Crossover from a delocalized to localized atomic excitation in an atom-waveguide interface

TL;DR

This paper theoretically explores the transition from delocalized to localized atomic excitations in an atom-waveguide system, revealing how disorder influences localization, entanglement, and spectral properties, with implications for photon storage.

Contribution

It introduces a detailed analysis of the localization transition in atom-waveguide interfaces considering long-range interactions and disorder effects, combining multiple spectral and entanglement measures.

Findings

Localization length decreases with disorder

Level statistics shift from repulsion to Poisson distribution

Entanglement entropy exhibits power-law scaling

Abstract

An atom-waveguide system, which presents one of the quantum interfaces that enable strong couplings between light and atoms, can support tightly-confined guided modes of light. In this distinctive quantum interface, we theoretically investigate the crossover from a delocalized to localized atomic excitation under long-range dipole-dipole interactions and lattice disorders. Both localization lengths of the excitation distributions and power-law scalings of dissipative von Neumann entanglement entropy show signatures of this crossover. We further calculate numerically the level statistics of the underlying non-Hermitian Hamiltonian, from which as the disorder strength increases, the gap ratio decreases and the intrasample variance increases before reaching respective saturated values. The mean gap ratio in the deeply localized regime is close to the one from Poisson statistics along with a relatively large intrasample variance, whereas in the nondisordered regime, a significant level repulsion emerges. Our results provide insights to study the non-ergodic phenomenon in an atom-waveguide interface, which can be potentially applied to photon storage in this interface under dissipations.