  We apply techniques of subriemannian geometry on Lie groups to laser-induced
population transfer in a three-level quantum system. The aim is to induce
transitions by two laser pulses, of arbitrary shape and frequency, minimizing
the pulse energy. We prove that the Hamiltonian system given by the Pontryagin
Maximum Principle is completely integrable, since this problem can be stated as
a ``$\k\oplus\p$ problem'' on a simple Lie group. Optimal trajectories and
controls are exhausted. The main result is that optimal controls correspond to
lasers that are ``in resonance''.
