Here I present a poster describing the recently developed extensions of the adiabatic theory to molecules.

In recent years there has been an increased interest in laser pulses in the mid-infrared and terahertz regimes in the strong field community. With such pulses it could become possible to measure molecular dynamics in detail. However, most theoretical methods are unable to describe what happens in these regimes, due to the large ranges of the dynamic variables involved. Unlike such methods, the adiabatic theory of ionization for atoms [1,2] works well in this regime, since it exploits the slow variations of the laser field compared to motion inside the atom. Here we present the recently developed extensions of the adiabatic theory to molecules (AAnf) [3]. It treats nuclear motion in addition to all interactions among nuclei, electrons and the laser field. We will demonstrate the accuracy of the theory by comparing with exact solutions of the time-dependent Schrödinger equation (TDSE). We will also show an application of the theory to explain why the energy width of the vibrational state distribution in the molecular ion shrinks when isotopes with heavier nuclear masses are used. Recently we have also been working on including the effect of rescattering into the theory. Building upon the work in Ref. [4], this makes it possible to recreate the nuclear wave packet in the molecular ion from measurements of the photo-electron distributions over nuclear vibrational states. [1] Tolstikhin O I, Morishita T, Watanabe S., Phys Rev A 81, 033415 (2010) [2] Tolstikhin O I, Morishita T., Phys Rev A 86, 043417 (2012) [3] Svensmark J, Tolstikhin O I, Morishita T., Phys Rev A 101, 053422 (2020) [4] Morishita T, Tolstikhin O I. Phys Rev A 96, 053416 (2017)

In recent years there has been an increased interest in laser pulses in the mid-infrared and terahertz regimes in the strong-field community. Here we present the recently developed adiabatic theory for molecules [PRA 101, 053422 (2020)]. This theory exploits the slowness of the nuclei and the variation of the external laser field compared to the electronic motion, and is thus well suited to describe interactions with long-wavelength pulses. It treats nuclear motion in addition to all interactions among nuclei, electrons and the laser field. We will demonstrate the accuracy of the theory by comparing with exact solutions of the time-dependent Schrödinger equation. We will also show an application of the theory to explain why the energy width of the vibrational state distribution in the molecular ion shrinks when isotopes with heavier nuclear masses are used. *This work was supported by funding from the JSPS.

Within strong field physics a lot of attention has lately been directed towards producing long wavelength laser pulses in the mid-infrared and terahertz regimes, which could make it possible to measure molecular dynamics in detail. However, most theoretical methods fail in these regimes, due to the large dynamic range of spatial separations and energies involved. The adiabatic theory of ionization [Phys. Rev. A 86, 043417 (2012)] exploits the fact that the field varies slowly for such pulses, and it therefore excels in providing accurate descriptions of the laser-molecule interactions. We will present a recently developed version of this adiabatic theory (AAnf) that is applicable to molecules [Phys. Rev. A 101, 053422 (2019)], and treats nuclear motion in addition to all interactions among nuclei, electrons and the laser field. First, we will demonstrate that the theory is accurate by comparing to exact numerical solutions of the time-dependent Schrödinger equation (TDSE) in absolute scale, see Figure~1. Next, we will show examples of applications of this theory to problems in strong-field physics. For instance, the theory can be used to examine the effect of using different isotopes on observables. Finally, we will also present preliminary results for processes in which an ionized electron rescatters on the molecular ion, including inelastic scattering channels.

The adiabatic theory of tunneling ionization has been successfully used to describe tunneling ionization of atoms [Phys. Rev. A 86, 043417 (2012)]. This theory works particularly well for describing systems in strong, slowly oscillating laser fields in the near and far-infrared parts of the spectrum; a regime of laser parameters that are currently receiving a lot of attention within strong field physics. In this work we seek to apply the adiabatic theory to molecular systems, while treating both nuclear and electronic degrees of freedom. We propose a theory that combines adiabatic theory with a variation of the well known Born-Oppenheimer approximation. The results of this theory is compared to accurate TDSE calculations.

We extend the adiabatic theory of strong-field ionization of molecules including nuclear motion developed in our previous paper [J. Svensmark et al., Phys. Rev. A 101, 053422 (2020)] to describe rescattering processes. The adiabatic regime in which the electronic timescale is much smaller than that of the nuclei and laser field is considered. The asymptotics of rescattering parts of the solution to the time-dependent Schrödinger equation (TDSE) and ionization amplitude are obtained, and thus vibrationally resolved photoelectron momentum distributions (PEMDs) in the whole range of the photoelectron momentum are found. The ionization dynamics is described in terms of a nuclear wave packet in the molecular ion created as a result of ionization of the molecule, its evolution until rescattering, and a nuclear wave packet after rescattering. This complements the three-step model by accounting for what happens with the nuclear subsystem between ionization and rescattering events. A uniform asymptotics defining the PEMDs near a backward rescattering caustic is obtained, which enables one to extract the nuclear wave packet after rescattering from the PEMDs. The theory is illustrated by comparing its predictions with accurate numerical results obtained by solving the TDSE for a one-dimensional molecule with one electronic and one internuclear degree of freedom modeling H_2.

The adiabatic theory of strong-field ionization of molecules with internuclear motion included into consideration is developed. Two adiabatic regimes in terms of the electronic, nuclear, and laser field timescales are considered. In the first regime, field is the slowest; that is, its timescale is much larger than the electronic and nuclear timescales. The corresponding theory generalizes the adiabatic theory of strong-field ionization of atoms and molecules with frozen nuclei [Phys. Rev. A 86, 043417 (2012)] by treating the internuclear motion on equal footing with the electronic motion. In the second regime, the active electron is the fastest; that is, its timescale is much smaller than that of the nuclei and laser field. The corresponding theory naturally involves the Born-Oppenheimer approximation. The two versions of the adiabatic theory are validated by comparing their predictions with accurate numerical results obtained by solving the time-dependent Schrödinger equation (TDSE) for a model diatomic molecule with one electronic and one internuclear degree of freedom. The adiabatic results are shown to converge to the TDSE results uniformly with respect to the laser field amplitude both in tunneling and over-the-barrier ionization regimes. Two applications of the theory to the analysis of strong-field effects associated with the internuclear motion are discussed.

We present the theory of tunneling ionization of molecules with both electronic and nuclear motion treated quantum mechanically. The theory provides partial rates for ionization into the different final states of the molecular ion, including both bound vibrational and dissociative channels. The exact results obtained for a one-dimensional model of H2 and D2 are compared with two approximate approaches, the weak-field asymptotic theory and the Born-Oppenheimer approximation. The validity ranges and compatibility of the approaches are identified formally and illustrated by the calculations. The results quantify that at typical field strengths considered in strong-field physics, it is several orders of magnitude more likely to ionize into bound vibrational ionic channels than into the dissociative channel.

In this dissertation the theory of tunneling ionization of molecules is presented and the results of numerical calculations are shown.

We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees of freedom. In the regime where the BO approximation is applicable, imaging of the BO nuclear wave function is demonstrated to be possible through reverse use of the reflection principle, when accounting appropriately for the electronic ionization rate. A qualitative difference between the exact and BO wave functions in the asymptotic region of large electronic distances is shown. Additionally, the behavior of the wave function across the turning line is seen to be reminiscent of light refraction. For weak fields, where the BO approximation does not apply, the weak-field asymptotic theory describes the spectrum accurately.