Generation of Many-body Entangled Atomic States in Waveguide-Coupled Atomic Arrays

Entangled many-body atomic states have promising potential for applications in quantum information and quantum devices. In this work, we propose a probabilistic protocol to generate many-body entangled states, such as Greenberger–Horne–Zeilinger (GHZ) states, in atoms coupled to waveguides. To this aim, we consider an initially uncorrelated ordered array of four-level atoms with a Π-type level structure coupled to a waveguide, with one of the atoms being initially excited. We analyze the dynamics of the collective atomic states and the emitted field, probabilistically heralding desired atomic states based on the specific photodetection measurements on the field. We demonstrate that once a desired atomic state is post-selected, successive iterations improve the fidelity of the protocol to generate entangled atomic states.