Pump-operator treatment of the ion-trap laser

We present a detailed treatment of a laser process that has been predicted for an experiment with a single trapped ${\mathrm{Ca}}^{+}$ ion. It is demonstrated how the complex multilevel system can be understood as a coherently pumped three-level scheme with time-delayed pumping out of the metastable lower laser level. This is described by a pump operator, which simplifies the numerical analysis substantially and allows for a treatment of more complicated systems.