Resonant pulse excitation leading to ionization

Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\gamma$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time $t$, $\Phi \mathrm{}\left(t\right)\mathrm{}$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\Phi \mathrm{}\left(t\right)\mathrm{}\approx sin\Phi \mathrm{}\left(t\right)\mathrm{}$ and $\Omega \mathrm{}\left(t\right)>\gamma$, where $\Omega \mathrm{}\left(t\right)\mathrm{}$ is the resonance Rabi frequency. The generalization of the two-level atom results to the $N$-level atom is discussed.