On the Emergence of a Polychromatic Photon from a Single Atom

Abstract

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.

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

“…The preceeding paper in this journal by Ole Keller (Keller 2002) deals with the early time range during emission, namely the temporal and spatial evolution of the wave function during the "birth" of a photon. Keller's approach is naturally governed by views typical for quantum mechanics.…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

“…The preceeding paper in this journal by Ole Keller (Keller 2002) deals with the early time range during emission, namely the temporal and spatial evolution of the wave function during the "birth" of a photon. Keller's approach is naturally governed by views typical for quantum mechanics.…”

Electrodynamic interaction between two atoms in near‐field contact

“…For hydrogen‐like systems analytical expressions can be obtained for the matrix elements 〈 i | P T | j 〉, and afterwards the integrals appearing in ) are easily carried out analytically. In Keller (2002a) a preliminary study (without numerical results) of the three‐level renormalization was given, but there wrong signs appeared in front of the various Δ ij S. Because a general relation,…”

“…Once the entanglement between the two atoms is included, the initial and final specifications of the system will necessarily be nonlocal, and it is not easy to understand the role of Einstein causality unless the G‐gauge Hamiltonian is employed. In recent years, the G‐gauge formalism has been used to study the emergence of a single polychromatic photon from a single atom (Keller, 2000, 2002a).…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

“…The preceeding paper in this journal by Ole Keller (Keller 2002) deals with the early time range during emission, namely the temporal and spatial evolution of the wave function during the "birth" of a photon. Keller's approach is naturally governed by views typical for quantum mechanics.…”

Electrodynamic interaction between two atoms in near‐field contact

“…For hydrogen‐like systems analytical expressions can be obtained for the matrix elements 〈 i | P T | j 〉, and afterwards the integrals appearing in ) are easily carried out analytically. In Keller (2002a) a preliminary study (without numerical results) of the three‐level renormalization was given, but there wrong signs appeared in front of the various Δ ij S. Because a general relation,…”

“…Once the entanglement between the two atoms is included, the initial and final specifications of the system will necessarily be nonlocal, and it is not easy to understand the role of Einstein causality unless the G‐gauge Hamiltonian is employed. In recent years, the G‐gauge formalism has been used to study the emergence of a single polychromatic photon from a single atom (Keller, 2000, 2002a).…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”

“…The preceeding paper in this journal by Ole Keller (Keller 2002) deals with the early time range during emission, namely the temporal and spatial evolution of the wave function during the "birth" of a photon. Keller's approach is naturally governed by views typical for quantum mechanics.…”

Electrodynamic interaction between two atoms in near‐field contact

“…For hydrogen‐like systems analytical expressions can be obtained for the matrix elements 〈 i | P T | j 〉, and afterwards the integrals appearing in ) are easily carried out analytically. In Keller (2002a) a preliminary study (without numerical results) of the three‐level renormalization was given, but there wrong signs appeared in front of the various Δ ij S. Because a general relation,…”

“…Once the entanglement between the two atoms is included, the initial and final specifications of the system will necessarily be nonlocal, and it is not easy to understand the role of Einstein causality unless the G‐gauge Hamiltonian is employed. In recent years, the G‐gauge formalism has been used to study the emergence of a single polychromatic photon from a single atom (Keller, 2000, 2002a).…”

The Emission of a Single Photon from a Single Atom or Molecule - An Experimenter's View

“…How do these heuristic findings compare with the view presented in the previous paper by Ole Keller (Keller 2002)? There, it was shown that within the "Lorenz zone of molecular influence" the speed of light may be different from the vaccuum speed of light and therefore indeed a photon may run from a position at the end of a wavetrain to its front.…”