Vibrational excitation of simple molecular ions in resonant and under-resonant strong laser fields: Dissociation and ionization of ppe and pde; laser-enhanced nuclear fusion in ddμ and dtμ

Excitation of H+ 2 with one-cycle laser pulses: shaped post-laser-field electronic oscillations, generation of higher- and lower-order harmonics

“…We can conclude therefore, that periodic elongation-contraction of the bond of H + 2 ( Figure 6) is controlled by compressing-expanding electron acceleration along the z axis ( Figure 7) which takes place with the period of τ shp ≈ 30 fs corresponding to the frequency ω shp = 2π/τ shp of shaped post-laser-field oscillations occurring with the carrier oscillation frequency ω osc ≃ 0.2278 au (corresponding to the wavelength of λ osc ≃ 200 nm). Similar electron-nuclei correlations were found in our recent work [3] where two-cycle laser pulses were used to excite H + 2 and a more detailed explanation is given for post-laser-field electron-nuclei correlations in terms of below-resonance vibrational frequency [9,15] and for the existence of characteristic oscillation frequency ω osc (corresponding to λ osc ≃ 200 nm) in terms of a continuum state Ψ C prepared by the laser pulses. Afterwards, at t > 7 − 9 fs, expectation values ρ demonstrate a rather smooth behavior, with the electron excursion along the transversal ρ coordinate being quite strongly dependent of the laser pulse amplitude used to excite H + 2 initially along the z axis.…”

“…While the appearance of electronic ρ-oscillations with the frequency ω ρ 1 ≈ ω osc being very close to the frequency of electronic z-oscillations could be expected, the "frequency-doubling" of electronic ρ-oscillations occurring at ω ρ 2 ≈ 2ω osc needs more explanations. Such a frequency-doubling of electronic z-oscillations by its ρ-oscillations occurring at ω ρ 2 ≈ 2ω osc was explained in our previous works [8,9] as follows. During electronic oscillations along the z axis, the electronic density is substantially delocal- ized also in the transversal, ρ direction, due to the wave properties of the electron.…”

“…where −e is the electron charge, M p and M e are the proton and the electron masses, respectively. The homonuclear H + 2 molecular ion does not have a permanent dipole moment, therefore its vibrational motion is excited only indirectly due to electronic motion induced by the laser field along the z axis [7][8][9]. Electronic motion along the transversal ρ axis occurs only due to the wave properties of the electron.…”

“…The numerical methods used to solve the three-dimensional Equation (2) have been described in our previous works [8,9]. In particular, the dissociation probability has been calculated with the time-and space-integrated outgoing flux for the nuclear coordinate R; the ionization probabilities have been calculated with the respective fluxes separately for the positive and the negative direction of the z axis as well as for the outer end of the ρ axis.…”

“…According to the well-known recollision model of Corkum [4], electron follows the field out-of-phase: the expectation value z(t) decreases when electric-field strength E(t) increases. Previously, a perfect electron-field out-of-phase following on the level of expectation values z of the laser-driven electronic degree of freedom have been found only in the infrared [8,9] and near-infrared [13] domains of the laser carrier frequency, with a large number of optical cycles per pulse duration t p being involved. It was also found in our previous work [14] that electrons of the extended H-H system follow the applied laser field out-of phase at the laser carrier frequency ω l < 0.1 au, and in-phase at ω l = 1 au, with the number of optical cycles per pulse duration being about 33.…”