# Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field

## TL;DR

This study investigates the transient behavior of a one-dimensional Holstein polaron under an external electric field using an advanced variational approach, revealing detailed dynamics, effects of exciton-phonon coupling, and differences in finite systems.

## Contribution

It introduces a multi-D₂ Ansatz method for accurately simulating Holstein polaron dynamics, aligning well with hierarchy equations and exploring effects of coupling and system size.

## Key findings

- Bloch oscillations observed from broad wave packets.
- Weak exciton-phonon coupling reduces current amplitude.
- Strong diagonal coupling causes exciton localization and decay of oscillations.

## Abstract

Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations.