Ab-initio non-relativistic quantum electrodynamics: Bridging quantum chemistry and quantum optics from weak to strong coupling

Understand

By applying the Born-Huang expansion, originally developed for coupled nucleus-electron systems, to the full nucleus-electron-photon Hamiltonian of non-relativistic quantum electrodynamics (QED) in the long-wavelength approximation, we deduce an exact set of coupled equations for electrons on photonic energy surfaces and the nuclei on the resulting polaritonic energy surfaces.

• This theory describes seamlessly many-body interactions between nuclei, electrons and photons including the quantum fluctuation of the electromagnetic field and provides a proper first-principle framework to describe QED-chemistry phenomena.
• Since the photonic surfaces and the corresponding non-adiabatic coupling elements can be solved analytically, the resulting expansion can be brought into a compact form which allows us to analyze aspects of coupled nucleus-electron-photon systems in a simple and intuitive manner.
• Furthermore, we discuss structural differences between the exact quantum treatment and Floquet theory and show how existing implementations of Floquet theory can be adjusted to adhere to QED.