It is argued that the photon tunneling process originates in an inability to localize photons completely in space. Seen in this perspective, optical tunneling experiments might allow one to obtain rich information on the photon localizability problem, that until now has been studied mainly theoretically. A rigorous analysis of the electrodynamics in the near-field zone of matter enables us to identify the transverse vector field and subsequently to use it to construct a first-quantized space–time theory for the photon birth process and to determine the source region of the photon. The present theory shows that optical tunneling never appears outside the photon’s source domain, and it is shown that an apparently superluminal response occurs as a consequence of the lack of complete photon localizability. No fundamental velocity is attached to this effect, which stems solely from quantum nonlocality. Starting from the Riemann–Silberstein vectors, which permit the introduction of a space–time description of a free polychromatic photon’s so-called energy wave function, a theoretical investigation of the near-field scattering of a single photon from a mesoscopic or microscopic (molecular, atomic) particle is presented. Inasmuch as the photon tunneling phenomenon appears to be an indispensable part of the near-field scattering process, it might be possible to establish a rigorous first-quantized theory of one-photon tunneling between macroscopic molecular solids by adding the tunneling contributions from the individual molecules.
It is argued that the photon tunneling process originates in an inability to localize photons completely in space. Seen in this perspective, optical tunneling experiments might allow one to obtain rich information on the photon localizability problem, that until now has been studied mainly theoretically. A rigorous analysis of the electrodynamics in the near-field zone of matter enables us to identify the transverse vector field and subsequently to use it to construct a first-quantized space–time theory for the photon birth process and to determine the source region of the photon. The present theory shows that optical tunneling never appears outside the photon’s source domain, and it is shown that an apparently superluminal response occurs as a consequence of the lack of complete photon localizability. No fundamental velocity is attached to this effect, which stems solely from quantum nonlocality. Starting from the Riemann–Silberstein vectors, which permit the introduction of a space–time description of a free polychromatic photon’s so-called energy wave function, a theoretical investigation of the near-field scattering of a single photon from a mesoscopic or microscopic (molecular, atomic) particle is presented. Inasmuch as the photon tunneling phenomenon appears to be an indispensable part of the near-field scattering process, it might be possible to establish a rigorous first-quantized theory of one-photon tunneling between macroscopic molecular solids by adding the tunneling contributions from the individual molecules.
A paradigm of optical (photon) tunneling appears in relation to the physics of frustrated total internal reflection (FTIR); see e.g., [123, 118, 50, 224, 51]. In the FTIR process evanescent fields play an indispensable role, and the fact that the source domains of transverse and longitudinal photons generated by a current density sheet (located at z = 0) extend outside the sheet, with a current density profile given by exp(−q‖|z|), indicates that the physics in the rim zone is crucial for an understanding of the photon tunneling process. We shall reach the FTIR tunneling process starting from a broader framework. Thus, it turns out that optical near-field interaction, spatial photon localization, and photon tunneling have the same roots. The considerations to follow also lead to connections to the photon measurement problem which we shall address in Part VIII. In a broader context the problem brings us in contact with the so-called measurement theory in quantum physics, which in itself raises deep questions about the physical/philosophical structure of human observations [168, 157, 247].
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.
Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric down-conversion light source, which produced correlated, but random, emissions of photon pairs. The two photons of a given pair were emitted in slightly different directions so that one photon passed through the tunnel barrier, while the other photon passed through the vacuum. The time delay for the tunneling photon relative to its twin was measured by adjusting the path length difference between the two photons in a Hong-Ou-Mandel interferometer, in order to achieve coincidence detection. We found that the photon transit time through the barrier was smaller than the twin photon’s transit time through an equal distance in vacuum, indicating that the process of tunneling in quantum mechanics is superluminal. Various conflicting theories of tunneling times are compared with experiment. An introduction to an introduction Tunneling, the quantum mechanical process by which a particle can penetrate a classically forbidden region of space, is one of the most mysterious phenomena of quantum mechanics. Yet it is one of the most basic and important processes in Nature, without which we could not even exist, for tunneling is involved in the very first step of the nuclear reaction, p + p → d + e + νe, which powers the Sun, the source of energy for life on the Earth. ∗ On appointment as a Miller Research Professor in the Miller Institute for Basic Research
Abstract The observation of superluminal transmission of photons created discussions of their reality and significance. To analyze the possibility of such phenomena in general, the most general method is employed based on the covariant theory of dispersion relations. It is shown that superluminal phenomena can only be realized as tunneling of excitations within the near field zone. On this basis, the main experimental data can be described as sequential processes of single photon scattering. Their temporal distribution is estimated by taking into account the scattering time. Thus, the difference is explained between the advance of the superluminal part of the light pulse (i.e., the transition time of single photons) and the signal velocity of the macroscopic pulse of light.
You might think that the great success of quantum electrodynamics (QED) would settle the debate on the nature of light to provide a clear view of its behavior, where the photon is regarded as the unit of excitation associated with a quantized mode of the electromagnetic (radiation) eld. However, Heisenberg’s uncertainty principle tells us that a state of denite momentum, energy, and polarization associated with a plane wave used as a basis function of quantization must be completely indenite in space and time. It suggests the diµculty of spatial localization of a photon as a particle. In fact, Newton and Wigner showed that a free photon, as a massless particle with spin 1, has no localized states on the basis of natural invariance requirements that localized states for which operators of the Lorentz group apply should be orthogonal to the undisplaced localized states, a§er a translation (Newton and Wigner 1949). According to them, one can obtain a general expression for a position operator for massive particles and for massless particles of spin 0 or 1/2, not for massless particles with nite spin, which indicates that there is no probability density for the position of the photon, and thus a position-representation wave function cannot be consistently introduced. It has also been shown that photons are not localizable, on the basis of imprimitive representations of the Euclidean group (Wightman 1962). It is now believed that photons are only weakly localizable, although single-photon states with arbitrarily fast asymptotic fallo of energy density exist, and that a lack of strict localizability is directly related to the absence of a position operator for a photon in free space and a positionrepresentation photon wave function (Hawton 1999).