Band Structure and Dynamics of Single Photons in Atomic Lattices

TL;DR

This paper investigates how the dimensionality of atomic lattices affects single-photon band structures and decay dynamics, revealing fundamental differences between 1D, 2D, and 3D arrays in radiative behavior and coherence.

Contribution

It introduces a comprehensive framework analyzing single-photon properties across different lattice dimensions, highlighting the transition from radiative to non-radiative regimes and coherent transport.

Findings

1D and 2D arrays are inherently radiative with oscillating decay rates.

3D lattices are non-radiative with decay only at Bragg resonances.

System dynamics shift from dissipative decay to coherent transport with increasing dimension.

Abstract

We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.