By coupling a probe transition to a Rydberg state using electromagnetically induced transparency (EIT) we map the strong dipole-dipole interactions onto an optical field. We characterize the resulting cooperative optical nonlinearity as a function of probe strength and density. We demonstrate good quantitative agreement between the experiment and an $N$-atom cooperative model for $N=3$ atoms per blockade sphere and the $n=60$ Rydberg state. The measured linewidth of the EIT resonance places an upper limit on the dephasing rate of the blockade spheres of $<110\mathrm{kHz}$.

• Received 21 June 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.193603