A general, analytic theory is presented of the excitation of a two-lev
el atom by a series of short optical laser pulses. The atom is assumed
to be isolated (collisionless) with radiative decay from upper to low
er state at rate gamma. The laser pulses are assumed to have a duratio
n t(p) such that gammat(p) << 1 (the transient regime), and the spacin
g between pulses t(r) is such that t(r) >> t(p). In this regime the at
omic density matrix is calculated as a function of time during each op
tical 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 foll
owed by radiative decay. The excited-state population in the steady st
ate 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 convent
ional lasers and free-electron lasers, can be effective in optical pum
ping of atoms.