Bound state of distant photons in waveguide quantum electrodynamics

Quantum correlations between distant particles remain enigmatic since the birth of quantum mechanics. Here we predict a novel kind of bound quantum state in the simplest one-dimensional setup of two interacting particles in a box. Paradoxically, two entangled particles become localized at the opposite edges of the box even though their interactions at large distance should seemingly play no role. Such states could be realized in the waveguide quantum electrodynamics platform, where an array of superconducting qubits or cold atoms is coupled to a waveguide. We demonstrate how long-range waveguide-mediated couplings enable interaction-induced quantum states separated by large distances. Similarly to Majorana fermions in the Kitaev model, such bound state of distant photons is immune to short-range interactions and could find applications in robust quantum information processing.