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

Abstract

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 eV, duration 0.23 ps and intensity 5 · 10 13 W 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 ps and intensity 3.44 · 10 14 W 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.

Enhanced harmonic generation in double-well potentials

“…We first consider the computational results for the dication, as it has been previously studied, to a certain extent [12,13]. In all of the calculations, ω = 0.057 a.u., corresponding to a wavelength of 800 nm (1.55 eV photon energy) and the pulse shape is E(t) = E o sin 2 (t/t p ), with t p = 20 fs.…”

“…While this was seen before in Ref. [12], we have gone beyond simple 3-level calculations and considered the full TDSE for the double-well potential. Nevertheless, it is clear why the 3level approximation works for A 2+ 2 : the ionic states, which form the upper degenerate levels in the Γ system, lie below the covalent states and are well separated in energy.…”

“…At a large internuclear separation, the ionic states become degenerate and strongly coupled, with a dipole moment approaching the internuclear separation R. Under these conditions, high order (>10) multiphoton coupling becomes very strong, to the point where multiphoton π pulses [3] and adiabatic transfer become possible [11]. This 3-level structure has been dubbed the Γ system [12]. It was suggested and later verified that the Γ system also leads to enhanced harmonic generation [12][13][14].…”

“…This 3-level structure has been dubbed the Γ system [12]. It was suggested and later verified that the Γ system also leads to enhanced harmonic generation [12][13][14]. Because homonuclear diatomic molecules often follow the predictions from 1D models and they have the charge transfer states which make up the upper levels in the Γ system, homonuclear diatomics at expanded internuclear separations may be an attractive target for generating harmonic radiation.…”

Multiphoton population dynamics in a three-level lambda system and the related light-scattering spectrum

“…For these conditions, Equations (16) and (18) for Ω (P ) (t) need to be multiplied by the factor e −i∆t . After including this factor we were not able to solve the Riccati Equation (9) in an exact analytic way. So, we solved numer-ically the GRWA version of Equations (6) for u and v (S(t) → Ω (P ) (t)) and then obtained the solid-line curves shown in Figure 3.…”