  A superfluid atomic gas is prepared inside an optical resonator with an
ultra-narrow band width on the order of the single photon recoil energy. When a
monochromatic off-resonant laser beam irradiates the atoms, above a critical
intensity the cavity emits superradiant light pulses with a duration on the
order of its photon storage time. The atoms are collectively scattered into
coherent superpositions of discrete momentum states, which can be precisely
controlled by adjusting the cavity resonance frequency. With appropriate pulse
sequences the entire atomic sample can be collectively accelerated or
decelerated by multiples of two recoil momenta. The instability boundary for
the onset of matter wave superradiance is recorded and its main features are
explained by a mean field model.
