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Strong Field Dynamics of Atoms and Molecules: History-dependent Functionals and Exact Kohn-Sham Potentials of the Time-dependent (multi-component) Density Functional Theory

Periodic Reporting for period 1 - AMO-dance (Strong Field Dynamics of Atoms and Molecules: History-dependent Functionals and Exact Kohn-Sham Potentials of the Time-dependent (multi-component) Density Functional Theory)

Reporting period: 2016-04-01 to 2018-03-31

The AMO-dance project aimed at four major objectives:
1)Deriving and establishing robust non-empirical Time-Dependent Density Functional Theory (TDDFT) functionals beyond the adiabatic approximation;
2)Using the developed functional to study strong field dynamics of many electron systems;
3)Developing a new algorithm for obtaining the exact potentials of the KS equations in Multi-Component TDDFT (MC-TDDFT);
4)Investigation of the exact KS-potentials of the MC-TDDFT for molecular (model) systems.

These objectives are of great importance in the field of quantum dynamics and in particular in describing the light-matter interaction atoms and molecules. This is due to the fact that the interaction between atoms and molecules with
ultra-short laser pulses with intensities comparable to the typical atomic and molecular binding forces gives rise to a variety of nonlinear phenomena that require a non-perturbative theoretical description due to their nonlinear nature.
In case of atoms, the major challenge is to treat an interacting many-electron problem that is driven out of equilibrium by an external ultrashort intense pulse. The case of molecules is yet more difficult, due to the involvement of the
additional nuclear degrees of freedom. In general, one needs to resort to a direct solution of the time-dependent Schrödinger equation (TDSE) that becomes computationally prohibitively expensive as soon as one deals with more than a few degrees of freedom.
Theoretically, the time-dependent density functional theory (TDDFT) lends itself as one of the most promising approaches to describe atoms and molecules exposed to ultra-short and strong laser pulses, given its unprecedented balance between accuracy and numerical feasibility. However, the accuracy of TDDFT depends on the approximation used for the exchange-correlation (xc) potential that is a functional of the entire history of the density and on the initial state , and inclusion of this “memory-dependence” necessitates non-locality in space. Almost all calculations today neglect the memory-dependence. Notorious failures of the usual approximations for a wide range of phenomena, in particular in strange-field dynamics, have frustrated the effort for TDDFT to be used reliably as a simple black-box tool.
Towards achieving the main goals of AMO-dance we have pursued the following strategies:
1)We have developed a new non-empirical functional beyond the adiabatic approximation by parametrising the memory-dependence part of the xc-functional. We have first identified the relevant terms from an exact analytical relation and then obtained the corresponding coefficients from an ensemble of numerically exact solutions of the TDSE for the same system.
2)We have implemented the developed functional to study Rabi oscillations using resonance on off-resonance laser fields and showed that the results are in a vey good agreement with the numerically exact solution of the TDSE that is available for the system we studied. I n particular, we have shown that our developed functional fulfils the recently developed exact condition for xc kernel, namely it fixes the problem of the spurious time-dependent resonances for adiabatic xc functionals.
3)Based on the Exact Factorization framework in its direct and reverse form we have developed an algorithm to calculate the exact potentials of the KS equations in Multi-Component TDDFT (MC-TDDFT).
We have investigated the KS potentials for two very important problems: the strong-field ionization of molecular systems and the correlated electron-photon states of cavity-QED.
We have accomplished all the deliverables we envisaged in the proposal. The results have been partially published and are accessible on the arXiv ( repository. There are at least two more papers in preparation to complete the dissemination of the project.

The AMO-dance xc kernel is of huge importance for the community of quantum dynamics and can be used to study a wide range of problems. It is indeed an step beyond the state-of the-art. The outcome of the investigations of the exact KS potentials of MC-TDDFT are the first important steps towards developing reliable approximations on the one hand. On the other hand, for instance the CREI study that is based on an exact time-dependent potential offers an alternative and powerful tool for interpretation of strong-field ionization of the molecules and sets a firm ground to extend the AMO-dance method to study the strong-field dynamics of molecules. Furthermore, the results of the correlated electron-photon states are an important step towards developing accurate xc functional for the emerging fields of cavity-QED chemistry established by the host supervisor. The QED step was conducted beyond what was proposed in the original AMO-dance project.
The scientific achievements of the AMO-dance project can be listed as follows:
1) The most remarkable outcome of the project has been the development of the first-ever memory-dependent xc kernel that fulfils the exact condition that was developed recently. This accomplishment of the project is indeed a major step beyond the state-of-the-art and it expected to open new avenues for the application of TDDFT that may lead to better understanding of quantum dynamics of matter out of equilibrium.
2) In addition to what was proposed in the original project, the first steps toward developing an initial-dependence functional was taken.
3) We have also shedded light on the exact KS-potentials of the MCDFT. This formally rigorous approach to study multicomponent systems was developed almost two decades ago. However, in spite of its elegance it has not been implemented to study quantum dynamics of multicomponent systems due to the lack proper xc functionals. Our investigations paves the way for developing such functionals by pinpointing essential features of the KS-potentials in two physically important processes.
4) We have also reported numbers of other fascinating results such as a new interpretive tool to understand the mechanism of strong-field ionization of molecules by introducing a new dynamical measure we dubbed time-resolved R-resolved ionization probability.
5)We have furthermore, investigated the correlated electron-photon states in cavity QED and showed the mechanism of polaritonic squeezing of the electronic states.
The time-resolved, R−resolved ionization probability, for hydrogen molecular ion and its Isotopolog