  The Area Theorem states that when a short optical pulse drives a quantum
two-level system, it undergoes Rabi oscillations in the probability of
scattering a single photon. In this work, we investigate the breakdown of the
Area Theorem as both the pulse length becomes non-negligible and for certain
pulse areas. Using simple quantum trajectories, we provide an analytic
approximation to the photon emission dynamics of a two-level system. Our model
provides an intuitive way to understand re-excitation, which elucidates the
mechanism behind the two-photon emission events that can spoil single-photon
emission. We experimentally measure the emission statistics from a
semiconductor quantum dot, acting as a two-level system, and show good
agreement with our simple model for short pulses. Additionally, the model
clearly explains our recent results [K. Fischer and L. Hanschke, et al., Nature
Physics (2017)] showing dominant two-photon emission from a two-level system
for pulses with interaction areas equal to an even multiple of $\pi$.
