  We experimentally investigate the spin dynamics of one and two neutral atoms
strongly coupled to a high finesse optical cavity. We observe quantum jumps
between hyperfine ground states of a single atom. The interaction-induced
normal mode splitting of the atom-cavity system is measured via the atomic
excitation. Moreover, we observe evidence for conditional dynamics of two atoms
simultaneously coupled to the cavity mode. Our results point towards the
realization of measurement-induced entanglement schemes for neutral atoms in
optical cavities.
