# Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using Anderson-Holstein model

## TL;DR

This paper presents a theoretical analysis of ultrafast electron tunneling in terahertz-STM experiments using the Anderson-Holstein model, capturing electron-electron and electron-phonon interactions with a novel variational method, and compares results to non-interacting models.

## Contribution

The paper introduces a variational non-Gaussian state approach to accurately analyze ultrafast dynamics in the Anderson-Holstein model, including Kondo physics and phonon effects, in the context of terahertz-STM experiments.

## Key findings

- Accurately reproduces Kondo screening and conductance properties.
- Demonstrates phonon-induced suppression of the Kondo resonance.
- Finds long-lived phonon oscillations after the pulse.

## Abstract

We analyze ultrafast tunneling experiments in which electron transport through a localized orbital is induced by a single cycle THz pulse. We include both electron-electron and electron-phonon interactions on the localized orbital using the Anderson-Holstein model and consider two possible filling factors, the singly occupied Kondo regime and the doubly occupied regime relevant to recent experiments with a pentacene molecule. Our analysis is based on variational non-Gaussian states and provides the accurate description of the degrees of freedom at very different energies, from the high microscopic energy scales to the Kondo temperature $T_K$. To establish the validity of the new method we apply this formalism to study the Anderson model in the Kondo regime in the absence of coupling to phonons. We demonstrate that it correctly reproduces key properties of the model, including the screening of the impurity spin, formation of the resonance at the Fermi energy, and a linear conductance of $2e^2/h$. We discuss the suppression of the Kondo resonance by the electron-phonon interaction on the impurity site. When analyzing THz STM experiments we compute the time dependence of the key physical quantities, including current, the number of electrons on the localized orbital, and the number of excited phonons. We find long-lived oscillations of the phonon that persist long after the end of the pulse. We compare the results for the interacting system to the non-interacting resonant level model.