  Scattering of light by matter has been studied extensively in the past. Yet,
the most fundamental process, the scattering of a single photon by a single
atom, is largely unexplored [1-3]. One prominent prediction of quantum optics
is the deterministic absorption of a traveling photon by a single atom,
provided the photon waveform matches spatially and temporally the time-reversed
version of a spontaneously emitted photon [4-12]. Here, we experimentally
address this prediction and investigate the influence of the temporal profile
of the photon on the scattering dynamics using a single trapped atom and
heralded single photons. In a time-resolved measurement of the atomic
excitation we find a 56(11)% increase of the peak excitation by photons with an
exponentially rising profile compared to a decaying one. This result
demonstrates that tailoring the envelope of single photons enables precise
control of the photon-atom interaction.
