@article{ParamonovSaalfrank2009,
  author    = {Paramonov, Guennaddi K. and Saalfrank, Peter},
  title     = {Time-evolution operator method for non-Markovian density matrix propagation in time and space representation : application to laser association of OH in an environment},
  issn      = {1050-2947},
  doi       = {10.1103/Physreva.79.013415},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@article{ParamonovKuehnBandrauk2016,
  author    = {Paramonov, Guennaddi K. and Kuehn, O. and Bandrauk, Andre D.},
  title     = {Shaped Post-Field Electronic Oscillations in H-2(+) Excited by Two-Cycle Laser Pulses: Three-Dimensional Non-Born-Oppenheimer Simulations},
  series = {The journal of physical chemistry : A, Molecules, spectroscopy, kinetics, environment \& general theory},
  volume    = {120},
  journal   = {The journal of physical chemistry : A, Molecules, spectroscopy, kinetics, environment \& general theory},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1089-5639},
  doi       = {10.1021/acs.jpca.5b11599},
  pages     = {3175 -- 3185},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}
@article{ParamonovKuehnBandrauk2017,
  author    = {Paramonov, Guennaddi K. and K{\"u}hn, Oliver and Bandrauk, Andr{\´e} D.},
  title     = {Excitation of H+ 2 with one-cycle laser pulses},
  series = {Molecular physics : MP ; an international journal in the field of chemical physics},
  volume    = {115},
  journal   = {Molecular physics : MP ; an international journal in the field of chemical physics},
  number    = {15/16},
  publisher = {Taylor \& Francis},
  address   = {London},
  issn      = {0026-8976},
  doi       = {10.1080/00268976.2017.1288938},
  pages     = {1846 -- 1860},
  year      = {2017},
  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 Schr{\"o}dinger 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.},
  language  = {en}
}
@article{ParamonovKlamrothLuetal.2018,
  author    = {Paramonov, Guennaddi K. and Klamroth, Tillmann and Lu, H. Z. and Bandrauk, Andre D.},
  title     = {Quantum dynamics, isotope effects, and power spectra of H-2(+) and HD+ excited to the continuum by strong one-cycle laser pulses: Three-dimensional non-Born-Oppenheimer simulations},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {98},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2469-9926},
  doi       = {10.1103/PhysRevA.98.063431},
  pages     = {16},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}