Optimally driving multiphoton transitions in the perturbative single-mode regime

The rate of m -photon transitions in matter, induced by an incident light field, depends on the field's m th -order coherence function. Consequently, the coherence properties of the light field may be shaped to increase the rate of multiphoton transitions. Here, we determine the optimal state of a weak fixed-intensity, narrow-band incident light field, with a restricted maximal photon number, that optimally drives m -photon transitions in the case of a short-lived atomic multilevel system. We show that, in this case, no quantum properties of the light field need to be exploited, but that classical mixtures of coherent states are optimal.