@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}
}
@misc{BandraukParamonov2014,
  author    = {Bandrauk, Andre D. and Paramonov, Guennaddi K.},
  title     = {Excitation of muonic molecules dd mu and dt mu by super-intense attosecond soft X-ray laser pulses: Shaped post-laser-pulse muonic oscillations and enhancement of nuclear fusion},
  series = {International journal of modern physics : E, Nuclear physics},
  volume    = {23},
  journal   = {International journal of modern physics : E, Nuclear physics},
  number    = {9},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-3013},
  doi       = {10.1142/S0218301314300148},
  pages     = {34},
  year      = {2014},
  abstract  = {The quantum dynamics of muonic molecular ions dd mu and dt mu excited by linearly polarized along the molecular (z)-axis super-intense laser pulses is studied beyond the Born-Oppenheimer approximation by the numerical solution of the time-dependent Schrodinger equation within a three-dimensional model, including the internuclear distance R and muon coordinates z and rho. The peak-intensity of the super-intense laser pulses used in our simulations is I-0 = 3.51 x 10(22) W/cm(2) and the wavelength is lambda(l) = 5nm. In both dd mu and dt mu, expectation values < z > and <rho > of muon demonstrate "post-laser-pulse" oscillations after the ends of the laser pulses. In dd mu post-laser-pulse z-oscillations appear as shaped nonoverlapping "echo-pulses". In dt mu post-laser-pulse muonic z-oscillations appear as comparatively slow large-amplitude oscillations modulated with small-amplitude pulsations. The post-laser-pulse rho-oscillations in both dd mu and dt mu appear, for the most part, as overlapping "echo-pulses". The post-laser-pulse oscillations do not occur if the Born-Oppenheimer approximation is employed. Power spectra generated due to muonic motion along both optically active z and optically passive rho degrees of freedom are calculated. The fusion probability in dt mu can be increased by more than 11 times by making use of three sequential super-intense laser pulses. The energy released from the dt fusion in dt mu can by more than 20 GeV exceed the energy required to produce a usable muon and the energy of the laser pulses used to enhance the fusion. The possibility of power production from the laser-enhanced muon-catalyzed fusion is discussed.},
  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}
}
@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{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{ParamonovSaalfrank2018,
  author    = {Paramonov, Guennaddi K. and Saalfrank, Peter},
  title     = {Muonic molecular ions pp mu and pd mu, driven by superintense VUV laser pulses},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {97},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2469-9926},
  doi       = {10.1103/PhysRevA.97.053408},
  pages     = {13},
  year      = {2018},
  abstract  = {The non-Born-Oppenheimer quantum dynamics of pp mu and pd mu molecular ions excited by ultrashort, superintense VUV laser pulses polarized along the molecular axis (z) is studied by the numerical solution of the time-dependent Schrodinger equation within a three-dimensional (3D) model, including the internuclear distance R and muon coordinates z and rho, a transversal degree of freedom. It is shown that in both pp mu and pd mu, muons approximately follow the applied laser field out of phase. After the end of the laser pulse, expectation values < z >, < p >, and < R > demonstrate "post-laser-pulse" oscillations in both pp mu and pd mu. In the case of pd mu, the post-laser-pulse oscillations of < z > and < R > appear as shaped "echo pulses." Power spectra, which are related to high-order harmonic generation (HHG), generated due to muonic and nuclear motion are calculated in the acceleration form. For pd mu it is found that there exists a unique characteristic frequency omega(pd mu)(osc) representing both frequencies of post-laser-pulse muonic oscillations and the frequency of nuclear vibrations, which manifest themselves by very sharp maxima in the corresponding power spectra of pd mu. The homonuclear pp p. ion does not possess such a unique characteristic frequency. The "exact" dynamics and power, and HHG spectra of the 3D model are compared with a Born-Oppenheimer, fixed-nuclei model featuring interesting differences: postpulse oscillations are absent and HHG spectra are affected indirectly or directly by nuclear motion.},
  language  = {en}
}
@article{BouaklineLorenzMelanietal.2017,
  author    = {Bouakline, Foudhil and Lorenz, Ulrich J. and Melani, Giacomo and Paramonov, Guennaddi K. and Saalfrank, Peter},
  title     = {Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {147},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {14},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.4994635},
  pages     = {11},
  year      = {2017},
  abstract  = {In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude—a few hundred fs for D-Si and a couple of ps for H-Si—, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schr{\"o}dinger equation.},
  language  = {en}
}