Electromagnetic wave dynamics in matter-wave superradiant scattering

We present a small-signal wave propagation theory on matter-wave superradiant scattering. We show, in a longitudinally excited condensate, that the backward-propagating, superradiantly generated optical field propagates with ultraslow group velocity and that the small-signal gain profile has a Bragg resonance. We further show a unidirectional suppression of optical superradiant scattering, and explain why matter-wave superradiance can occur only when the pump laser is red detuned. This is the first analytical theory on field propagation in matter-wave superradiance that can explain all matter-wave superradiance experiments to date that used a single-frequency, long-pulse, red-detuned laser.