A quantum model for collective recoil lasing

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 Schr\"{o}dinger 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 Schr\"{o}dinger equation obeys to the classical Vlasov equation. On the contrary, for $\bar \rho\le 1$, 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

The Semiclassical and Quantum Regimes of Superradiant Light Scattering from a Bose-Einstein Condensate

We show that many features of the recent experiments of Schneble et al. [D. Schneble, Y. Torii, M. Boyd, E.W. Streed, D.E. Pritchard and W. Ketterle, Science vol. 300, p. 475 (2003)], which demonstrate two different regimes of light scattering by a Bose-Einstein condensate, can be described using a one-dimensional mean-field quantum CARL model, where optical amplification occurs simultaneously with the production of a periodic density modulation in the atomic medium. The two regimes of light scattering observed in these experiments, originally described as ``Kapiza-Dirac scattering'' and ``Superradiant Rayleigh scattering'', can be interpreted as the semiclassical and quantum limits respectively of CARL lasing.Comment: 10 pages, 5 figures - to appear in Journal of Optics

Microscopic theory of photonic band gaps in optical lattices

We propose a microscopic model to describe the scattering of light by atoms in optical lattices. The model is shown to efficiently capture Bragg scattering, spontaneous emission and photonic band gaps. A connection to the transfer matrix formalism is established in the limit of a one-dimensional optical lattice, and we find the two theories to yield results in good agreement. The advantage of the microscopic model is, however, that it suits better for studies of finite-size and disorder effects.Comment: 5 pages, 6 figure

Atomic interaction effects in the superradiant light scattering from a Bose-Einstein condensate

We investigate the effects of the atomic interaction in the Superradiant Rayleigh scattering from a Bose-Einstein condensate driven by a far-detuned laser beam. We show that for a homogeneous atomic sample the atomic interaction has only a dispersive effect, whereas in the inhomogeneous case it may increase the decay of the matter-wave grating.Comment: 12 pages, 4 figures, presented to the XII International Laser Physics Workshop, August 24-29, Hamburg, to be published in Laser Physic

Quantum theory of SASE FEL

We describe a free-electron laser (FEL) in the Self-Amplified Spontaneous Emission (SASE) regime quantizing the electron motion and taking into account propagation effects. We demonstrate quantum purification of the SASE spectrum, i.e. in a properly defined quantum regime the spiking behavior disappears and the SASE power spectrum becomes very narrow

Recoil-induced subradiance in a cold atomic gas

Subradiance, i.e. the cooperative inhibition of spontaneous emission by destructive interatomic interference, can be realized in a cold atomic sample confined in a ring cavity and lightened by a two-frequency laser. The atoms, scattering the photons of the two laser fields into the cavity-mode, recoil and change their momentum. Under proper conditions the atomic initial momentum state and the first two momentum recoil states form a three-level degenerate cascade. A stationary subradiant state is obtained after that the scattered photons have left the cavity, leaving the atoms in a coherent superposition of the three collective momentum states. After a semiclassical description of the process, we calculate the quantum subradiant state and its Wigner function. Anti-bunching and quantum correlations between the three atomic modes of the subradiant state are demonstrated

Mirror-assisted coherent backscattering from the Mollow sidebands

In front of a mirror, the radiation of weakly driven large disordered clouds presents an interference fringe in the backward direction, on top of an incoherent background. Although strongly driven atoms usually present little coherent scattering, we here show that the mirror-assisted version can produce high contrast fringes, for arbitrarily high saturation parameters. The contrast of the fringes oscillates with the Rabi frequency of the atomic transition and the distance between the mirror and the atoms, due to the coherent interference between the carrier and the Mollow sidebands of the saturated resonant fluorescence spectrum emitted by the atoms. The setup thus represents a powerful platform to study the spectral properties of ensembles of correlated scatterers

Superradiant evolution of radiation pulses in a free-electron laser

We demonstrate analytically and numerically superradiant spiking behavior in the leading and trailing regions of a radiation pulse propagating within a long electron pulse in a single-pass, high-gain free-electron laser (FED). A single superradiant spike is observed when the radiation pulse is shorter than a cooperation length Lc. We show this work may be relevant to the understanding of the spiking behavior in the FEL oscillator, and to possible spiking mechanisms in a perturbed steady-state amplifier