Elements of a new quantum electrodynamic theory which might enable one to obtain a better understanding of the linear and nonlinear interaction between atomic systems in near-field contact is presented. To follow the space-time dynamics in the atomic near-field zone an electromagnetic propagator formalism with polychromatic photons is constructed. A first-quantized description based on the photon energy wave function for free polychromatic photons is extended in such a manner that the birth process of the photon, which takes place in the near-field zone of the source, can be followed. In order to be able to describe harmonic generation processes in near-field optics polychromatic photons of the simple wave-train type are used. The wave mechanical (first-quantized) description based on wave-train photons is upgraded to a field-theoretic (second-quantized) formalism using a new so-called propagator gauge which is closely related to the Poincaré gauge underlying the multipole description of quantum electrodynamics.
Elements of a new quantum electrodynamic theory which might enable one to obtain a better understanding of the linear and nonlinear interaction between atomic systems in near-field contact is presented. To follow the space-time dynamics in the atomic near-field zone an electromagnetic propagator formalism with polychromatic photons is constructed. A first-quantized description based on the photon energy wave function for free polychromatic photons is extended in such a manner that the birth process of the photon, which takes place in the near-field zone of the source, can be followed. In order to be able to describe harmonic generation processes in near-field optics polychromatic photons of the simple wave-train type are used. The wave mechanical (first-quantized) description based on wave-train photons is upgraded to a field-theoretic (second-quantized) formalism using a new so-called propagator gauge which is closely related to the Poincaré gauge underlying the multipole description of quantum electrodynamics.
A theoretical study of elements of the quantum electrodynamic interaction between two single-electron atoms in near-field contact is presented. The framework of the study is an electromagnetic propagator formalism that allows one to describe the near-field space-time interaction in such a manner that the Einstein causality and lack of photon localizability are manifest. First we set up the atom-field Hamiltonian in the so-called G-gauge, starting from the Coulomb Hamiltonian, and thereafter we show that this leads to a correct propagator description for the retarded part of the transverse electromagnetic field (operator). In the G-gauge approach, renormalization of the two-particle energy level structure stemming from the transverse self-field occurs. The intraparticle renormalization is calculated for a three-level atom (it is trivial for a two-level atom), and the interparticle renormalization, which depends on the atomic separation, is determined for two two-level atoms. The magnitude of the energy renormalization is always finite in our theory because we do not consider the atoms to be point-like objects from an electromagnetic point of view. Throughout, we relate our G-gauge formalism to the multipole theory often used in studies of interatomic electrodynamics.
Recent attempts to establish a space-time description of single-photon emission from single atoms (or molecules) are reviewed. In the wake of historical remarks on the so-called Lorenz zone of molecular influence, characteristics of the power-law confined birth domain of the photon are discussed within the framework of a field-unquantized formalism. In contrast to the common believe it is shown that the birth domain can be (and is) exponentially localized if the photon emerges from a pure spin transition. As a paradigm of exponential localization we discuss the emergence of a radio-frequency photon from the hydrogen hyperfine structure. Starting from the first-quantized description of the energy wave function of a polychromatic photon in vacuo, we introduce a propagator description of the photon embryo, and argue that the single-photon tunnelling process is a fingerprint of our inability to localize photons in space-time. With this understanding optical tunnelling appears as an indispensable part of all single photon-atom scattering processes. In the final part of the review we briefly describe how the formalism can be upgraded from single-photon wave mechanics to a field-quantized description based on wave packet (wave train) electrodynamics. In this new formalism, in which the polychromatic photon embryo is included as an integral part of the polychromatic field quanta, the electrons of the atom (or molecule) move not only in the self-consistent Coulomb potential but also in the transverse potential created by the particles themselves. A rigorous relativistic quantum electrodynamic theory of wave train photon emission from single atoms emerges in the horizon.
When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wavemechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.
A review is given of the space-time wave mechanics of single photons, a subject with an almost century long history. The Landau-Peierls photon wave function, which is related nonlocally to the electromagnetic field is first described, and thereafter the so-called energy wave function, based on the positive-frequency Riemann-Silberstein vectors, is discussed. Recent attempts to understand the birth process of a photon emerging from a single atom are summarized. The polychromatic photon concept is introduced, and it is indicated how the wave mechanics of polychromatic photons can be upgraded to wave train quantum electrodynamics. A brief description of particle (photon) position operators is given, and it is shown that photons usually are only algebraically confined in an emission process. Finally, it is demonstrated that the profile of the birth domain of a radio-frequency photon emitted in a hyperfine spin transition shows an exponential falloff with the distance from the atomic nucleus. The length parameter in this falloff is the Bohr radius.
A field-quantized electromagnetic propagator description emphasizing the spatial localization of light emitted from a single-electron atom is presented. With the aim of obtaining a better insight into the quantum electrodynamics in the near-field zone of the atom, two approaches, formally different but equivalent in respect to their physical predictions, are studied. From the Maxwell equations, among the transverse operators, a transverse propagator picture in which the source region for the field is identified with the spatial domain occupied by the transverse current density of the atom emerges. In this picture the field propagation is isotropic and always retarded. By identifying the source region with that of the total atomic current, the transverse propagator becomes anisotropic, and attains a nonretarded self-field part and a near-field part different from zero only for spacelike events. By changing the Coulomb Lagrangian, a nonrelativistic Hamiltonian formalism adequate for reconciling the photon concept with the anisotropic propagator picture is introduced. In this formalism the transverse self-field energy is transferred to the particle Hamiltonian, and the interaction Hamiltonian now includes an interaction between the retarded field and the transverse self-field dynamics. The link between the standard (nonpropagator) theory, often used to argue that the total electromagnetic field is always retarded, and the transverse propagator theory is established. The equivalence between the two approaches is proved by demonstrating that the standard theory in fact includes a nonretarded response in the spatial domain occupied by the longitudinal part of the induced atomic current density.
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.