Physics – Condensed Matter
Scientific paper
2001-02-20
Physics
Condensed Matter
submitted for publication on Phys. Rev. A
Scientific paper
10.1016/S0030-4018(01)01293-7
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.
Bonifacio Rodolfo
Gatelli M.
Piovella Nicola
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