  State mapping between atoms and photons, and photon-photon interactions play
an important role in scalable quantum information processing. We consider the
interaction of a two-level atom with a quantized \textit{propagating} pulse in
free space and study the probability $P_e(t)$ of finding the atom in the
excited state at any time $t$. This probability is expected to depend on (i)
the quantum state of the pulse field and (ii) the overlap between the pulse and
the dipole pattern of the atomic spontaneous emission. We show that the second
effect is captured by a single parameter $\Lambda\in[0,8\pi/3]$, obtained by
weighting the dipole pattern with the numerical aperture. Then $P_e(t)$ can be
obtained by solving time-dependent Heisenberg-Langevin equations. We provide
detailed solutions for both single photon Fock state and coherent states and
for various temporal shapes of the pulses.
