Quantum Electromagnetism Research Articles

Taylor's formula on the separating complex plane and its applications

This article begins by exploring split-complex numbers, also known as dual or double numbers, a mathematical concept that extends the real number system by creating a commutative ring with a zero divisor. Furthermore, the paper extends the Taylor series theory from the real analysis domain to the domain of split-complex numbers, thereby establishing the corresponding Taylor formula on the split-complex plane. The introduction of split-complex numbers opens up new perspectives and provides new tools for the modeling and analysis of quantum systems. In the field of electromagnetism, the application of split-complex numbers also demonstrates its potential, contributing to a more precise description of the behavior of electromagnetic fields under specific conditions. These theoretical advancements are expected to further promote research in the field of split-complex analysis, playing a more critical role in important branches of physics such as quantum mechanics and electromagnetism, thereby facilitating the development of related theories and the emergence of innovative practical applications.

On the Directivity of Radiating Quantum Electromagnetic Systems

On the Directivity of Radiating Quantum Electromagnetic Systems

Understanding the natural units and their hidden role in the laws of physics

The natural units of measure lauded by Max Planck more than 100 years ago are underutilized today. Many physical constants, including the Planck constant, the gravitational constant, the speed of light, vacuum permittivity, and vacuum permeability consist of natural units in their unit dimensions. The natural units are present in all formulas containing these constants. The defining characteristic of the natural units is an alignment of unit values at the Planck scale. This alignment gives a computational basis of proportionality from which the correlated properties and dynamics of elementary particles, including wavelength, period, mass, momentum, and energy, manifest in equal or inversely proportional ratios of the Planck scale. These correlations explain many of the defining equations of quantum mechanics, classical gravity, and electromagnetism.

Dynamics of Exciton Formation in Planar Nanostructures under the Action of a Quantum Electromagnetic Field under Nonlinearity Conditions

Dynamics of Exciton Formation in Planar Nanostructures under the Action of a Quantum Electromagnetic Field under Nonlinearity Conditions

Some Selected Unsolved Problems in Classical and Quantum Electromagnetics

Some Selected Unsolved Problems in Classical and Quantum Electromagnetics

Observation of ultra-large Rabi splitting in the plasmon-exciton polaritons at room temperature

Abstract Modifying the light–matter interactions in the plasmonic structures and the two-dimensional (2D) materials not only advances the deeper understanding of the fundamental studies of many-body physics but also provides the opportunities for exploration of novel 2D plasmonic polaritonic devices. Here, we report the plasmon-exciton coupling in the hybrid system with a plasmonic metasurface which can confine the electric field in an extremely compact mode volume. Because of the 2D feature of the designed and fabricated Al plasmonic metasurface, the confined electronic field is distributed in the plane with the same orientation as that of the exciton dipole moment in the transition metal dichalcogenides monolayers. By finely tuning the geometric size of the plasmonic nanostructures, we can significantly modify the dispersion relation of the coupled plasmon and the exciton. Our system shows a strong coupling behavior with an achieved Rabi splitting up to ∼200 meV at room temperature, in ambient conditions. The effective tailoring of the plasmon-exciton coupling with the plasmonic metasurfaces provides the testing platform for studying the quantum electromagnetics at the subwavelength scale as well as exploring plasmonic polariton Bose–Einstein condensation at room temperature.

Interaction effects from the elastodynamic scattering by two symmetric spherical cavities

The scattering of harmonic waves has been studied extensively for problems in quantum mechanics, acoustics, electromagnetics, and elasticity. Solutions to elastodynamic problems are the basis for ultrasonic non-destructive evaluation measurement models. Therefore, in this study, we investigate the use of the boundary element method (BEM) in the frequency domain using an off-boundary technique in which the observation points are taken inside the scattering object. This methodology removes both non-integrable singularities from the domain of integration along with avoiding ill-conditioning effects that occur at fictitious eigenfrequencies of which both require using special computationally demanding procedures to obtain solutions. Additionally, we employ both free and half-space fundamental solutions (Green’s displacement tensors) to investigate the elastodynamic scattering of an incident, plane, time-harmonic longitudinal wave in the frequency domain of a homogeneous, isotropic, and linear elastic solid with one or two spherical cavities. The half-space fundamental solution reduces the number of required boundary elements in half, which significantly reduces computational resource requirements. We only consider spherical cavities in this paper to illustrate the full and half-space off-boundary BEM and analyze the interaction effects associated with the elastodynamic scattering by two symmetric spherical cavities. To verify the validity of the free and half-space off-boundary BEM formulations, surface displacement results are compared with existing surface displacement results and show good agreement. Finally, the half-space off-boundary BEM is used to illustrate the interaction effects of the back and forward scattered displacement fields as a function of the distance from the spherical cavities.

