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 o
f 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.
