Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Frontiers in Optics

Quantum States in the Multipole Approach to Maxwell Theory of Light

Michele Marrocco

Published Jan 1, 2015• 0 citations
Publisher

Abstract

Fundamental aspects of quantum optics are reproduced within the multipole approach to Maxwell theory of light. Results are given for Fock states, vacuum field and photon statistics of chaotic and coherent light.
DOI
10.1364/fio.2015.jw2a.39

Related papers

An Actual Discussion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields

Alfred Rieckers

Abstract This is the first part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light-quanta (subsequently also referred to as “photons”) with classical electromagnetic fields that he formulated in 1909 via a purely verbal description. There, the overlap of many of the hypothetical local force fields, surrounding the photonic energy points, should produce the well–known classical Maxwell fields. We claim that, alone from such a logical connection, that apparently did not receive sufficient attention in the literature, one may draw essential conclusions on the photon states. In the present paper, we give a historical overview of Einstein’s photon conceptions until 1927. We extract hints from his formulations, that lead from his local force fields to Schrödinger wave functions, which reproduce the conserved integrals for energy, momentum, and angular momentum of Maxwell theory in form of Hilbert space expectations. Also a preliminary multi–photon theory, including Glauber states, is shown to be motivated by Einstein’s composite photons with possibly (incoherently!) overlapping force fields. In the resulting Fock space theory, gained by symmetrizing the many–photon states the goal of a fusion theory is, however, not realizable. In the subsequent companion paper “On sectorial photon theories reconstructing Einstein’s early fusion picture for light” (referred to as Rieckers 2025) our conclusions are extended to photon states that surpass Fock space theory by describing actual infinitely many photons. These are shown to cover also classical light states in terms of collective structures. Appealing to the more recent mathematical tools of convex state space approach and algebraic quantum field theory, we suggest there mathematical realizations of Einstein’s fusion program.

International Journal of Theoretical Physics•Feb 25, 2025•2 citations

The quantum theory of light

Stephen Mark Barnett, John Jeffers

We present a brief introduction to the quantum theory of light as it is understood in the field of quantum optics. Our aim is not to review the topic, which would require a very extensive article (or even a book of several volumes) but rather to provide sufficient background to set the ideas in the following papers in their correct context.This article is part of the theme issue 'The quantum theory of light'.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 24, 2024•2 citations

New frontiers in quantum electrodynamics and quantum optics

Asım Orhan Barut

A review of recent progress in the borderline areas of quantumelectrodynamics, quantumoptics, and quantum theory of measurement. The first section begins with a review of quantum optics, followed by contributions on the coherence, interference, and squeezing of light. The second section reviews the

•Jan 1, 1990•110 citations

On Sectorial Photon Theories Reconstructing Einstein’s Early Fusion Picture for Light

Alfred Rieckers

Abstract This is the second part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light. While in the foregoing paper “An Actual Discusion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields” (referred to as Rieckers 2025) our conclusions ended with the historical ab initio motivation and mathematical elaboration of a multi-photon theory in Fock space, we now start from the non–separable C*-Weyl algebra gained by abstracting the Fock–represented Weyl algebra. To the rich state space of this antiliminary observable algebra we apply notions of a convex state space approach to identify sub–theories that cover classical field states (including the vacuum with classical zero–field), that are possibly decorated by photonic quantum noise. The main emphasis is laid on direct integrals over irreducible, disjoint representations of the C*-Weyl algebra, decomposing the effective photon theory into sectors. Certain limits of smeared central field operators suggest a mathematical realization of Einstein’s early photon notion consisting of an energy point surrounded by a local force field (respective wave function). Macroscopic classical Maxwell fields are gained by superposing the expectation values of products of those composite photon operators. The ontological status of the explicated photon notion is discussed. Connections to Einstein’s historic photon theory, summarized in Rieckers (2025), as well as to quantum optical applications are hinted at throughout the paper.

International Journal of Theoretical Physics•Feb 25, 2025•2 citations

Elements of the wave-particle duality of light

Borys Jagielski

The following Master’s thesis is concerned with several aspects of the wave-particle duality of light. It is loosely divided in three parts. In the first part we consider historical, theoretical and experimental aspects of the duality problem. We explain how the notion of duality has developed through the last 400 years. We discuss theoretical underpinnings of the duality emodied by Maxwell’s electromagnetic theory, quantization of electromagnetic modes, Fock’s states and coherent states. We critically review several experiments which serve to demonstrate the corpuscular or undulatory behaviour of light and matter; in particular we present how the photoelectric effect and the Compton effect can be explained using the undulatory model, and we critically review Grangier, Roger and Aspect correlation experiment.\n\nIn the second part we describe two illustrative experiments on the duality of light conducted at Quantum Optics Laboratory at University of Oslo. The results of the experiment allow us to discuss how coincidence measurements can be used to exhibit the corpuscular behaviour of light, and how Mach-Zender interferometry performed at very low intensity can be used to exhibit the undulatory behaviour at\nthe (assumed) single-photon level. In addition, in the second part we review elements of theories closely associated with the experiment and the experimental setup: optical coherence, photocount and photon\nstatistics, beam splitter models and Gaussian beams. A proposition for extending the semiclassical model is given, and shortcomings of the present beam splitter models are discussed.\n\nIn the third part of the thesis we consider first Afshar’s experiment and some of the critical response that it has been met with. Then we discuss how the wave-particle duality is to be understood in the\nstandard interpretation of quantum mechanics, and how it could possibly be explained using either an alternative model for light or an alternative interpretation of quantum mechanics, and what difficulties such explanations present.