The Bethe-Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules.

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum electrodynamics has been "established" by the mid-twentieth century, primarily as a scattering theory. To describe atoms and molecules, it is important to consider bound states. In the nonrelativistic quantum mechanics framework, bound states can be efficiently computed using robust and general methodologies with systematic approximations developed for solving wave equations. With the sight of the development of a computational quantum electrodynamics framework for atomic and molecular matter, the field theoretic Bethe-Salpeter wave equation expressed in space-time coordinates, its exact equal-time variant, and emergence of a relativistic wave equation, is reviewed. A computational framework, with initial applications and future challenges in relation with precision spectroscopy, is also highlighted.

Fundamental Connections in Differential Geometry: Quantum Field Theory, Electromagnetism, Chemistry and Fluid Mechanics

Fundamental Connections in Differential Geometry: Quantum Field Theory, Electromagnetism, Chemistry and Fluid Mechanics

About Non-relativistic Quantum Mechanics and Electromagnetism

We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the quantum electrodynamics (QED). This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.

Electromagnetic analogs of quantum mechanical tunneling

In this paper, we introduce the theoretical framework underlying our proposed methodology of verification and validation (V&V) for quantum mechanical emission models using analogous macroscopic electromagnetic systems. We derive the correspondence between quantum mechanics and electromagnetism using the transfer matrix approach and describe the electromagnetic analog that will be used to anchor the atomistic quantum tunneling simulations. Finally, we illustrate this correspondence by comparing the quantum mechanical and electromagnetic systems for some simple, analytically soluble examples and outline future V&V work based on the framework presented here.

Light Interaction With an Ensemble of Quantum Dots [Guest Editorial

The quantum technologies series of articles started with the basics of quantum electromagnetics and then turned to deal with various promising applications. These range from the computation of the Casimir force to the analysis of interactions between electromagnetic waves and large molecules behaving as nanoantennas. Another article outlined the advantages of more futuristic higher level applications, such as quantum radars and lidars. Recent articles in the series covered device-level performance, including the quantum electrodynamics of plasmonic waveguides and construction of transmon qubits. Similarly, the present contribution, “Numerical Simulations of Laser Pulse Propagation in Quantum Active Media,” deals with the semiclassical analysis of field interaction with a collection of quantum dots, posing a heavy computational challenge. One typically sidesteps this by deriving a homogeneous behavior. But this leaves out interesting design opportunities. This article takes a different approach to the self-consistent analysis of a large ensemble of quantum dots. It combines analysis methods that are well known in the electromagnetics community together with predictor–corrector methods to solve for the evolution of the polarization of quantum dots. Interestingly, the approach correctly predicts experimentally observed behavior.

Quantum enabled functional neuroimaging: the why and how of magnetoencephalography using optically pumped magnetometers

ABSTRACT Non-invasive imaging has transformed neuroscientific discovery and clinical practice, providing a non-invasive window into the human brain. However, whilst techniques like MRI generate ever more precise images of brain structure, in many cases, it’s the function within neural networks that underlies disease. Here, we review the potential for quantum-enabled magnetic field sensors to shed light on such activity. Specifically, we describe how optically pumped magnetometers (OPMs) enable magnetoencephalographic (MEG) recordings with higher accuracy and improved practicality compared to the current state-of-the-art. The paper is split into two parts: first, we describe the work to date on OPM-MEG, detailing why this novel biomagnetic imaging technique is proving disruptive. Second, we explain how fundamental physics, including quantum mechanics and electromagnetism, underpins this developing technology. We conclude with a look to the future, outlining the potential for OPM-MEG to initiate a step change in the understanding and management of brain health.

Smartphone-based Surface Plasmon Resonance Sensors: a Review.

The surface plasmon resonance (SPR) is a phenomenon based on the combination of quantum mechanics and electromagnetism, which leads to the creation of charge oscillations on a metal–dielectric interface. The SPR phenomenon creates a signal which measures refractive index change at the metal–dielectric interface. SPR-based sensors are being developed for real-time and label-free detection of water pollutants, toxins, disease biomarkers, etc., which are highly sensitive and selective. Smartphones provide hardware and software capability which can be incorporated into SPR sensors, enabling the possibility of economical and accurate on-site portable sensing. The camera, screen, and LED flashlight of the smartphone can be employed as components of the sensor. The current article explores the recent advances in smartphone-based SPR sensors by studying their principle, components, application, and signal processing. Furthermore, the general theoretical and practical aspects of SPR sensors are discussed.

