Europhys. Lett.
Volume 69, Number 1, January 2005
Page(s) 55 - 60
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 08 December 2004
Europhys. Lett., 69 (1), pp. 55-60 (2005)
DOI: 10.1209/epl/i2004-10308-1

A quantum model for collective recoil lasing

R. Bonifacio1, M. M. Cola1, N. Piovella1 and G. R. M. Robb2

1  Dipartimento di Fisica, Università degli Studi di Milano, INFM & INFN Via Celoria 16, Milano I-20133, Italy
2  Department of Physics, University of Strathclyde - Glasgow, G4 0NG, UK

received 19 July 2004; accepted in final form 29 October 2004
published online 8 December 2004

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 $\bar{\rho}$ which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit $\bar{\rho}\gg 1$, in which the Wigner function associated to the Schrödinger equation obeys to the classical Vlasov equation. On the contrary, for $\bar{\rho}\le1$, 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.

42.50.Fx - Cooperative phenomena in quantum optical systems.
41.60.Cr - Free-electron lasers.
42.50.Vk - Mechanical effects of light on atoms, molecules, electrons, and ions.

© EDP Sciences 2005