Multiphoton resonance in a three-level system with nearly degenerate excited states

An analytic study is presented of the efficient multiphoton excitation and strong harmonic generation in three-level systems specified by a pair of nearly degenerate, strongly dipole-coupled excited states. Such systems are physically formed by the three lowest states in, e.g., the hydrogen atom or evenly charged homonuclear diatomic molecular ions under reasonably chosen laser intensities. As a detailed analytic result, we found that the laser pulse of photon energy $2{.}05\text{eV}$, duration $0{.}23\text{ps}$ and intensity $5\cdot 10^{13}\,\frac{\text{W}}{\text{cm}^2}$ is able to produce complete inversion of the initial population in the hydrogen atom through the 5-photon excitation. At the same photon energy, the pulse of duration $0{.}41\text{ps}$ and intensity $3{.}44\cdot 10^{14}\,\frac{\text{W}}{\text{cm}^2}$ was found to produce the same effect in the molecular ion but through the 9-photon excitation. We show that the accompanying scattering of light has very rich spectrum differing substantially from that of the two-level system.