Quantum Phenomena in Electromagnetics [Guest Editorial

Quantum phenomena are attracting increasing interest in various areas within electromagnetics. The article “Plasmonic Waveguides: Enhancing Quantum Electrodynamic Phenomena at Nanoscale,” by Ying Li and Christos Argyropoulos, continues this series on quantum technologies. While the article aims to explain plasmonic phenomena (sources near metal surfaces) at a quantum level, it also devotes significant attention to the use of the classical Green’s function in rigorous quantum theory and calculations. This provides a bridge from the familiar (classical electromagnetics) to what may be, for some readers, the unfamiliar (quantum electromagnetics) for dispersive and lossy environments.

Quantum Electromagnetics Technology [Special Series: Guest Editorial

The article “Quantum Radars and Lidars: Concepts, Realizations, and Perspectives,” by Gregory Slepyan, Svetlana Vlasenko, Dmitri Mogilevtsev, and Amir Boag is one that stretches the imaginations of conventional practitioners of radar technology. The quantum advantage that quantum sensing will deliver is too great to be ignored, even though naysayers may not agree on this path. Also, the knowledge base in quantum technologies is incredibly thin, and, hopefully, this article will spur more engineers and scientists to take up the challenge of working in this area, sharing their experience and knowhow as well as expanding the knowledge base. We have seen the recent exciting growth in quantum computing technology, and we wish for the same excitement in quantum sensing technology. The ability to use entangled photon pairs to enhance the detection of weak photons will be beneficial to other applications, such as quantum sensing and quantum imaging in biomedical engineering and health care. Entangled photon pairs are also useful in quantum communication.

A New Form of Quantum Mechanical Wave Equation Unifying Quantum Mechanics and Electro-Magnetics

The Schr?dinger differential equation is what we usually solve for the microscopic particles in non-relativistic quantum mechanics. Niels Bohr suggested the power two of the (usually) complex answer shows the probability of the particle’s existence at a point of space. Also, the time dependence of Schrodinger wave equation is one whereas for light in electromagnetism is two. In this paper, we show a solution for both problems. We derive a Wave Equation for the energy of every system. This electromagnetic wave equation is shown to convert to those classical (i.e. the Schrodinger) and special relativistic (i.e. Klein-Gordon) quantum mechanical equations. Also, accordingly there definitely is a physical meaning to answer to this wave equation. And therefore, switching the probabilistic interpretation of quantum mechanics to a deterministic one as (Albert) Einstein demanded.

Comparing Classical and Quantum Electromagnetics: Part 3 [Special Series: Guest Editorial

Quantum technology is becoming increasingly important with the recent advancements in quantum computers. The article “Casimir Force: Vacuum Fluctuation, Zero-Point Energy, and Computational Electromagnetics,” by Xia et al., summarizes how to calculate the Casimir force in the simplest fashion. It gives a brief overview of quantum theory and quantum weirdness. It then explains the role of quantum theory in electromagnetics and how the Casimir energy is equal to the sum of the zero-point energies of different modes in a system. The zero-point energy gives rise to vacuum fluctuations that persist down to zero temperature. Next, the article shows how to find the electromagnetic modes of an electromagnetic system using computational electromagnetics. The authors discuss the use of the argument principle as a way of finding this sum of zero-point energies indirectly. Moreover, a broadband fast multipole algorithm is discussed that is error controllable from statics to microwave frequencies. As a result, both attractive and repulsive Casimir forces are demonstrated with some complex structures.

Dependence of evanescent wave polarization on the losses of guided optical modes

Spin-momentum locking of evanescent waves describes the relationship between the propagation constant of an evanescent mode and the polarization of its electromagnetic field, giving rise to applications in light nano-routing and polarimetry among many others. The use of complex numbers in physics is a powerful representation in areas such as quantum mechanics or electromagnetism; it is well known that a lossy waveguide can be modelled with the addition of an imaginary part to the propagation constant. Here we explore how these losses are entangled with the polarization of the associated evanescent tails for the waveguide, revealing a well-defined mapping between waveguide losses and the Poincar\'e sphere of polarizations, in what could be understood as a "polarization-loss locking" of evanescent waves. We analyse the implications for near-field directional coupling of sources to waveguides, as optimized dipoles must take into account the losses for a perfectly unidirectional excitation. We also reveal the potential advantage of calculating the angular spectrum of a source defined in a complex, rather than the traditionally purely real, transverse wavevector space formalism.

Comparing Classical and Quantum Electromagnetics: Part 2 [Special Series: Guest Editorial

The articles in this special section represent the second of a series that focus on quantum technologies. These articles bridge the gap between classical electromagnetics and quantum electromagnetics. The article “Quantum Maxwell’s Equations Made Simple,” by Chew et al., in particular, introduces quantum mechanics and how it relates to quantum electromagnetics.