Light-matter interactions within the Ehrenfest–Maxwell–Pauli–Kohn–Sham framework: fundamentals, implementation, and nano-optical applications (original) (raw)
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2018
We present the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli-Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit for the effective nuclei the formalism reduces to coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations. We present an implementation of the approach in the real-space real-time code Octopus. For the implementation we use the Riemann-Silberstein formulation of classical electrodynamics and rewrite Maxwell's equations in Schr\"odinger form. This allows us to use existing time-evolution algorithms developed for quantum-m...
Technische Universität Berlin Berlin, 2019
Light-matter interactions have always been an essential aspect of research. They cover the main properties of light and matter in atomic and molecular systems, in condensed phase, in chemical reactions, and in optics. This thesis presents a feasible implementation to simulate three-dimensional, real-time, real-space, self-consistently coupled light-matter systems based on the theoretical background of a generalized Pauli-Fierz field theory. Due to the one-to-one correspondence between external fields and internal variables, we use a Kohn-Sham construction to approach the many-body problem in a non-relativistic low energy regime. The formalism leads in mean-field and effective nuclei approximation to coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations. Insgesamt bietet die Implementierung damit eine praktikable Möglichkeit vollständig gekoppelte Systeme zu simulieren, z.B. für die Nanooptik, Nanoplasmonik oder Elektrokatalyse, um nur einige zu nennen.
Quantum electrodynamics in modern optics and photonics: tutorial
Journal of the Optical Society of America B, 2020
One of the key frameworks for developing the theory of light–matter interactions in modern optics and photonics is quantum electrodynamics (QED). Contrasting with semiclassical theory, which depicts electromagnetic radiation as a classical wave, QED representations of quantized light fully embrace the concept of the photon. This tutorial review is a broad guide to cutting-edge applications of QED, providing an outline of its underlying foundation and an examination of its role in photon science. Alongside the full quantum methods, it is shown how significant distinctions can be drawn when compared to semiclassical approaches. Clear advantages in outcome arise in the predictive capacity and physical insights afforded by QED methods, which favors its adoption over other formulations of radiation–matter interaction.
Interaction of atomic systems with quantum vacuum beyond electric dipole approximation
Scientific Reports, 2020
The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, L...
Optical Processes in Organic Materials and Nanostructures II, 2013
We present a pseudoparticle nonequilibrium Green function formalism as a tool to study the coupling between plasmons and excitons in nonequilibrium molecular junctions. The formalism treats plasmon-exciton couplings and intra-molecular interactions exactly, and is shown to be especially convenient for exploration of plasmonic absorption spectrum of plexitonic systems, where combined electron and energy transfers play an important role. We demonstrate the sensitivity of the molecule-plasmon Fano resonance to junction bias and intra-molecular interactions (Coulomb repulsion and intra-molecular exciton coupling). The electromagnetic theory is used in order to derive self-consistent field-induced coupling terms between the molecular and the plasmon excitations. Our study opens a way to deal with strongly interacting plasmon-exciton systems in nonequilibrium molecular devices. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/17/2013 Terms of Use: http://spiedl.org/terms Proc. of SPIE Vol. 8827 88270C-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/17/2013 Terms of Use: http://spiedl.org/terms
Multi-physical modeling and multi-scale computation of nano-optical responses
Contemporary Mathematics, 2013
We survey recent progresses on multi-physical modeling and multiscale computation of nano-optical responses. The semi-classical theory treats the evolution of the electromagnetic (EM) field and the motion of the charged particles concurently by coupling Maxwell equations with Quantum Mechanics. A new efficient computational framework is proposed in [1, 2] by integrating the Time Dependent Current Density Functional Theory (TD-CDFT). This leads to the coupled Maxwell-Kohn-Sham equations determining the EM field as well as the current and electron densities simultaneously. In the regime of linear responses, a self-consistent multi-scale method is proposed to deal with the well separated space scales. Progresses are also made on developing adaptive Finite Element Methods for the Kohn-Sham equation [3, 4].
The role of virtual photons in nanoscale photonics
Annalen der Physik, 2014
The fundamental theory of processes and properties associated with nanoscale photonics should properly account for the quantum nature of both the matter and the radiation field. A familiar example is the Casimir force, whose significant role in nanoelectromechanical systems is widely recognised; the correct representation invokes the creation of short-lived virtual photons from the vacuum. In fact, there is an extensive range of nanophotonic interactions in which virtual photon exchange plays a vital role, mediating the coupling between particles. This review surveys recent theory and applications, also exhibiting novel insights into key electrodynamic mechanisms. Examples are numerous and include: laser-induced inter-particle forces known as optical binding; non-parametric frequency-conversion processes especially in rare-earth doped materials; light-harvesting polymer materials that involve electronic energy transfer between their constituent chromophores. An assessment of these and the latest prospective applications concludes with a view on future directions of research.
A Multiscale Method for Optical Responses of Nanostructures
SIAM Journal on Applied Mathematics, 2013
We introduce a new framework for the multiphysical modeling and multiscale computation of nano-optical responses. The semiclassical theory treats the evolution of the electromagnetic field and the motion of the charged particles self-consistently by coupling Maxwell equations with quantum mechanics. To overcome the numerical challenge of solving the high-dimensional many-body Schrödinger equations involved, we adopt the time-dependent current density functional theory. In the regime of linear responses, this leads to a linear system of equations determining the electromagnetic field as well as the current and electron densities simultaneously. A self-consistent multiscale method is proposed to deal with the well-separated space scales. Numerical examples are presented to illustrate the resonant condition.
The Journal of Chemical Physics
X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecularorbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.