Theory of the Collective Many-body Subradiance in Waveguide QED

TL;DR

This paper develops an analytical framework for understanding the most subradiant modes in finite waveguide QED systems, revealing universal N^{-3} linewidth scaling and boundary effects.

Contribution

It introduces a non-Hermitian Hamiltonian approach with a Bragg-edge ansatz to unify boundary interference, finite-size effects, and dipole interactions in subradiance.

Findings

Subradiant linewidths scale as N^{-3} universally.

Deep-subwavelength regimes show even-odd oscillations in decay rates.

The energy shift approaches a boundary-dependent constant with N^{-2} corrections.

Abstract

We present an analytical theory for the most subradiant modes in a finite one-dimensional emitter array coupled to either an ideal or a nonideal waveguide. Using an effective non-Hermitian Hamiltonian together with a Bragg-edge open-boundary ansatz, we derive compact eigenvalue expressions showing that the linewidths of the most subradiant states exhibit a universal N^{-3} scaling in both cases. However, in the deep-subwavelength regime, the decay rates display even-odd oscillations due to boundary interference. Furthermore, we demonstrate that the collective energy shift of the most subradiant state approaches a constant value that depends on the atomic separation, with the leading finite-size correction scaling as N^{-2}. These results unify the roles of Bragg-edge interference, finite-size effects, and near-field dipole-dipole interactions in shaping ultranarrow, strongly shifted subradiant resonances, providing a transparent framework beyond the ideal-waveguide limit and opening potential applications in subradiant spectroscopy and waveguide-QED-based sensing.