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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 ωosc ≃ 0.2265 au (corresponding to the period of τosc ≃ 0.671 fs and the wavelength of λosc ≃ 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 ωρ 1 ≈ ωosc and ωρ 2 ≈ 2ωosc. Power spectra associated with the electronic motion show higher- and lower-order harmonics with respect to the driving field.
Non-Born-Oppenheimer quantum dynamics of H-2(+) and HD+ excited by single one-cycle laser pulses linearly polarized along the molecular (z) axis have been studied within a three-dimensional model, including the internuclear distance R and electron coordinates z and rho, by means of the numerical solution of the time-dependent Schrodinger equation on the timescale of about 200 fs. Laser carrier frequencies corresponding to the wavelengths of lambda(l) = 400 and 50 nm have been used and the amplitudes of the pulses have been chosen such that the energies of H-2(+) and HD+ are above the dissociation threshold after the ends of the laser pulses. It is shown that excitation of H-2(+) and HD+ above the dissociation threshold is accompanied by formation of vibrationally "hot" and "cold" ensembles of molecules. Dissociation of vibrationally "hot" molecules does not prevent the appearance of post-laser-pulse electronic oscillations, parallel z oscillations, and transversal rho oscillations. Moreover, dissociation of "hot" molecules does not influence characteristic frequencies of electronic z and rho oscillations. The main difference between the laser-induced quantum dynamics of homonuclear H-2(+) and its heteronuclear isotope HD+ is that fast post-laser-pulse electronic z oscillations in H-2(+) are regularly shaped with the period of tau(shp) approximate to 30 fs corresponding to nuclear oscillations in H-2(+), while electronic z oscillations in HD+ arise as "echo pulses" of its initial excitation and appear with the period of tau(echo) approximate to 80 fs corresponding to nuclear motion in HD+. Accordingly, corresponding power spectra of nuclear motion contain strong low-frequency harmonics at omega(shp) = 2 pi/tau(shp) in H2(+) and omega(echo) = 2 pi/tau(echo) in HD+. Power spectra related to both electronic and nuclear motion have been calculated in the acceleration form. Both higher- and lower-order harmonics are generated at the laser wavelength lambda(l) = 400 nm, while only lower-order harmonics are well pronounced at lambda(l) = 50 nm. It is also shown that a rationalized harmonic order, defined in terms of the frequency of the laser-induced electronic z oscillations, agrees with the concept of inversion symmetry for electronic motion in diatomic molecules.
Quantum dynamics of H-2(+) excited by two-cycle laser pulses with laser carrier frequencies corresponding to the wavelengths lambda(1) = 800 and 200 nm (corresponding to the periods tau(1) = 2.667 and 0.667 fs, respectively) and being linearly polarized along the molecular axis have been studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrodinger equation within a three-dimensional (3D) model, including the internuclear distance R and electron coordinates z and rho. The amplitudes of the pulses have been chosen such that the energies of H-2(+) after the ends of the laser pulses, < E > approximate to-0.515 au, were close to the dissociation threshold of H-2(+). It is found that there exists a certain characteristic oscillation frequency omega(osc) = 0.2278 au (corresponding to the period tau(osc) = 0.667 fs and the wavelength lambda(osc) = 200 nm) that plays the role of a "carrier" frequency of temporally shaped oscillations of the expectation values <-partial derivative V/partial derivative z) emerging after the ends of the laser pulses, both at lambda(1) = 800 nm and at lambda(1) = 200 nm. Moreover, at lambda(1) = 200 nm, the expectation value < z > also demonstrates temporally shaped oscillations after the end of the laser pulse. In contrast, at lambda(1) = 800 nm, the characteristic oscillation frequency omega(osc) = 0.2278 au appears as the frequency of small-amplitude oscillations of the slowly varying expectation value < z > which makes, after the end of the pulse, an excursion with an amplitude of about 4.5 au along the z axis and returns back to < z > approximate to 0 afterward. It is found that the period of the temporally shaped post-field oscillations of <-partial derivative V/partial derivative z > and < z >, estimated as tau(shp) approximate to 30 fs, correlates with the nuclear motion. It is also shown that vibrational excitation of H-2(+) is accompanied by the formation of "hot" and "cold" vibrational ensembles along the R degree of freedom. Power spectra related to the electron motion in H-2(+) calculated for both the laser-driven z and optically passive rho degrees of freedom in the acceleration form proved to be very interesting. In particular, both odd and even harmonics can be observed.
An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted O+H -> OH association reaction in an environment. The suggested approach is based on the application of the time-evolution operator to the "closed-system" part of the overall Hamiltonian and transformation of the open-system equation of motion to the Heisenberg picture suitable for numerical propagation. A dual role of the system-environment coupling with respect to the infrared (ir) laser-driven association of OH is demonstrated: the association probability is increased due to the coupling at relatively weak laser fields, but decreased at strong laser fields. Moreover, at a certain strength of the ir laser field, the association probability does not depend on the strength of the system-bath coupling at all.