Correlated Electron-Photon Excitations within Quantum Electrodynamical Density-functional Theory

Novel experiments in cavity QED is at the interface between quantum optics and chemistry. Ab initio methods that treats an interacting many-electron system coupled to photons on an equal quantized footing has been developed and it's termed Quantum-Electrodynamical Density-Functional theory (QEDFT) [1]. The Kohn-Sham scheme of QEDFT has been used to study ground-state properties of an interacting electron-photon system [2]. Here, we present an ab-initio linear-response (LR) formalism that allows to calculate excited states phenomena for general matter-photon coupled systems. Beside the usual density-density response function known in time-dependent DFT, we have three new response functions due to coupling matter to photons. We reformulate the response functions and develop a numerically feasible and tractable pseudo-eigenvalue problem for the coupled electron-photon system. We present first principle calculations for excited state properties for a specific molecule coupled to a cavity photon. Furthermore, we show using LR in QEDFT that Maxwell's equation for coupled matter-photon system are modified.

[1] M. Ruggenthaler et al., Phys. Rev. A 90, 012508 (2014)
[2] J. Flick et al., Proc. Natl. Acad. Sci. USA 112, 15285–15290 (2015)