  Optical nonlinearities typically require macroscopic media, thereby making
their implementation at the quantum level an outstanding challenge. Here we
demonstrate a nonlinearity for one atom enclosed by two highly reflecting
mirrors. We send laser light through the input mirror and record the light from
the output mirror of the cavity. For weak laser intensity, we find the
vacuum-Rabi resonances. But for higher intensities, we find an additional
resonance. It originates from the fact that the cavity can accommodate only an
integer number of photons and that this photon number determines the
characteristic frequencies of the coupled atom-cavity system. We selectively
excite such a frequency by depositing at once two photons into the system and
find a transmission which increases with the laser intensity squared. The
nonlinearity differs from classical saturation nonlinearities and is direct
spectroscopic proof of the quantum nature of the atom-cavity system. It
provides a photon-photon interaction by means of one atom, and constitutes a
step towards a two-photon gateway or a single-photon transistor.
