Eur. Phys. J. B (2018) 91: 194
https://doi.org/10.1140/epjb/e2018-90243-1

Regular Article

Shedding light on correlated electron–photon states using the exact factorization^★

¹ Nano-Bio Spectroscopy group, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Av. Tolosa 72, 20018 San Sebastián, Spain
² Donostia International Physics Center (DIPC), Manuel de Lardizabal 5, 20018 San Sebastián, Spain
³ IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

^a e-mail: aliabedik@gmail.com

Received: 10 April 2018
Received in final form: 7 June 2018
Published online: 30 August 2018

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 Schrödinger 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.