Variational Theory of Nonrelativistic Quantum Electrodynamics

Area of Science:

• Quantum electrodynamics (QED)
• Solid-state physics
• Quantum optics

Background:

• Ultrastrong light-matter coupling is crucial for controlling material properties and manipulating light.
• Existing theories struggle to quantitatively describe QED phenomena in complex electronic and photonic systems.

Purpose of the Study:

• Develop a quantitative, non-relativistic theory for general quantum electrodynamics (QED) systems.
• Provide a framework for understanding light-matter interactions in complex systems.

Main Methods:

• Developed a variational theory incorporating an effective photonic vacuum.
• Formulated general equations for multielectron systems coupled to photonic modes.
• Applied the theory to a multilevel emitter coupled to optical modes.

Main Results:

• Derived a compact, semianalytical formula for ground and excited state energies.
• The formula accurately describes systems across all coupling regimes.
• Developed a nonperturbative theory for Lamb shifts and Casimir-Polder forces.

Conclusions:

• The variational theory offers highly accurate, nonperturbative descriptions of QED systems.
• Introduces new physical concepts like the Casimir energy of an atom in a cavity.
• Paves the way for ab initio calculations of QED phenomena.