Superradiant light scattering and grating formation in cold atomic vapours

A semi-classical theory of coherent light scattering from an elongated sample of cold atoms exposed to an off-resonant laser beam is presented. The model, which is a direct extension of that of the collective atomic recoil laser (CARL), describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample. It provides a simple physical picture of the recent observation of collective light scattering from a Bose-Einstein condensate [S. Inouye et al., Science N.285, p. 571 (1999)]. In addition, the model provides an analytical description of the temporal evolution of the scattered light intensity which shows good quantitative agreement with the experimental results of Inouye et al.Comment: submitted to Optics Communications, LaTex version, 2 postscript figure

Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate

We extend the semiclassical model of the collective atomic recoil laser (CARL) to include the quantum mechanical description of the center-of-mass motion of the atoms in a Bose-Einstein condensate (BEC). We show that when the average atomic momentum is less than the recoil momentum $\hbar\vec q$, the CARL equations reduce to the Maxwell-Bloch equations for two momentum levels. In the conservative regime (no radiation losses), the quantum model depends on a single collective parameter, $\rho$, that can be interpreted as the average number of photons scattered per atom in the classical limit. When $\rho\gg 1$, the semiclassical CARL regime is recovered, with many momentum levels populated at saturation. On the contrary, when $\rho\le 1$, the average momentum oscillates between zero and $\hbar\vec q$, and a periodic train of $2\pi$ hyperbolic secant pulses is emitted. In the dissipative regime (large radiation losses) and in a suitable quantum limit, a sequential superfluorescence scattering occurs, in which after each process atoms emit a $\pi$ hyperbolic secant pulse and populate a lower momentum state. These results describe the regular arrangement of the momentum pattern observed in recent experiments of superradiant Rayleigh scattering from a BEC.Comment: submitted for publication on Phys. Rev.

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

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

Effects of atomic diffraction on the Collective Atomic Recoil Laser

We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.Comment: plain tex, 10 pages, 10 figure

Optical bistability in sideband output modes induced by squeezed vacuum

We consider $N$ two-level atoms in a ring cavity interacting with a broadband squeezed vacuum centered at frequency $\omega_{s}$ and an input monochromatic driving field at frequency $\omega$. We show that, besides the central mode (at \o), many other {\em sideband modes} are produced at the output, with frequencies shifted from $\omega$ by multiples of $2(\omega -\omega_{s})$. Here we analyze the optical bistability of the two nearest sideband modes, one red-shifted and the other blue-shifted.Comment: Replaced with final published versio

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

Comparison of Recoil-Induced Resonances (RIR) and Collective Atomic Recoil Laser (CARL)

The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky and G. Grynberg, Phys. Rev. A {\bf 46}, 1426 (1992)] and the collective atomic recoil laser (CARL) [ R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods A {\bf 341}, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the RIR and CARL formalisms are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit considered in this paper is $qP_{0}/M\omega_{q}\gg 1$, while the CARL limit is $qP_{0}/M\omega_{q}\lesssim 1$, where $$ is the magnitude of the difference of the wave vectors of the pump and probe fields, $P_{0}$ is the width of the atomic momentum distribution and $$ is a recoil frequency. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how the gain arises in a system which, at first glance, might appear to have vanishing gain. Moreover, it is shown that the calculations, carried out in perturbation theory have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.Comment: 16 pages, 1 figure. Submitted to Physical Review

Non dissipative decoherence of Rabi oscillations

We present a simple theoretical description of two recent experiments where damping of Rabi oscillations, which cannot be attributed to dissipative decoherence, has been observed. This is obtained considering the evolution time or the Hamiltonian as random variables and then averaging the usual unitary evolution on a properly defined, model-independent, probability distribution.Comment: 4 pages, RevTe