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arXiv:2410.02349 · Physical Review A

Atoms near a conducting wedge: Decay rates and entanglement around a corner

Romuald Kilianski, Robert G. Bennett

Published Dec 16, 2024• 1 citation
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Abstract

The behavior of an atomic system is influenced by introducing a metallic surface. This work explores how the decay landscape can be altered by the presence of sharp corners. We utilize analytical expressions for Hertz and vector potentials in the presence of a perfectly conducting wedge with arbitrary opening angle to obtain the relevant electrostatic Green's functions. We use these to examine two scenarios: the modified spontaneous decay of a single atom, which leads us to speculate about potential applications in microscopy, and the case of a more fundamental, theoretical interest, the behavior of an entangled pair of atoms near a corner. The latter, when two atoms are positioned “out of the line of sight,” opens up a possible line of investigation into devices that are able to “see around corners.” Published by the American Physical Society 2024

DOI
10.1103/physreva.110.062812

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The behavior of an atomic system is influenced by introducing a metallic surface. This work explores how the decay landscape can be altered by the presence of sharp corners. We utilize analytical expressions for Hertz and vector potentials in the presence of a perfectly conducting wedge with arbitrary opening angle to obtain the relevant electrostatic Green's functions. We use these to examine two scenarios: the modified spontaneous decay of a single atom, which leads us to speculate about potential applications in microscopy, and the case of a more fundamental, theoretical interest, the behavior of an entangled pair of atoms near a corner. The latter, when two atoms are positioned “out of the line of sight,” opens up a possible line of investigation into devices that are able to “see around corners.” Published by the American Physical Society 2024
Over the past ten years, our group has investigated the effects of confinement on atoms inside metallic micron–sized cavities in order to elucidate some basic phenomena in the field of cavity quantum electrodynamics (QED). The first of these was the inhibition of spontaneous emission from an atom inside a cavity. This was followed by a laser spectroscopic measurement of the van der Waals interaction between a single Rydberg atom and a gold cavity, which showed that a simple electrostatic model of the atom–cavity interaction is correct when the cavity is small enough. More recently, the retarded Casimir–Polder force was measured between a ground state sodium atom and a large cavity, demonstrating that the van der Waals potential fails at long enough range and that the vacuum fluctuations of the field then have an important role in the interaction of the atom with the cavity. Our group is now pushing forward these investigations to study cavities whose walls have losses and dispersion, where the theory of cavity QED is significantly more complicated. With real surfaces, we have to deal with the complex dielectric response ε(ω) of the material, which exhibits frequency–dependent absorption and dispersion. One particularly interesting case is when a downward transition in the atom is resonant with an excitation of the cavity walls. This opens a new branch for the atomic decay: as an alternative to creating a photon within the space surrounded by the cavity walls the atomic decay can now create an electromagnetic excitation of the walls themselves. Another novel feature of our experiments is that the Bohr frequencies of the atom are close to the kT/h, where T is room temperature. We therefore expect to be able to measure effects associated with QED at finite temperature; in other words, to study how the blackbody radiation affects our experiments. By conducting experiments with real surfaces, we hope to elucidate and perhaps simplify the theoretical models used to describe these systems.
The behavior of Rydberg atoms near metal surfaces in the presence of an external electric field has been examined theoretically to evaluate their potential use as an experimental probe of electron tunneling processes at surfaces. These ab initio calculations reveal strong hybridization that leads to a shift and broadening of the Rydberg levels that depend sensitively on the atom-surface separation and the strength of the applied electric field. A range of external fields exists, however, for which the Rydberg atoms ionize at sufficiently large atom-surface separations that, even in the presence of image charge attraction, the resulting positive ions can escape the surface and provide an experimentally observable signal. \textcopyright{} 1996 The American Physical Society.
The behavior of Rydberg atoms near metal surfaces in the presence of an external electric field has been examined theoretically to evaluate their potential use as an experimental probe of electron tunneling processes at surfaces. These ab initio calculations reveal strong hybridization that leads to a shift and broadening of the Rydberg levels that depend sensitively on the atom-surface separation and the strength of the applied electric field. A range of external fields exists, however, for which the Rydberg atoms ionize at sufficiently large atom-surface separations that, even in the presence of image charge attraction, the resulting positive ions can escape the surface and provide an experimentally observable signal. \textcopyright{} 1996 The American Physical Society.
Quadrupole radiation of an atom in an arbitrary environment is investigated within classical as well as quantum electrodynamical approaches. Analytical expressions for decay rates are obtained in terms of the Green's function of Maxwell equations. The equivalence of both approaches is shown. General expressions are applied to analyze the quadrupole decay rate of an atom placed between two half spaces with arbitrary dielectric constant. It is shown that in the case where the atom is close to the surface, the total decay rate is inversely proportional to the fifth power of distance between an atom and a plane interface.
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It is a well known fact that the presence of material bodies in the vicinity of an atom affects its interaction with the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous-emission rate of a given excited atom is altered when this atom is placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism upon which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom, but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. The oscillatory pattern for the spontaneous-emission rate of the atom as we vary its relative position to the wedge as well as the phenomenon of suppression are shown by a few graphs.