Variational theory of non-relativistic quantum electrodynamics

Abstract

The ability to achieve ultra-strong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and fundamentally new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our ansatz is the notion of an effective photonic vacuum whose modes are different than the modes in the absence of light-matter coupling. This variational formulation leads to a set of general equations that can describe the ground state of multi-electron systems coupled to many photonic modes in real space. As a first step towards a new ab initio approach to ground and excited state energies in QED, we apply our ansatz to describe a multi-level emitter coupled to many optical modes, a system with no analytical solution. We find a compact semi-analytical formula which describes ground and excited state energies to less than 1% error in all regimes of coupling parameters allowed by sum rules. Additionally, our formulation provides essentially a non-perturbative theory of Lamb shifts and Casimir-Polder forces, as well as suggesting new physical concepts such as the Casimir energy of a single atom in a cavity. Our method should give rise to highly accurate descriptions of phenomena in general QED systems, such as Casimir forces, Lamb shifts, spontaneous emission, and other fluctuational electrodynamical effects.

arXiv comment6 pages, 2 figures

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Cited by in corpus (28)

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• Challenges in Plasmonic Catalysis
• Molecular polaritons for controlling chemistry with quantum optics
• Quantum Nanophotonics in Two-Dimensional Materials
• Polaritonic Coupled-Cluster Theory
• Resolution of Gauge Ambiguities in Molecular Cavity Quantum Electrodynamics
• Theoretical methods for ultrastrong light-matter interactions
• Molecular orbital theory in cavity QED environments
• Weak-to-Strong Light-Matter Coupling and Dissipative Dynamics from First Principles
• Cavity magnon-polaritons in cuprate parent compounds
• The Vacua of Dipolar Cavity Quantum Electrodynamics
• Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems based on the Fluctuation-Dissipation Theorem
• Variational Lang-Firsov approach plus Møller-Plesset perturbation theory with applications to ab initio polariton chemistry
• Real-Space, Real-Time Approach to Quantum-Electrodynamical Time-Dependent Density Functional Theory
• Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
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• Collective strong coupling in a plasmonic nanocavity
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• Virial relations for electrons coupled to quantum field modes
• Understanding polaritonic chemistry from ab initio quantum electrodynamics
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces
• Nonperturbative electromagnetic nonlinearities, n-photon reflectors, and Fock-state lasers based on deep-strong coupling of light and matter
• The light-matter correlation energy functional of the cavity-coupled two-dimensional electron gas via quantum Monte Carlo simulations
• Eigenvalues and Eigenstates of Quantum Rabi Model
• Deformed Explicitly Correlated Gaussians
• Two electrons in harmonic confinement coupled to light in a cavity