Complete population transfer in a three-state quantum system by a train of pairs of coincident pulses

A technique for complete population transfer between the two end states $\mathrm{\mid }1⟩$ and $\mathrm{\mid }3⟩$ of a three-state quantum system with a train of $N$ pairs of resonant and coincident pump and Stokes pulses is introduced. A simple analytic formula is derived for the ratios of the pulse amplitudes in each pair for which the maximum transient population $P_2(t)$ of the middle state $\mathrm{\mid }2⟩$ is minimized, $P_2^{\max }={\sin }^2(\pi \mathrm{/}4N)$. It is remarkable that, even though the pulses are on exact resonance, $P_2(t)$ is damped to negligibly small values even for a small number of pulse pairs. The population dynamics resembles generalized $\pi$-pulses for small $N$ and stimulated Raman adiabatic passage for large $N$ and therefore this technique can be viewed as a bridge between these well-known techniques.