We study experimentally the optical dipole trapping of a cloud of cold atoms in a
high-finesse cavity in the parameter regime where the atomic back-action on the cavity
mode is significant. Back-action based effects lead to state selective optical manipulation
schemes. We identify a parameter range where the collective back action of the atoms
is needed for the trapping, i.e. a single atom would not be trapped under the same
laser drive conditions. The collective self-trapping is demonstrated by the observation
of a significant increase of the trapping time as a function of the atom number. The
atomic back action on the cavity field gives rise to a simultaneous real-time monitoring
of the number of trapped atoms. This is used to show a non-exponential collapse of
the atom trap.
