Nonradiative interaction and entanglement between distant atoms

We show that nonradiative interactions between atomic dipoles placed in a waveguide can give rise to deterministic entanglement at ranges much larger than their resonant wavelength. The range increases as the dipole resonance approaches the waveguide's cutoff frequency, caused by the giant density of photon modes near cutoff, a regime where the standard (perturbative) Markov approximation fails. We provide analytical theories for both the Markovian and non-Markovian regimes, supported by numerical simulations, and discuss possible experimental realizations.