Shedding Light on Correlated Electron-Photon States using the Exact Factorization

TL;DR

This paper extends the Exact Factorization framework to correlated electron-photon systems, defining potentials that capture electron-photon interactions and analyzing their features in a model system.

Contribution

It introduces a formalism with exact scalar and vector potentials for electron-photon systems, enabling a purely electronic Schrödinger equation that accounts for correlations.

Findings

Exact scalar potential exhibits step-and-peak structures.

Analytical approximation captures key features of the scalar potential.

Insights into photon-assisted phenomena like delocalization and squeezing.

Abstract

The Exact Factorization framework is extended and utilized to introduce the electronic-states of correlated electron-photon systems. The formal definitions of an exact scalar potential and an exact vector potential that account for the electron-photon correlation are given. Inclusion of these potentials to the Hamiltonian of the uncoupled electronic system leads to a purely electronic Schr\"odinger equation that uniquely determines the electronic states of the complete electron-photon system. For a one-dimensional asymmetric double-well potential coupled to a single photon mode with resonance frequency, we investigate the features of the exact scalar potential. In particular, we discuss the significance of the step-and-peak structure of the exact scalar potential in describing the phenomena of photon-assisted delocalization and polaritonic squeezing of the electronic excited-states. In addition, we develop an analytical approximation for the scalar potential and demonstrate how the step-and-peak features of the exact scalar potential are captured by the proposed analytical expression.