  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.
