# Bound states in the continuum for an array of quantum emitters

## TL;DR

This paper investigates bound states in the continuum in a system of equally spaced quantum emitters coupled to a one-dimensional boson field, analyzing both approximate and exact solutions for small numbers of emitters.

## Contribution

It provides a detailed analysis of bound states in the continuum for quantum emitter arrays, including explicit solutions for three and four emitters, considering both distant and finite spacing effects.

## Key findings

- Degenerate eigenspaces of bound states identified for distant emitters.
- Explicit solutions obtained for systems with three and four emitters.
- Finite spacing and dispersion effects influence the bound state energies.

## Abstract

We study the existence of bound states in the continuum for a system of n two-level quantum emitters, coupled with a one-dimensional boson field, in which a single excitation is shared among different components of the system. The emitters are fixed and equally spaced. We first consider the approximation of distant emitters, in which one can find degenerate eigenspaces of bound states corresponding to resonant values of energy, parametrized by a positive integer. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding also nonperturbative effects. We explicitly solve the cases n=3 and n=4.