We demonstrate that squeezed states of the radiation field in a free-electron laser are possible only in the small gain and inverse regimes. Moreover, in these regimes, the feasibility of generating squeezed radiation is severely constrained by the quantum fluctuations in the initial states of the electron beam.
A theory is developed for the interaction of coherent electromagnetic (EM) radiation with a free electron gas and for the influence of the plasma on the photon statistics of the radiation field. Two important possibilities for generating squeezed states are shown: Squeezed states can be generated by the interaction of a one-mode laser with a plasma in a cavity; squeezed states can be generated by transmitting coherent radiation through the plasma. The maximal squeezing of the radiation obtained in the latter case is equal to the reciprocal of the dielectric constant of the plasma. Inside the plasma the EM field is represented by quasiphotons. Their dispersion relations are derived by using Bogoliubov transformations together with a self-consistency requirement for the motion of the electrons interacting with these quasiphotons. The squeezing processes are found to be strong when the frequency of the radiation is a little above the plasma frequency. By adding a constant magnetic field in the direction of propagation of the EM wave different amounts of squeezing are obtained for right- and left-circularly polarized EM waves.
The photon statistics of a free-electron laser at steady state are investigated in the classical regime under the assumption of small gain per pass. A Fokker-Planck--type equation is derived for the photon-number distribution. Strong-signal results are presented, together with analytical expressions for the photon-number fluctuations, and the results are compared to the ordinary laser. It is shown that the radiation is not in a Glauber coherent state, and that the intensity fluctuations are classical, i.e., independent of \ensuremath{\Elzxh}.