TY - BOOK

T1 - Study of the isotope-dependence of molecular high-harmonic generation in D2 and H2

AU - Ruhmann, Marc

N1 - Doctoral thesis

PY - 2019

Y1 - 2019

N2 - This thesis comprises a numerical study of high-order harmonic generation (HHG) in the hydrogen molecule H2 and its heavier isotope D2. HHG refers to the emission of high-frequency radiation by an atom or molecule when it is subject to a strong laser field. It can be explained as a series of three steps: ionization, continuum travel of the freed electron and recombination of the electron with the parent ion, releasing its acquired energy as a high-energy photon. Our central focus lies on how the harmonic signal strength differs between the isotopologues, quantified by the ratio of the emitted harmonic intensities (harmonic ratio). The molecular analogue of the Lewenstein model predicts a dependence of the dipole moment, and consequently the harmonic intensity, on the vibrational autocorrelation function. This function measures the overlap of the vibrational ground state of the neutral molecule and the time-dependent state evolving on the Born-Oppenheimer potential energy curve of the ion while the electron is in the continuum. The duration of the time evolution is determined by the time of ionization and recombination of the participating electron. The heavier nuclear mass of D2 leads to a slower vibration than in H2, which affects the time dependence of the autocorrelation and ultimately the intensity of the harmonic radiation. The analytical expression of the HHG dipole moment is typically simplified with the help of the saddle-point approximation, which leads to thepeculiar result of complex-valued electron ionization and recombination times. We study the autocorrelation and in particular the ratio of autocorrelations of D2/H2 in the context of these complex times. We do so separately for the short and long trajectories, which are two distinct kinds of trajectories the electron follows during its continuum journey. The study consists of two parts. The first is purely theoretical where we compare autocorrelation ratios with harmonic ratios acquired by numerical solution of the time-dependent Schr¨odinger equation. The second consists of a comparison of the theoretical results with harmonic ratios determined by experiment. The theoretical comparison in the first part is done for two orientations of the molecular axis relative to the linearly polarized electric field of the driving laser pulse, parallel and perpendicular. Moreover, we employ two models of the autocorrelation function in the comparison. One uses real-valued times originating from the semiclassical three-step model and an LCAO-approximated dipole-transition matrix element. The other makes use of the complexvalued saddle-point times and an exact transition matrix element, calculated numerically via exact scattering states of the model potentials. The comparison with the experiment involves the study of the Stark effect as well as molecular alignment distributions. Additionally, also the PACER method (Probing Attosecond dynamics by Chirp-Encoded Recollision) is employed. That is, the molecular vibrational motion is reconstructed from the experimental observables on an attosecond time scale. Finally, the comparison between theory and experiment is carried out for the ammonia molecule NH3 and its heavier counterpart ND3 as well.

AB - This thesis comprises a numerical study of high-order harmonic generation (HHG) in the hydrogen molecule H2 and its heavier isotope D2. HHG refers to the emission of high-frequency radiation by an atom or molecule when it is subject to a strong laser field. It can be explained as a series of three steps: ionization, continuum travel of the freed electron and recombination of the electron with the parent ion, releasing its acquired energy as a high-energy photon. Our central focus lies on how the harmonic signal strength differs between the isotopologues, quantified by the ratio of the emitted harmonic intensities (harmonic ratio). The molecular analogue of the Lewenstein model predicts a dependence of the dipole moment, and consequently the harmonic intensity, on the vibrational autocorrelation function. This function measures the overlap of the vibrational ground state of the neutral molecule and the time-dependent state evolving on the Born-Oppenheimer potential energy curve of the ion while the electron is in the continuum. The duration of the time evolution is determined by the time of ionization and recombination of the participating electron. The heavier nuclear mass of D2 leads to a slower vibration than in H2, which affects the time dependence of the autocorrelation and ultimately the intensity of the harmonic radiation. The analytical expression of the HHG dipole moment is typically simplified with the help of the saddle-point approximation, which leads to thepeculiar result of complex-valued electron ionization and recombination times. We study the autocorrelation and in particular the ratio of autocorrelations of D2/H2 in the context of these complex times. We do so separately for the short and long trajectories, which are two distinct kinds of trajectories the electron follows during its continuum journey. The study consists of two parts. The first is purely theoretical where we compare autocorrelation ratios with harmonic ratios acquired by numerical solution of the time-dependent Schr¨odinger equation. The second consists of a comparison of the theoretical results with harmonic ratios determined by experiment. The theoretical comparison in the first part is done for two orientations of the molecular axis relative to the linearly polarized electric field of the driving laser pulse, parallel and perpendicular. Moreover, we employ two models of the autocorrelation function in the comparison. One uses real-valued times originating from the semiclassical three-step model and an LCAO-approximated dipole-transition matrix element. The other makes use of the complexvalued saddle-point times and an exact transition matrix element, calculated numerically via exact scattering states of the model potentials. The comparison with the experiment involves the study of the Stark effect as well as molecular alignment distributions. Additionally, also the PACER method (Probing Attosecond dynamics by Chirp-Encoded Recollision) is employed. That is, the molecular vibrational motion is reconstructed from the experimental observables on an attosecond time scale. Finally, the comparison between theory and experiment is carried out for the ammonia molecule NH3 and its heavier counterpart ND3 as well.

U2 - 10.15488/4319

DO - 10.15488/4319

M3 - Doctoral thesis

CY - Hannover

ER -