# Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Resonance Interaction between Two Uniformly Accelerating Atoms: The Scalar Field Case

^{2}), as a function of the atomic acceleration. In the plots, the value used for ${\omega}_{0}$ is the ionization energy of

^{87}Rb, and the distances $L=D$ and z have been chosen in such a way that the plots cover near, intermediate, and far zones, for both perpendicular and parallel alignments of the atoms. The plots show that the resonance interaction energy depends on the acceleration and the geometric configuration of the two atoms with respect to the plate (perpendicular or parallel alignment) and that it can be enhanced or inhibited, depending on the atomic acceleration.

## 3. Resonance Interaction for Two Accelerating Atoms Interacting with the Electromagnetic Field

#### 3.1. Atoms Aligned Perpendicularly to the Plate

^{2}($2.2\times {10}^{-6}$ eV, in our units), $z={10}^{-8}$ m ($\sim 5\times {10}^{-2}$ eV

^{−1}), $L=1.5\times {10}^{-8}$ m ($\sim 7.5\times {10}^{-2}$ eV

^{−1}), and $\hslash {\omega}_{0}=4.17$ eV, obtaining $\delta E\simeq 4.4\times {10}^{-10}$ eV. This energy shift is about 4 orders of magnitude smaller than the Lamb shift for the $n=2$ level of the hydrogen atom. Although quite small, we expect that such an energy shift should be measurable using high-resolution spectroscopy, provided the assumed constant acceleration could be reached.

#### 3.2. Atoms Aligned Parallel to the Plate

## 4. Summary

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 1.**Pictorial description of the first geometrical configuration considered for the physical system: two atoms placed on the z-axis, perpendicular to the plate, and uniformly accelerating along the x-direction.

**Figure 2.**Pictorial description of the second geometrical configuration considered for the physical system: two atoms aligned along the y-axis, parallel to the plate, and uniformly accelerating along the x-direction.

**Figure 3.**Resonance interaction energy between the two atoms (units: eV/λ

^{2}, where the coupling constant λ in our units is dimensionless), as a function of the atomic acceleration, for two different geometric configurations. Blue continuous line: atoms positioned on the z-axis, which is perpendicular to the plate. Green dashed line: atoms along the y-axis, which is parallel to the plate. For comparison, the yellow dot-dashed line and the red dotted line respectively refer to the case of inertial atoms aligned in a perpendicular or parallel direction relative to the plate. The plots show that the interaction depends on the acceleration and on the geometric configuration of the two-atom system relative to the mirror. Parameters, in the units used, are chosen such that L = D = 7.5 × 10

^{−2}eV

^{−1}, z = 2.0 × 10

^{−2}eV

^{−1}, and ω

_{0}= 4.17 eV.

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**MDPI and ACS Style**

Zhou, W.; Passante, R.; Rizzuto, L. Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary. *Symmetry* **2018**, *10*, 185.
https://doi.org/10.3390/sym10060185

**AMA Style**

Zhou W, Passante R, Rizzuto L. Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary. *Symmetry*. 2018; 10(6):185.
https://doi.org/10.3390/sym10060185

**Chicago/Turabian Style**

Zhou, Wenting, Roberto Passante, and Lucia Rizzuto. 2018. "Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary" *Symmetry* 10, no. 6: 185.
https://doi.org/10.3390/sym10060185