A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?

Abstract

We investigate two key representative semiclassical approaches for propagating resonant energy transfer between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum-classical mismatch leads to a violation of causality, i.e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with Förster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short range interactions or long range causality? Apparently, one cannot have one's cake and eat it too.

arXiv comment2 figures, 21 pages

References in corpus (7)

• Strong coupling between surface plasmon polaritons and emitters
• Interfacing single photons and single quantum dots with photonic nanostructures
• Topical Review: optics of exciton-plasmon nanomaterials
• Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions
• Analysis of the quantum-classical Liouville equation in the mapping basis
• Mixed Quantum-Classical Electrodynamics: Understanding Spontaneous Decay and Zero Point Energy
• Theory of Dipole Induced Electromagnetic Transparency

Cited by in corpus (9)

• Quasiclassical Modeling of Cavity Quantum Electrodynamics
• Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics
• Semiclassical Real-Time Nuclear-Electronic Orbital Dynamics for Molecular Polaritons: Unified Theory of Electronic and Vibrational Strong Couplings
• A Comparison of Different Classical, Semiclassical and Quantum Treatments of Light-Matter Interactions: Understanding Energy Conservation
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• Predictive Semiclassical Model for Coherent and Incoherent Emission in the Strong Field Regime: The Mollow Triplet Revisited
• Understanding the Nature of Mean-Field Semiclassical Light-Matter Dynamics: An Investigation of Energy Transfer, Electron-Electron Correlations, External Driving and Long-Time Detailed Balance
• MQED-QD: An Open-Source Package for Quantum Dynamics Simulation in Complex Dielectric Environments
• Polariton-induced Purcell effects via a reduced semiclassical electrodynamics approach