Extended Data Fig. 1: Single-mode polariton spectrum.

a, Photons at the waist of our twisted optical cavity (red) couple with strength g to the 5S1/2 → 5P3/2 transition of a gas of cold 87Rb atoms, which is subsequently coupled with strength Ω to the highly excited 111D5/2 Rydberg state using an additional laser (blue). b, These couplings cause excitations of the atom-cavity system to propagate as polaritons—quasiparticles combining photons with collective atomic excitations. c, The transmission spectrum of the cavity with atoms present directly reveals the narrow dark polariton flanked by two broad bright polariton peaks. The solid curve shows a fit of the cavity electromagnetically induced transparency spectrum to the measured transmission (see ref. 32, Supplementary equation (7)).