  Scattering is an elementary probe for matter and its interactions in all
areas of physics. Ultracold atomic gases provide a powerful platform in which
control over pair-wise interactions empowers us to investigate scattering in
quantum many-body systems. Past experiments on colliding Bose-Einstein
condensates have revealed many important features, including matter-wave
interference, halos of scattered atoms, four-wave mixing, and correlations
between counter-propagating pairs. However, a regime with strong stimulation of
spontaneous collisions analogous to superradiance has proven elusive. Here we
access that regime, finding that runaway stimulated collisions in condensates
with modulated interaction strength cause the emission of matter-wave jets
which resemble fireworks. Jets appear only above a threshold modulation
amplitude and their correlations are invariant even as the ejected atom number
grows exponentially. Hence, we show that the structures and occupations of the
jets stem from the quantum fluctuations of the condensate. Our findings
demonstrate the conditions for runaway stimulated collisions and reveal the
quantum nature of the matter-wave emission.
