Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

Johannes Flick,Angel Rubio,Michael Ruggenthaler,Heiko Appel

doi:10.1021/acs.jctc.6b01126

Abstract

In this work, we illustrate the recently introduced concept of the cavity Born–Oppenheimer approximation [Flick et al. PNAS2017, 10.1073/pnas.1615509114] for correlated electron–nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground-state electronic potential-energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double-well structure. This change is accompanied by a splitting of the electronic ground-state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time-dependent setup, we show how the dynamics in correlated light-matter systems can be understood in terms of population transfer between potential energy surfaces. This work at the interface of quantum chemistry and quantum optics paves the way for the full ab initio description of matter-photon systems.

Highlights

Recent experimental progress has made it possible to study light-matter interactions in the regime of strong and ultra-strong light-matter coupling
This work is structured into three sections: (i) First, the theoretical framework is introduced where we demonstrate how the concept of the Born-Oppenheimer approximation can be generalized to matter-photon coupled systems. (ii) We apply this theoretical framework to study a prototypical electron-photon system, where the photon couples resonantly to an electronic transition. (iii) The last section is devoted to a model system of a electron, a nuclei and photons, where a photon mode couples to a vibrational excitation
In the coupling region indicated by (I), we find a single minimum in the potential energy surfaces (PES) and ∆n is located perpendicular to the polarization direction, while in the coupling regime (II), we find two minima and a double well structure in the PES and ∆n is located along the direction of the polarization of the photon mode

Summary

Introduction

Recent experimental progress has made it possible to study light-matter interactions in the regime of strong and ultra-strong light-matter coupling. We illustrate the recently introduced concept of the cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon problems in detail. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum.

Results

Conclusion