Effects of atomic diffraction on the collective atomic recoil laser

We formulate a wave-atom-optics theory of the collective atomic recoil laser (CARL) 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 atomic 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 this temperature regime one can no longer ignore the effects of matter-wave diffraction on the atomic center-of-mass motion.