Nonstandard introduction to squeezing of the electromagnetic field

This article contains a review of an alternative theory of squeezing, based entirely on the wave function description of the squeezed states. Quantum field theoretic approach is used to describe the squeezing of the electromagnetic field in its most complete form that takes into account temporal and spatial characteristics of the squeezed state. An analog of the Wigner function for the full electromagnetic field is introduced and expressed in terms of second order correlation functions. The field-theoretic approach enables one to study the propagation of the ``squeezing wave'' in space-time. A simple example of weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.Comment: Presented at the XXXVIII Cracow School of Theoretical Physics, Zakopane, June 1-10, 1998. To be published in Acta Physica Polonica

Photon wave function

Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, the photon wave function exists as long as it can be precisely defined and made useful.Comment: 52 pages, review pape

Quantum fluctuations of geometry in hot Universe

The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The field configurations are described by the linearized Riemann-Weyl tensor without any reference to the metric. The probability distribution of various configurations is described by the Wigner functional of the gravitational field. It has a foam-like structure, dominant configurations are those with large changes of geometry at nearby points. In the high-temperature limit one obtains the Bolzmann distribution that enables one to identify the expression for the total energy of the gravitational field. The appearance of the same expression for the total energy when the gravitational field is treated as a collection of gravitons and as the high-temperature limit of the Wigner functional proves the consistency of the whole procedure. Striking differences are found between the fluctuations of the electromagnetic field and the gravitational field, among them is the divergence in the gravitational case of the probability distribution at zero temperature. This divergence is of the "infrared type" because it occurs in integrals over the wave vector at small $k$.Comment: 11 pages A new significantly expanded versio

Uncertainty relation for focal spots in light beams

Uncertainty relations for light pulses found in [Phys. Rev. A {\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the two-dimensional plane perpendicular to the direction of the beam propagation which is more interesting for realistic beams. This uncertainty relation connects the area of the focal spot with the spectrum of transverse photon momenta. The shape of the beam that saturates the uncertainty relation is very close to a Gaussian. The directions of the electric and magnetic field vectors are those of the circularly polarized plane wave. Our uncertainty relation for the focal spot is quite general but we were able to determine the value of the lower bound only for beams made of many photons.Comment: To appear in Phys. Rev.

The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism

It is shown that the use of the Riemann-Silberstein (RS) vector greatly simplifies the description of the electromagnetic field both in the classical domain and in the quantum domain. In this review we describe many specific examples where this vector enables one to significantly shorten the derivations and make them more transparent. We also argue why the RS vector may be considered as the best possible choice for the photon wave function.Comment: Topical revie

Canonical separation of angular momentum of light into its orbital and spin parts

It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part

Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons

All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation. We present here analytic exact solutions, eigenstates of the total angular momentum component $M_z$, that come very close to this notion. These new solutions of the Dirac equation have also intricate topological properties similar to the hopfion solutions of the Maxwell equations.Comment: Submitted to Phys. Rev.

Dynamical rotational frequency shift

The term rotational frequency shift (RFS) has been used in different contexts and it was given different meanings. Other terms have also been used (azimuthal Doppler shift, angular Doppler shift) to describe various related phenomena. In this article we stick to the meaning of the rotational frequency shift given by us in Phys. Rev. Lett.78, 2539 (1977). In order to make a clear distinction between our RFS and other related shifts we use the term dynamical RFS (DRFS). We will study the spectral properties of radiation emitted by rotating quantum sources.Comment: To appear in The Angular Momentum of Light, edited by D. Andrews and M. Babiker, CUP 201

Gravitational waves carrying orbital angular momentum

Spinorial formalism is used to map every electromagnetic wave into the gravitational wave (within the linearized gravity). In this way we can obtain the gravitational counterparts of Bessel, Laguerre-Gauss, and other light beams carrying orbital angular momentum

Quantum-mechanical description of optical beams

Quantum mechanics of photons is derived from the theory of representations of the Poincar\'e group developed by Wigner. This theory places helicity as the most fundamental property; angular momentum and polarization are secondary characteristics. The properties of the beams of light are shown to be fully determined by the quantum states of the photons. Polarization of light beams is explained as the freedom to chose an arbitrary combination of the helicity states. Quantum mechanics of photons enables one to give a precise meaning to the concept of wave-particle duality.Comment: 14 pages, Tutorial revie