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Optical and Quantum Electronics

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01.11.2018

Single photon two-level atom interactions in 1-D dielectric waveguide: quantum mechanical formalism and applications

verfasst von: Fatih Dinç, İlke Ercan

Erschienen in: Optical and Quantum Electronics | Ausgabe 11/2018

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Abstract

In this paper, we propose an effective model to describe the interactions between a two-level atom and scattered light in a 1-D dielectric waveguide. The proposed formalism allows us to incorporate the effect of changing optical media inside the continuum while demonstrating a non-classical derivation of Fresnel Law. We obtain the transport characteristics of the two-level system, explore its high-Q bandreject filter property and discuss the implications of radiative and non-radiative dissipation. In addition, we apply our formalism to a modified Fabry–Pérot interferometer and show the variation in its spontaneous emission characteristics with changing interferometer length. Finally, we conclude with further remarks on the link between the waveguide and cavity quantum electrodynamics.

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In this article, operators will be expressed using hats (such as \(\hat{f}\)) and unit-vectors will be expressed using the inverse-hats (such as \(\check{k}\)). This representation is adapted from Dr. Austin J Hedeman’s course notes at University of California Berkeley.

A more detailed discussion for the derivation of the Hamiltonian can be found in Chapter 7 of Dutra (2005).

It is important to note that in this calculation, we neglect the contribution from some interference terms which are not individually zero. Hence, our result remains as an approximation in the region where the contribution from these interference terms can be neglected, i.e. \(\frac{|n_1-n_2|}{n_1+n_2}<< 1\).

This representation of the interaction Hamiltonian differs from (1) in the two following ways: The field operators \(\phi (x)\) are replaced with \(\phi ^{(n)}(x)\) and the group velocity \(v_g\) of the photons is replaced with \(v_g/n\) to incorporate the effect of dielectric medium, \(v_g\) corresponding to the group velocity in vacuum.

We note that this is just an order approximation. A more accurate result can be obtained numerically for a given parameter set. Especially for the boundary cases, where \(\varGamma =n\varGamma _n\) and \(\varGamma = \varGamma _n /n\), this result proves to be quite accurate.

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Titel: Single photon two-level atom interactions in 1-D dielectric waveguide: quantum mechanical formalism and applications
verfasst von: Fatih Dinç
İlke Ercan
Publikationsdatum: 01.11.2018
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 11/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-018-1658-y

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