EXCITATION OF AN ATOM BY A TRAIN OF SHORT PULSES

A general, analytic theory is presented of the excitation of a two-level atom by a series of short optical laser pulses. The atom is assumed to be isolated (collisionless) with radiative decay from upper to lower state at rate gamma. The laser pulses are assumed to have a duration t(p) such that gammat(p) << 1 (the transient regime), and the spacing between pulses t(r) is such that t(r) >> t(p). In this regime the atomic density matrix is calculated as a function of time during each optical pulse. An analytic expression for the atomic state (Bloch vector) after n optical pulses is also derived. For large n the atomic state converges to a repeating (steady state) cycle of pump excitation followed by radiative decay. The excited-state population in the steady state can be large but only if the spacing between pulses t(r) is small so that gammat(r) less than or similar to 0.5. These results indicate that lasers that produce trains of pulses, such as mode-locked conventional lasers and free-electron lasers, can be effective in optical pumping of atoms.