Maxwell-Hartree-Fock Approach to Ab-initio Quantum Electrodynamics
Nicholas Rivera, Massachusetts Institute of Technology
Recent experiments in optics have shown that light can be confined and accessed with modal volumes approaching a cubic nanometer. In this deeply nanoscopic regime, the interaction between matter and photons is no longer weak and is described by non-perturbative quantum electrodynamics (QED). Theoretical descriptions of non-perturbative QED, beyond the very simplest systems, remain elusive. In this work, we present a formalism to analyze ground states and excited states of coupled systems of light and matter in the non-perturbative regime. Our approach, which we call the Maxwell-Hartree-Fock (MHF) approach, is a variational one, taking the ground state as a non-interacting state of electrons and photons whose respective wavefunctions are determined by each other. We also supplement the basic ansatz of MHF theory with a self-consistent Møller-Plesset correction in order to self-consistently include correlation effects in the QED ground state. We apply this method to find the ground state of a two-level system strongly coupled to a continuum of highly confined plasmonic modes. We find several effects beyond the usual perturbation theory treatment. For example, we find that the coupling of the emitter and the plasmons can be suppressed as the electron comes closer to the plasmonic system. This results from modification of the orbitals by van der Waals forces associated with plasmonic vacuum fluctuations. We also find from the perspective of the plasmon modes that the shape of the electromagnetic mode can be substantially altered in the region around the two-level system, and that this shape modification depends self-consistently on how the electronic orbitals are modified by the plasmons. Our results are of fundamental significance, as they imply a new mechanism that regulates light-matter coupling besides typical effects like quantum nonlocality. Our results are also of fundamental significance because it is the first real-space approach to understanding how photonics is modified by ultrastrong light-matter coupling.
Abstract Author(s): Nicholas Rivera