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 polarised 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 ω_osc ≃ 0.2265 au (corresponding to the period of τ_osc ≃ 0.671 fs and the wavelength of λ_osc ≃ 201 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 ≈ ω_osc and ω^ρ ₂ ≈ 2ω_osc. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.

KEYWORDS:

• One-cycle laser pulses
• post-laser-field electronic oscillations
• generation of higher and lower harmonics

Acknowledgment

This work has been financially supported by the Deutsche Forschungsgemeinschaft through the SFB 652 (G.K.P., O.K.), which is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Deutsche Forschungsgemeinschaft [Grant Number SFB 652].