  Cold atoms in optical high-Q cavities are an ideal model system for
long-range interacting particles. The position of two arbitrary atoms is,
independent on their distance, coupled by the back-scattering of photons within
the cavity. This mutual coupling can lead to collective instability and
self-organization of a cloud of cold atoms interacting with the cavity fields.
This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed
theoretically for years, but was observed only recently in our lab. The
CARL-effect is closely linked to superradiant Rayleigh Scattering, which has
been intensely studied with Bose-Einstein condensates in free space. By adding
a resonator the coherence time of the system, in which the instability occurs,
can be strongly enhanced. This enables us to observe cavity-enhanced
superradiance with both Bose-Eisntein condensed and thermal clouds and allows
us to close the discussion about the role of quantum statistics in superradiant
scattering.
