  We demonstrate entanglement generation of two neutral atoms trapped inside an
optical cavity. Entanglement is created from initially separable two-atom
states through carving with weak photon pulses reflected from the cavity. A
polarization rotation of the photons heralds the entanglement. We show the
successful implementation of two different protocols and the generation of all
four Bell states with a maximum fidelity of (90+-2)%. The protocol works for
any distance between cavity-coupled atoms, and no individual addressing is
required. Our result constitutes an important step towards applications in
quantum networks, e.g. for entanglement swapping in a quantum repeater.
