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

Abstract

Non Born-Oppenheimer quantum dynamics of H + 2 excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schrödinger equation within a three-dimensional model, including the internuclear separation, R, and the electron coordinates z and ρ. Laser carrier frequencies corresponding to the wavelengths λ l = 25 nm through λ l = 400 nm were used and the amplitudes of the pulses were chosen such that the energy of H + 2 was close to its dissociation threshold at the end of any laser pulse applied. It is shown that there exists a characteristic oscillation frequency ωosc ≃ 0.2265 au (corresponding to the period of τosc ≃ 0.671 fs and the wavelength of λosc ≃ 200 nm) that manifests itself as a "carrier" frequency of temporally shaped oscillations of the time-dependent expectation values z and ∂V /∂z that emerge at the ends of the laser pulses and exist on a timescale of at least 50 fs. Time-dependent expectation values ρ and ∂V /∂ρ of the optically-passive degree of freedom, ρ, demonstrate post-laser-field oscillations at two basic frequencies ω ρ 1 ≈ ωosc and ω ρ 2 ≈ 2ωosc. Power spectra associated with the electronic motion show higher-and lower-order harmonics with respect to the driving field.

Quantum coherent control of H3+ formation in strong fields

“…25 Following strong-field ionization, some electrons remain in a coherent superposition of excited states (or Rydberg states), which oscillate with frequencies that closely correspond to the harmonics of the laser. 26,27 These excited states are highly susceptible to further ionization depending on the properties of the pulse.…”