The physics of the photon vacuum, one-photon wave packets, and bi-photons are the subjects of the books SECTION II. Here we present an overview of these subjects paying particular attention to fundamental aspects. Cavity elec- trodynamics is often used to study free-photon states. However, such states constitutes an idealization since photon-matter interaction always is present at least in the surface region of the cavity wall. This means that even a photon- empty state does not exist in a rigorous physical sense. The transverse gauge photon states coupled to the wall of a closed cavity is discussed in a novel man- ner on the basis of a microscopic version of the Ewald-Oseen extinction theorem. Single-photon physics is introduced with background in the mean position state introduced in Chapter 3 . It is shown that a wave-packet one-photon wave func- tion in direct space satisfies a dynamical equation of a a Hamilton-like form. Quantum states containing two photons may be entangled, and such states are here called bi-photons. Using wave-packet bases for the two photons, a brief discussion of entangled transverse gauge photon states is given both in Hilbert space and direct space.
The physics of the photon vacuum, one-photon wave packets, and bi-photons are the subjects of the books SECTION II. Here we present an overview of these subjects paying particular attention to fundamental aspects. Cavity elec- trodynamics is often used to study free-photon states. However, such states constitutes an idealization since photon-matter interaction always is present at least in the surface region of the cavity wall. This means that even a photon- empty state does not exist in a rigorous physical sense. The transverse gauge photon states coupled to the wall of a closed cavity is discussed in a novel man- ner on the basis of a microscopic version of the Ewald-Oseen extinction theorem. Single-photon physics is introduced with background in the mean position state introduced in Chapter 3 . It is shown that a wave-packet one-photon wave func- tion in direct space satisfies a dynamical equation of a a Hamilton-like form. Quantum states containing two photons may be entangled, and such states are here called bi-photons. Using wave-packet bases for the two photons, a brief discussion of entangled transverse gauge photon states is given both in Hilbert space and direct space.
A brief account of the connection between the photon little group and gauge in- variance is given, considering the four-potential as the wave function of the photon. In most textbooks single photons are associated to the quanta of monochromatic plane-wave components of the electromagnetic field. However, polychromatic superposition of such states may also represent single photons. Having established the framework for polychromatic single-photon states in Hilbert space, and upon a discussion of the mean value and variance of the photon Hamilton operator for polychromatic states, we turn our attention to- wards the single-photon description in direct space. A photon wave function in direct space is obtained via the inner product of the photon mean position state (introduced in Chapter 3 ) and the Hilbert space polychromatic single-photon state. Noting that the photon is a relativistic object a rigorous polychromatic photon wave function is, in the continuum superposition of monochromatic plane-wave components, obtained noting the form of the relativistically invari- ant volume element in wave-vector space. We establish a wave-packet basis for single-photon states in Hilbert space, and the related photon wave functions. Thereafter, multi-photon wave packets are discussed, and the equal-time com- mutator relations between the wave packets are discussed, and the equal-time commutator relations between the wave-packet annihilation and creation oper- ators set up. As an example, we focus on two-photon wave packet states. We finish the chapter by a discussion of the two-photon concept and two-photon wave mechanics, analysing in particular the physical difference between two photons and bi-photons (an entangled state of two photons).
Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.
The wave aspect of light is observed experimentally through interference phenomena, and in a certain sense such observations always require a division of the given (initial) light field into two or more space-time parts. The division can only be done by introducing matter (massive particles) in the field region, and the light-matter interaction inevitably changes the initial state of the field. Not least when one is dealing with single and few-photon interference, it is good to remember again a central point of Niels Bohr, namely that no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon. It turns out that it is possible to observe interference with a quantized electromagnetic field which contains only one photon. Since the irreversible final detection destroys the photon, it is in practice necessary to repeat the experiment starting from the same initial (given) conditions. Below we shall discuss the basics of single-photon interference in the simplest terms.
