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Journal of Physics Conference Series

Singular behavior of the photon density of states and the self-energy function of an electron in photonic crystal

R. Kh. Gainutdinov, Хамадеев Марат Актасович, D N Avramenko, K A Ziyatdinova, М. Х. Салахов

Published Nov 24, 2014• 0 citations
Publisher

Abstract

We show that Van Hove singularities in the behavior of the photon density of states in a photonic crystal results in a singular behavior of the self-energy functions of atomic states that describe the interaction of the atom with vacuum. This is shown to have a significant effect on processes of quantum interference from atoms in the PC medium.

DOI
10.1088/1742-6596/560/1/012007

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We show that Van Hove singularities in the behavior of the photon density of states in a photonic crystal results in a singular behavior of the self-energy functions of atomic states that describe the interaction of the atom with vacuum. This is shown to have a significant effect on processes of quantum interference from atoms in the PC medium.
The interaction between atoms placed into cavities of a one-dimensional photonic crystal (PC) and the radiation self-field is studied. Dispersion relations and photonic density of states for a one-dimensional PC consisting of gallium arsenide and vacuum layers in one case, and metamaterial and vacuum layers in the other case are calculated by the transition matrix method. Variations of the self-energy correction to the 1 s state energy of the hydrogen atom are considered as functions of the optical contrast and relative thickness one-dimensional PC layers.
Abstract The self-energy correction to the mass of an atomic electron placed into a void of the photonic crystal medium is investigated. In this study the one-dimensional photonic crystal made from gallium arsenide and vacuum layers is considered. We show that the electron mass change gives rise not only to the shifts of the atomic energies but also to the nonradiative transitions between atomic levels. These transitions add new channels to a decay of an atomic state that leads to a quantum interference between these channels.
Photonic crystals (PCs) are periodic systems that consist of dielectrics with different refractive indices. Photonic crystals have many potential technological applications. These applications are mainly based on the photonic bang gap effect. However the band gap is not only effect that follows from the periodic changing of the refractive index in the photonic crystal. The periodic change of the photon-matter interaction in photonic crystal medium gives rise to the fact that the mass of an electron in the photonic crystal must differ from its mass in vacuum. Anisotropy of a photonic crystal results in the dependence of the electromagnetic mass correction on the orientation of the electron momentum in a photonic crystal. This orientation dependence in turn gives rise to the significant correction to the transition frequencies in an atom placed in air voids of a photonic crystal. These corrections are shown to be comparable to the atomic optical frequencies. This effect allows one to control the structure of the atomic energy levels and hence to control resonance processes. It can serve as the basis for new line spectrum sources. The effect provides new ways of realization of quantum interference between decay channels that can be important for quantum information science.
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Photonic crystals are periodic systems that consist of dielectrics with different refractive indices. They are designed to act on photons in contrast to semiconductor crystals whose periodicity affects the motion of electrons. Here we consider the interaction of an atomic electron with its own radiation field in the case when the atom is placed in air voids of a photonic crystal and is not in mechanical contact with the vibrational degrees of freedom of the dielectric host. A strong modification of this interaction from that in free space is shown to change the rest mass of the electron, and this has a significant effect on the shift of the atomic energy levels. This shift is investigated by using the example of atomic hydrogen in a high-index-contrast photonic crystal. The found effect may be of interest both from fundamental and practical points of view.