [2], where quantum mechanics is indeed important. In order to investigate the emergence and the properties of this limit of FEL operation, a collaboration of the Helmholtz-Zentrum Dresden-Rossendorf e. V. and the Institute of Quantum Physics was established.
The recoil due to the scattering of the electron by the photons of the wiggler and the laser field is the relevant quantity which determines the transition from classical to quantum (see Fig. 2) in the FEL [3]. Since the recoil depends linearly on the Planck constant \( \hbar \) we obtain the deep quantum limit when the recoil is the dominating momentum scale. In this regime we can describe the electron dynamics as an effective two-level system.