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Casimir-Polder potential on an excited atom near an atomic array

Annyun Das, Kanu Sinha

Abstract

We develop a microscopic description of the fluctuation-mediated Casimir-Polder (CP) shifts on a 'test' two-level atom placed near a two-dimensional atomic array of two-level atoms. We derive the resonant and off-resonant CP potentials experienced by the excited test atom using fourth-order perturbation theory, under the assumption that the test atom resonance is far detuned from those of the array atoms. The total potential on the test atom can be described as the sum of the pairwise resonant and off-resonant potentials resulting from its interaction with the individual atoms of the array. We analyze the asymptotic scaling of CP shifts as a function of the test atom-array separation, and its dependence on various system parameters: array spacing and size, and dipole orientation of the array atoms. Our results bridge the description of CP potential across two distinct regimes: (i) from a single-atom limit where we recover the well-known two-atom Van der Waals potential, (ii) to a macroscopic boundary limit, where we demonstrate new asymptotic scaling laws. We demonstrate that these scaling laws can be tuned via the microscopic parameters of the atomic array, establishing atomically-controlled arrays as a versatile platform for tailoring fluctuation-induced QED phenomena.

Casimir-Polder potential on an excited atom near an atomic array

Abstract

We develop a microscopic description of the fluctuation-mediated Casimir-Polder (CP) shifts on a 'test' two-level atom placed near a two-dimensional atomic array of two-level atoms. We derive the resonant and off-resonant CP potentials experienced by the excited test atom using fourth-order perturbation theory, under the assumption that the test atom resonance is far detuned from those of the array atoms. The total potential on the test atom can be described as the sum of the pairwise resonant and off-resonant potentials resulting from its interaction with the individual atoms of the array. We analyze the asymptotic scaling of CP shifts as a function of the test atom-array separation, and its dependence on various system parameters: array spacing and size, and dipole orientation of the array atoms. Our results bridge the description of CP potential across two distinct regimes: (i) from a single-atom limit where we recover the well-known two-atom Van der Waals potential, (ii) to a macroscopic boundary limit, where we demonstrate new asymptotic scaling laws. We demonstrate that these scaling laws can be tuned via the microscopic parameters of the atomic array, establishing atomically-controlled arrays as a versatile platform for tailoring fluctuation-induced QED phenomena.
Paper Structure (26 sections, 53 equations, 3 figures, 3 tables)

This paper contains 26 sections, 53 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Casimir-Polder potential of the test atom
  4. Asymptotic scaling laws and dependence on array parameters
  5. Crossover from single-atom to macroscopic medium limit
  6. Asymptotic CP shifts for $z$-oriented array dipoles
  7. Non-retarded regime $\left( z/\lambda_0\ll1\right)$
  8. Retarded regime $( z/\lambda_0\gg 1)$
  9. Resonant CP potential as a function of array size
  10. Asymptotic CP shifts for $x$-oriented array dipoles
  11. Non-retarded regime $\left( z\ll\lambda_0 \right)$
  12. Retarded regime $\left( z\gg \lambda_0\right)$
  13. Resonant CP potential as a function of array size
  14. Conclusions and Outlook
  15. Acknowledgements
  16. ...and 11 more sections

Figures (3)

  • Figure 1: Schematic representation of the model. We consider an excited two-level test atom with transition frequency $\omega_0$ placed atop a 2D square lattice of $N$ two-level atoms with transition frequency $\omega_M$ and lattice constant $a$. The array is in the $xy$-plane, with the test atom placed at a distance $z$ above the central array atom along the $z$-axis.
  • Figure 2: The resonant shift $\Delta\omega^\mathrm{R}$ is plotted for $N=100$ (dash-dotted green), $N=10^6$ (dashed orange), and $N=10^{10}$ (solid blue) array atoms, obtained by performing a numerical sum over all lattice points using Eq. \ref{['Eq:omegaR']} for a fixed $\tilde{a}\approx 10^{-2}$.
  • Figure 3: The resonant shift $\Delta\omega^\mathrm{R}$ is plotted for $N=100$ (dash-dotted green), $N=10^6$ (dashed orange), and $N=10^{10}$ (solid blue) array atoms, obtained by performing a numerical sum over all lattice points using Eq. \ref{['Eq:omegaR']} for a fixed $\tilde{a}\approx 10^{-2}$.