Cooperative Optical Non-Linearity in a Blockaded Rydberg EnsembleThis thesis describes the first demonstration of a cooperative optical non linearity based on Rydberg excitation. Whereas in conventional non linear optics the non linearity arises directly from the interaction between light and matter, in a cooperative process it is mediated by dipole dipole interactions between light induced excitations. For excitation to high Rydberg states where the electron is only weakly bound, the dipole dipole interactions are