# Extremely subradiant states in a periodic one-dimensional atomic array

## TL;DR

This paper investigates long-lived subradiant states in a one-dimensional atomic array, revealing how to optimize their properties for potential applications in nanophotonics and quantum optics.

## Contribution

It introduces a theoretical framework for understanding subradiant states in atomic chains, including effects of additional interaction channels like waveguide modes.

## Key findings

- Subradiant states have linewidths decreasing faster than previously known.
- Long-lived states are achievable even with additional interaction channels.
- Subradiant states influence transmission and reflection spectra, enabling interaction-induced transparency.

## Abstract

We study the subradiant collective states of a periodic chain of two-level atoms with either transversal or longitudinal transition dipole moments with respect to the chain axis. We show that long-lived subradiant states can be obtained for the transversal polarization by properly choosing the chain period for a given number of atoms in the case of no open diffraction channels. These highly subradiant states have a linewidth that decreases with the number of atoms much faster than it was shown previously. In addition, our study shows that such states are present even if there are additional interaction channels between the atoms, i.e. they interact via waveguide mode of an optical nanofiber for instance. We develop a theoretical framework allowing to describe the spectral properties of the system in terms of contributions from each collective eigenstate and we show that subradiant states manifest themselves in the transmission and reflection spectra, allowing to observe interaction-induced transparency in a very narrow spectral range. Such long-lived collective states may find potential applications in nanophotonics and quantum optics.