This thesis reports on major steps towards the realization of scalable quantum networks. It
addresses the experimental implementation of a deterministic interaction mechanism between
flying optical photons and a single trapped atom. In particular it demonstrates the
nondestructive detection of an optical photon. To this end single rubidium atoms are trapped
in a three-dimensional optical lattice at the center of an optical cavity in the strong
coupling regime. Full control over the atomic state - its position its motion and its
electronic state - is achieved with laser beams applied along the resonator and from the side.
When faint laser pulses are reflected from the resonator the combined atom-photon state
acquires a state-dependent phase shift. In a first series of experiments this is employed to
nondestructively detect optical photons by measuring the atomic state after the reflection
process. Then quantum bits are encoded in the polarization of the laser pulse and in the
Zeeman state of the atom. The state-dependent phase shift mediates a deterministic universal
quantum gate between the atom and one or two successively reflected photons which is used to
generate entangled atom-photon atom-photon-photon and photon-photon states out of separable
input states.
