Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics

Abstract

Recent experimental progress in the field of cavity quantum electrodynamics allows to study the regime of strong interaction between quantized light and complex matter systems. Due to the coherent coupling between photons and matter-degrees of freedom, polaritons -- hybrid light-matter quasiparticles -- emerge, which can significantly influence matter properties and complex processes such as chemical reactions (strong coupling). In this thesis we propose a way to overcome these problems by reformulating the coupled electron-photon problem in an exact way in a different, purpose-build Hilbert space, where no longer electrons and photons are the basic physical entities but the polaritons. Representing an N-electron-M-mode system by an N-polariton wave function with hybrid Fermi-Bose statistics, we show explicitly how to turn electronic-structure methods into polaritonic-structure methods that are accurate from the weak to the strong-coupling regime. We elucidate this paradigmatic shift by a comprehensive review of light-matter coupling, as well as by highlighting the connection between different electronic-structure methods and quantum-optical models. This extensive discussion accentuates that the polariton description is not only a mathematical trick, but it is grounded in a simple and intuitive physical argument: when the excitations of a system are hybrid entities a formulation of the theory in terms of these new entities is natural. Finally, we discuss in great detail how to adopt standard algorithms of electronic-structure methods to adhere to the new hybrid Fermi-Bose statistics. Guaranteeing the corresponding nonlinear inequality constraints in practice requires a careful development, implementation and validation of numerical algorithms. This extra numerical complexity is the price we pay for making the coupled matter-photon problem feasible for first-principle methods.

arXiv commentdoctoral thesis

References in corpus (73)

• Strong coupling between surface plasmon polaritons and emitters
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Strong light-matter coupling in two-dimensional atomic crystals
• Ultrastrong coupling regimes of light-matter interaction
• On the Integrability of the Rabi Model
• An optically stimulated superconducting-like phase in K3C60 far above equilibrium Tc
• A Search for Time Variation of the Fine Structure Constant
• Conductivity in organic semiconductors hybridized with the vacuum field
• Cavity-controlled chemistry in molecular ensembles
• Ultrastrong coupling of the cyclotron transition of a two-dimensional electron gas to a THz metamaterial
• Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems
• Real-Space Mesh Techniques in Density Functional Theory
• Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
• Selective scattering between Floquet-Bloch and Volkov states in a topological insulator
• Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials
• Extraordinary exciton conductance induced by strong coupling
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• A natural orbital functional for the many-electron problem
• Time-dependent density functional theory for strong electromagnetic fields in crystalline solids
• Multiple Rabi Splittings under Ultra-Strong Vibrational Coupling
• Terahertz light-matter interaction beyond unity coupling strength
• Light-matter decoupling in the deep strong coupling regime: The breakdown of the Purcell effect
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Quantum marginal problem and N-representability
• Cavity Casimir-Polder forces and their effects in ground state chemical reactivity
• Resolution of Gauge Ambiguities in Ultrastrong-Coupling Cavity QED
• Cavity Born-Oppenheimer Approximation for Correlated Electron-Nuclear-Photon Systems
• Ab-initio multi-scale simulation of high-harmonic generation in solids
• Superradiant Phase Transitions and the Standard Description of Circuit QED
• Time-dependent density functional theory for many-electron systems interacting with cavity photons
• Ab-initio non-relativistic quantum electrodynamics: Bridging quantum chemistry and quantum optics from weak to strong coupling
• Breakdown of gauge invariance in ultrastrong-coupling cavity QED
• Adaptively Compressed Exchange Operator
• Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition
• Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory
• A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
• Cavity QED of Strongly Correlated Electron Systems: A No-go Theorem for Photon Condensation
• Light-Matter Response in Non-Relativistic Quantum Electrodynamics: Quantum Modifications of Maxwell's Equations
• Global Method for Electron Correlation
• Cavity correlated electron-nuclear dynamics from first principles
• Excitonic spectral features in strongly-coupled organic polaritons
• Collective conical intersections through light-matter coupling in a cavity
• Real-time solutions of coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations: fundamentals, implementation, and nano-optical applications
• Density functional theory for strongly interacting electrons
• Pinning of Fermionic Occupation Numbers
• Virtual photons in the ground state of a dissipative system
• Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws
• Time-dependent Kohn-Sham approach to quantum electrodynamics
• Spectral density and metal-insulator phase transition in Mott insulators within RDMFT
• Rabi Oscillations and Few-Level Approximations in Time-Dependent Density Functional Theory
• Density functional theory beyond the linear regime: Validating adiabatic LDA
• The Free Electron Gas in Cavity Quantum Electrodynamics
• Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory
• Dipole-dipole shift of quantum emitters coupled to surface plasmons of a nano-wire
• Cavity antiresonance spectroscopy of dipole coupled subradiant arrays
• Manipulating quantum materials with quantum light
• Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
• Diverging exchange force and form of the exact density matrix functional
• Propagating two-particle reduced density matrices without wavefunctions
• Density-functional Study of Small Molecules within the Krieger-Li-Iafrate Approximation
• Large-scale all-electron density functional theory calculations using an enriched finite element basis
• Universal Concept of Complexity by the Dynamic Redundance Paradigm: Causal Randomness, Complete Wave Mechanics, and the Ultimate Unification of Knowledge
• Light-matter hybrid-orbital-based first-principles methods: the influence of the polariton statistics
• Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
• Reduced Density Matrix Functional Theory for Bosons
• Depolarization shift of the superradiant phase transition
• Macroscopic QED - concepts and applications
• Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
• Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability
• Exact Maps in Density Functional Theory for Lattice Models
• Kinetic-Energy Density-Functional Theory on a Lattice
• Local bottom-up effective theory of non-local electronic interactions