  We study the optomechanical interaction of a Bose-Einstein condensate with a
single longitudinal mode of an ultra-high finesse standing wave optical
resonator. As a unique feature the resonator combines three extreme regimes,
previously not realized together, i.e., strong cooperative coupling, cavity
dominated scattering with a Purcell factor far above unity, and sub-recoil
resolution provided by a cavity damping rate smaller than four times the single
photon recoil frequency. We present experimental observations in good agreement
with a two-mode model predicting highly non-linear dynamics with signatures as
bistability, hysteresis, persistent oscillations, and superradiant
back-scattering instabilities.
