Abstract
Free Electron Laser (FEL) and Collective Atomic Recoil Laser
(CARL) are described by the same model of classical equations for
properly defined scaled variables. These equations are extended
to the quantum domain describing the particle's motion by a
Schrödinger equation coupled to a self-consistent radiation
field. The model depends on a single collective parameter
which represents the maximum number of photons
emitted per particle. We demonstrate that the classical model is
recovered in the limit >> 1, in which the Wigner
function associated to the Schrödinger equation obeys to the
classical Vlasov equation. On the contrary, for ⩽ 1,
a new quantum regime is obtained in which both FELs and CARLs
behave as a two-state system coupled to the self-consistent
radiation field and described by Maxwell-Bloch equations.