Time-dependent density functional theory for many-electron systems interacting with photons: tddft for cavity-qed

Abstract

Experimental progress in the fields of cavity and circuit quantum electrodynamics (QED) opens a possibility to study many-electron systems strongly interacting with quantum light. Obviously, the classical treatment of external fields prevents application of the standard TDDFT to this new class of problems. Here I present a generalization of TDDFT for many-electron systems strongly coupled to quantum electromagnetic modes of a microcavity. I show that the full electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows to calculate the above basic variables by solving selfconsistent equations for noninteracting particles. I suggest possible strategies for approximating exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular, I show that it naturally leads to TDDFT for many-particle systems coupled to the Caldeira-Leggett bath of harmonic oscillators.