Quasi-flat band enables subradiant two-photon bound states

TL;DR

This paper theoretically investigates the long radiative lifetime of two-photon bound states in a waveguide with a two-level atom array, revealing a connection to a quasi-flat band and edge effects that hinder photon escape.

Contribution

It uncovers a transformation from a non-Hermitian to a nearest-neighbor model explaining the long lifetime and links lifetime oscillations to the bound pair's dispersion.

Findings

Maximum bound pair lifetime at specific array period.

Divergence of effective mass at certain conditions.

Oscillations of lifetime linked to quasi-flat band dispersion.

Abstract

We study theoretically the radiative lifetime of bound two-particle excitations in a waveguide with an array of two-level atoms, realising a 1D Dicke-like model. Recently, Zhang et al. [arXiv:1908.01818] have numerically found an unexpected sharp maximum of the bound pair lifetime when the array period $d$ is equal to $1/12$th of the light wavelength $\lambda_0$]. We uncover a rigorous transformation from the non-Hermitian Hamiltonian with the long-ranged radiative coupling to the nearest-neigbor coupling model with the radiative losses only at the edges. This naturally explains the puzzle of long lifetime: the effective mass of the bound photon pair also diverges for $d=\lambda_0/12$, hampering an escape of photons through the edges. We also link the oscillations of the lifetime with the number of atoms to the nonmonotous quasi-flat-band dispersion of the bound pair.