Quantization of the Electromagnetic Field: Photons

Krishna Thyagarajan

Hristo Tonchev

This paper describes two cases of interaction between a quantized electromagnetic field and two different XY spin molecules; one with spins ½, and the other with spins 1. Both interact with a quantized electromagnetic field, with one of the spins in the chain interacting with the electromagnetic field. The interaction between the field mode and the spin chain with spins 1 is described by the one- and two-photon Jaynes-Cummings model (JC model). On the other hand, the interaction between the spins ½ and the electromagnetic field is described only by the one-photon Jaynes-Cummings model. Analytical and numerical calculations were made for the case of a different number of photons in the field mode, a different number of spins, and a different position of spin, interacting with the electromagnetic field. The invariant and block structures of such a chain are shown with a comparison made between the evolution of the magnetic moment and the number of photons in both cases.

Прохоров Лев Васильевич

Sergey I. Kharitonov, Svetlana Nikolaevna Khonina, Nikolay Lvovich Kazanskiy

This work deals with a hot topic of using quantum approaches in advanced telecommunications. Here, the major trend involves exploiting a flow of individual photons for signal transmission, because the photon is impossible to split, measure, copy, or imperceptibly delete. Such manipulations destroy the photon, prohibiting it to reach the recipient. Before the field quantization can be implemented, a problem of the electromagnetic field propagation needs first to be solved within classical electrodynamics, with dynamic quantities then replaced by the corresponding operators. This work describes a procedure for the electromagnetic field quantization in a waveguide with superconducting walls. In an optical fiber with inhomogeneous refractive index, the modes are shown to be non-orthogonal, so that the field can only approximately be quantized using the basis of waveguide modes. Expressions for operators of the electric and magnetic fields are derived, which may prove helpful for calculating both dynamic and other characteristics of the electromagnetic field, including nonclassical states of the electromagnetic field.

Galina A. Nemova

Igor A. Ivanov, Kyung Taec Kim

We consider ionization of an atom by the electromagnetic field in a Fock state $|N\ensuremath{\rangle}$: An eigenvector of the operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{N}}_{\mathbit{k},\ensuremath{\lambda}}={\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathbit{k},\ensuremath{\lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathbit{k},\ensuremath{\lambda}}$ of the number of photons in the mode $\mathbit{k},\ensuremath{\lambda}$. We treat the electromagnetic field in a quantized way, which allows us to obtain the photon picture of the strong field ionization. We obtain, in particular, probability distributions for the number of absorbed photons in the process of strong field ionization for atomic systems governed by short-range and Coulomb potentials.