Diphotons in a nonlinear Fabry-Pérot resonator: Bound states of interacting photons in an optical ‘‘quantum wire’’

We propose a high-Q Fabry-P\'erot resonator with cylindrical mirrors, operating near fundamental mode and filled with an alkali vapor, as the photonic analog to the electronic quantum wire. The internal photons constitute a 1D Bose gas with pairwise interactions. We solve for the two-photon bound state which determines a resonance for the two-photon transmission function. Emphasis is placed on the experimental feasibility of observing these quasiparticles.