The photon, an abstract concept belonging to a global vacuum, only manifests itself during interaction with matter. Fundamentals of Photon Physics describes the richly faceted, basic theory of photon-matter interaction, selecting a wide number of topics. Together with the author’s book Light -- The Physics of the Photon (CRC, 2014), both written on a scholarly level, the reader is given a comprehensive exposition of photon wave mechanics, quantum optics and quantum electrodynamics (QED). Divided into 10 parts, the book begins by exploring the relation between photon wave mechanics and quantum field theory. It then describes the theories of zero- and one-photon states and that of bi-photons. After discussing conservation laws, Lagrangian formulations, geometric phase and topology, the author turns towards the theory of photon scattering, emphasizing a density matrix operator approach and the role of microscopic extinction theorems. The book next focuses on mesoscopic QED, devoting particular attention to collective jellium excitations and photon-spin interactions. Special attention is given to the basics of the photon-magnon interaction and nonlinear superconductor electrodynamics, including the nonlinear Meissner rectification phenomenon, before studying the theory of transverse photons tied to (dressing) massive particles. The last three parts take the reader on a journey to topics usually not treated in books on photon- matter interaction. Beginning with photons in curved space-time structures and in spatially curved media, e.g. Möbius bands, the author discusses the extension of QED to the electro-weak interaction at an introductory level. Fundamentals of Photon Physics ends with the establishment of the set of isovector Maxwell equations in non-Abelian SO(3) gauge theory, leading to the celebrated hedgehog monopole model. Ole Keller is professor emeritus of theoretical physics at Aalborg University, Denmark. He earned his Licentiate (∼ PhD) degree in semiconductor physics from the Danish Technical University in Copenhagen in 1972, and the Doctor of Science degree from the University of Aarhus (1996). In 1989 he was appointed as the first professor in physics at Aalborg University by Margrethe Den Anden, queen of Denmark. The same year he was admitted to Kraks Blaa Bog, a prestigious Danish biographical dictionary which (citatum) ”Includes men and women, whose life story could have an interest for a wider public”. He is a fellow of the Optical Society of America. He has written the books entitled Quantum Theory of Near-Field Electrodynamics (Springer, 2011) and LIGHT - The Physics of the Photon (CRC, 2014), as well as the monographs Local Fields in the Electrodynamics of Mesoscopic Media (Physics Reports, 1996) and On the Theory of Spatial Localization of Photons (Physics Reports, 2005). He is the editor of the books Nonlinear Optics in Solids (Springer, 1990), Studies in Classical and Quantum Nonlinear Optics (Nova Science, 1995) and Notions and Perspectives of Nonlinear Optics (World Scientific, 1996). In recent years he has carried out theoretical research in fundamental photon physics, microscopic few-photon diffraction, mesoscopic and Möbius band electrodynamics, and studied magnetic monopole theory based on QED and the isovector Maxwell equations in non-Abelian gauge symmetry.
Within the framework of a two-dimensional microscopic, purely quantum mechanical model, we analyse the dynamics of single-photon wave packets interacting with optical elements (beam splitters, mirrors), modelled as systems of two-level atoms. That is, we utilize a two-dimensional cavity to simulate the quantum behaviour of simple optical components and networks made thereof. The field is quantized using the canonical procedure, and only the basis states with one unit of excitation are included. This, however, covers linear optical phenomena. The field is taken to interact with localized atoms through a dipole interaction. Using different configurations of atoms, and choosing their frequencies to be resonant or off-resonance, we can model mirrors, beam splitters, focusing devices and multicomponent systems. Thus we can model arbitrary linear networks of optical components. We show the time evolution of a photon wave packet in an interferometer as an example. As the state of the field is known at each instant, spectral properties and spatial coherence can immediately be obtained from the simulations. We also know the states of the two-level atoms constituting the components, which allows us to consider their quantum behaviour. Here the decay of an excited atom into the vacuum state of the electromagnetic field in the two-dimensional cavity is studied.
Abstract This book is unique in covering phenomena in photon- matter interactions in a unified way over a range of many orders in energy. The quantum field theoretic approach to the fully relativistic theory of quantum electrodynamics (QED) is presented together with the non- relativistic theory in both confined and unconfined geometries. The predictions of QED have been verified to a greater accuracy than any other physical theory. Moreover QED is a paradigm for other gauge theories and is presented in such a way that the generalisation to other gauge theories is natural. Gauge and Poincare symmetry properties and the non-existence of a photon wave function are thoroughly discussed. Starting from the Dirac equation the non-relativistic interaction of the electron with the electromagnetic field is derived as an effective Hamiltonian of multipole expansions. Much of quantum optics is based on the lowest order dipole approximation. From this point on the treatment of fully relativistic QED and quantum optics is done in parallel. Applications of perturbation theory such as Compton and Moller scattering and the theory photdetection are given. After the impressive successes of QED, the limitation of the theory and the necessity of electroweak theory and quantumchromodynamics are discussed. The remaining chapters are devoted to quantum optics inside cavaties. Various approaches to open systems such as master equations are discussed within the context of active systems (e.g. the laser) and passive systems. Semi- classical approximarions are shown to imply a rich non- linear dynamics including chaos for certain parameter regimes. The effect of fluctuations on such non-linear dynamics is also studied. The final chapter is devoted to highly non- classical states of the light field such as photon number, squeezed and two photon entangled states. The latter are studied for the important system of parametric down conversion and the localisation properties of photons are characterised in terms of asympotic tails in photodetection probabilities as a function of time delay. The range of the book has wider benefits. Workers in quantum optics will gain a deeper understanding of the foundations of their subject and field theorists will see concrete examples of open systems, which are beginning to impinge on fundamental theories.