Linear response in relativistic quantum-electrodynamical density functional theory

The quest to control the properties of matter has produced ingenious techniques utilizing, for example, lasers or optical cavities. In cavities, light is squeezed into a small volume resulting in strong coupling between the cavity modes and matter. Unlike intense laser radiation, the interaction with light in cavities does not heat up and damage molecules and materials. Proper theoretical description of cavity control of materials necessitates quantized treatment of cavity modes due to the strong coupling. Therefore, the theoretical framework of choice is quantum electrodynamics (QED). However, the state-of-the-art in practice is based on non-relativistic QED or even further simplified few-level models. Quantum electrodynamical density functional theory (QEDFT) [1, 2] has emerged as a bridge between quantum chemistry and quantum optics, combining an ab initio description of matter with a quantized description of light. In this work, we introduce relativistic QEDFT [3] in the linear response regime for molecules in optical cavities. The developed methodology combines a four-component Dirac-Kohn-Sham treatment of electrons with a quantized description of photons included as dynamical variables. The relativistic level of theory allows for studying heavy element-containing molecules. The linear response formalism is used to describe their excitation spectra as influenced by cavities. In addition, the method can be employed to describe radiative decay from first principles via the interaction of molecules with a photonic bath.

[1] M. Ruggenthaler, J. Flick, C. Pellegrini, H. Appel, I.V. Tokatly, A Rubio, Phys. Rev. A (2014), 90, 012508.

[2] J. Flick, D. M. Welakuh, M. Ruggenthaler, H. Appel and A. Rubio, ACS Photonics (2019), 6, 2757.

[3] M. Ruggenthaler, F. Mackenroth and D. Bauer, Phys. Rev. A (2011), 84, 042107.