•Jan 1, 2009•5 citations

Quantum Physics of Light and Matter - Quantum Field Theory of Light

Luca Salasnich

Springer eBooks•Jan 1, 2020•0 citations
Abstract This is the first part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light-quanta (subsequently also referred to as “photons”) with classical electromagnetic fields that he formulated in 1909 via a purely verbal description. There, the overlap of many of the hypothetical local force fields, surrounding the photonic energy points, should produce the well–known classical Maxwell fields. We claim that, alone from such a logical connection, that apparently did not receive sufficient attention in the literature, one may draw essential conclusions on the photon states. In the present paper, we give a historical overview of Einstein’s photon conceptions until 1927. We extract hints from his formulations, that lead from his local force fields to Schrödinger wave functions, which reproduce the conserved integrals for energy, momentum, and angular momentum of Maxwell theory in form of Hilbert space expectations. Also a preliminary multi–photon theory, including Glauber states, is shown to be motivated by Einstein’s composite photons with possibly (incoherently!) overlapping force fields. In the resulting Fock space theory, gained by symmetrizing the many–photon states the goal of a fusion theory is, however, not realizable. In the subsequent companion paper “On sectorial photon theories reconstructing Einstein’s early fusion picture for light” (referred to as Rieckers 2025) our conclusions are extended to photon states that surpass Fock space theory by describing actual infinitely many photons. These are shown to cover also classical light states in terms of collective structures. Appealing to the more recent mathematical tools of convex state space approach and algebraic quantum field theory, we suggest there mathematical realizations of Einstein’s fusion program.
Abstract This is the second part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light. While in the foregoing paper “An Actual Discusion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields” (referred to as Rieckers 2025) our conclusions ended with the historical ab initio motivation and mathematical elaboration of a multi-photon theory in Fock space, we now start from the non–separable C*-Weyl algebra gained by abstracting the Fock–represented Weyl algebra. To the rich state space of this antiliminary observable algebra we apply notions of a convex state space approach to identify sub–theories that cover classical field states (including the vacuum with classical zero–field), that are possibly decorated by photonic quantum noise. The main emphasis is laid on direct integrals over irreducible, disjoint representations of the C*-Weyl algebra, decomposing the effective photon theory into sectors. Certain limits of smeared central field operators suggest a mathematical realization of Einstein’s early photon notion consisting of an energy point surrounded by a local force field (respective wave function). Macroscopic classical Maxwell fields are gained by superposing the expectation values of products of those composite photon operators. The ontological status of the explicated photon notion is discussed. Connections to Einstein’s historic photon theory, summarized in Rieckers (2025), as well as to quantum optical applications are hinted at throughout the paper.
The following Master’s thesis is concerned with several aspects of the wave-particle duality of light. It is loosely divided in three parts. In the first part we consider historical, theoretical and experimental aspects of the duality problem. We explain how the notion of duality has developed through the last 400 years. We discuss theoretical underpinnings of the duality emodied by Maxwell’s electromagnetic theory, quantization of electromagnetic modes, Fock’s states and coherent states. We critically review several experiments which serve to demonstrate the corpuscular or undulatory behaviour of light and matter; in particular we present how the photoelectric effect and the Compton effect can be explained using the undulatory model, and we critically review Grangier, Roger and Aspect correlation experiment.\n\nIn the second part we describe two illustrative experiments on the duality of light conducted at Quantum Optics Laboratory at University of Oslo. The results of the experiment allow us to discuss how coincidence measurements can be used to exhibit the corpuscular behaviour of light, and how Mach-Zender interferometry performed at very low intensity can be used to exhibit the undulatory behaviour at\nthe (assumed) single-photon level. In addition, in the second part we review elements of theories closely associated with the experiment and the experimental setup: optical coherence, photocount and photon\nstatistics, beam splitter models and Gaussian beams. A proposition for extending the semiclassical model is given, and shortcomings of the present beam splitter models are discussed.\n\nIn the third part of the thesis we consider first Afshar’s experiment and some of the critical response that it has been met with. Then we discuss how the wave-particle duality is to be understood in the\nstandard interpretation of quantum mechanics, and how it could possibly be explained using either an alternative model for light or an alternative interpretation of quantum mechanics, and what difficulties such explanations present.