Collective Dipole-Dipole Interactions in an Atomic Array

TL;DR

This paper investigates how collective dipole-dipole interactions in atomic arrays influence excitation dynamics and radiation, revealing symmetry effects, subradiant states, and tunable collective properties through band structure analysis.

Contribution

It introduces a band structure approach to analyze collective atomic interactions and demonstrates control over radiation properties by adjusting laser angle.

Findings

Excitation probability grows or decays logarithmically depending on laser detuning.

Symmetry at specific atomic spacings causes symmetric excitation and radiation patterns.

Presence of subradiant states disrupts the general trend for certain spacings.

Abstract

The coherent dipole-dipole interactions of atoms in an atomic array are studied. It is found that the excitation probability of an atom in an array parallel to the direction of laser propagation ($\boldsymbol{\hat{k}}$) will either grow or decay logarithmically along $\boldsymbol{\hat{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $\delta r = j\lambda/2$, where $j$ is an integer, causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array. For atomic separations of $\delta r < \lambda/2$, the appearance of a collection of extremely subradiant states ($\Gamma\sim 0$), disrupts the described trend. In order to interpret the results from a finite array of atoms, a band structure calculation in the $N\rightarrow \infty$ limit is conducted where the decay rates and the Collective Lamb Shifts of the eigenmodes along the Brillouin zone are shown. Finally, the band structure of an array strongly affects its scattered radiation, allowing one to manipulate the Collective Lamb Shift as well as the decay rate (from superradiant to subradiant) by changing the angle of the driving laser.