## Abstract

Photons do not interact with each other directly. Here, we make photons more interesting by generating strong interactions between them. We coherently couple slowly propagating photons to strongly-interacting atomic Rydberg states in a cold, dense atomic gas. In the dissipative regime, one photon scatters the neighboring photons [1]. In the dispersive regime, photons are attracted to form a two-photon bound state [2]. These results open up the possibility for realizing all-optical switching, deterministic photonic quantum logic, and strongly interacting photonic many-body systems. In particular, we are investigating novel quantum states resulting from three or more interacting photons, as well as a single-photon CNOT gate based on flip-flop dipole-dipole interactions.

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