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Quantizing the electromagnetic field near two-sided semitransparent mirrors

Nicholas Furtak-Wells, Lewis A. Clark, Robert Purdy, Almut Beige

Published Apr 13, 2018• 0 citations
Publisher

Abstract

© 2018 American Physical Society. This paper models light scattering through flat surfaces with finite transmission, reflection, and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model also accounts for the presence of mirror images and the possible exchange of energy between the electromagnetic field and the mirror surface. To test our model, we derive the spontaneous decay rate and the level shift of an atom in front of a semitransparent mirror as a function of its transmission and reflection rates. When considering limiting cases and using standard approximations, our approach reproduces well-known results but it also paves the way for the modeling of more complex scenarios.

DOI
10.25405/ncl.34354680

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© 2018 American Physical Society. This paper models light scattering through flat surfaces with finite transmission, reflection, and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model also accounts for the presence of mirror images and the possible exchange of energy between the electromagnetic field and the mirror surface. To test our model, we derive the spontaneous decay rate and the level shift of an atom in front of a semitransparent mirror as a function of its transmission and reflection rates. When considering limiting cases and using standard approximations, our approach reproduces well-known results but it also paves the way for the modeling of more complex scenarios.
This paper models light scattering through flat surfaces with finite transmission, reflection, and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model also accounts for the presence of mirror images and the possible exchange of energy between the electromagnetic field and the mirror surface. To test our model, we derive the spontaneous decay rate and the level shift of an atom in front of a semitransparent mirror as a function of its transmission and reflection rates. When considering limiting cases and using standard approximations, our approach reproduces well-known results but it also paves the way for the modeling of more complex scenarios.
Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semitransparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.
Atom-field interactions near optical interfaces have a wide range of applications in quantum technology. Motivated by this, this paper revisits the spontaneous emission of atomic dipoles in the presence of a two sided semi-transparent mirror. First we review the main properties of the quantised electromagnetic field near a semi-transparent mirror. To do so, we employ a quantum mirror image detector method which maps the experimental setup which we consider here onto analogous free space scenarios. We emphasise that the local density of states of the electromagnetic field depends on the reflection rates of both sides of the mirror surface. Hence it is not surprising that also the spontaneous decay rate of an atomic dipole in front of a semi-transparent mirror depends on both reflectance rates. Although the effect which we describe here only holds for relatively short atom-mirror distances, it can aid the design of novel photonics devices.
Atomic interactions have a wide range of potential applications in quantum technology but are, unfortunately, usually relatively short-range. In this thesis a novel approach to quantising the electromagnetic field in the presence of two-sided semi-transparent mirrors with finite transmission, reflection and absorption rates is presented. The image-detector method allows one to correctly reproduce the appropriate dynamics of wave packets in the presence of semi-transparent mirrors by mapping onto analogous free-space scenarios meaning photons are characterised as they are in free space. Moreover, radiating atoms in the presence of semi-transparent mirrors exhibit modified spontaneous emission rates due to boundary conditions imposed on the electromagnetic field. Through the image-detector method mirror-mediated dipole-dipole interactions are predicted which modify atomic spontaneous emission rates. The spontaneous emission rates explicitly depend on the optical properties of the semi-transparent mirror and these mirror-mediated dipole-dipole interactions are considered to be long range, as atoms placed several wavelengths from the mirror still exhibit modified spontaneous emission rates. In addition, the model readily extends to describe optical cavities. The results presented in this thesis are expected to pave the way for the modelling of more complex scenarios and for designing novel photonic devices for quantum technology applications, such as non-invasive glucose-sensing technology.
The local observables of the quantised electromagnetic field near a mirror-coated interface depend strongly on the properties of the media on both sides. In macroscopic quantum electrodynamics, this fact is taken into account with the help of optical Green’s functions which correlate the position of an observer with all other spatial positions and photon frequencies. Here we present an alternative, more intuitive approach and obtain the local field observables with the help of a quantum mirror image detector method. In order to correctly normalise electric field operators, we demand that spontaneous atomic decay rates simplify to their respective free space values far away from the reflecting surface. Our approach is interesting, since mirror-coated interfaces constitute a common basic building block for quantum photonic devices.
Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localized and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantized electromagnetic field in the presence of optical elements that are local objects. Therefore, in this paper, we take an alternative approach and quantize the electromagnetic field in position space. Taking into account the negative- and the positive-frequency solutions of Maxwell's equations, we construct annihilation operators for highly localized field excitations with bosonic commutator relations. These provide natural building blocks of wave packets of light and enable us to construct locally acting interaction Hamiltonians for two-sided semi-transparent mirrors.