SummaryThis thesis reports on the experimental implementation of a deterministic interaction mechanism between flying optical photons and a single trapped atom. 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. In a second series of experiments, quantum bits are encoded in the polarization of the laser pulse and in the Zeeman state of the atom. The state-dependent phase shift then 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.3 4