Photon echo in the super-radiant light scattering from a Bose-Einstein condensate

Super-radiant Rayleigh scattering from a Bose-Einstein condensate, driven by a single far-detuned laser beam, is strongly limited by dephasing due to inhomogeneous broadening. We demonstrate that the dephasing can be reversed applying a Bragg pulse of area $\pi$ after the first superradiant scattering, stimulating a superradiant echo and inducing a further transfer of atoms from the initial condensate to a condensate with relative momentum $2ħk$ in the direction of the laser.