Phase modulation induced by cooperative effects in electromagnetically induced transparency

We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency setup at high density. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local field induced phase modulation and show that it distinctively differs from the nonlinear self-phase modulation a strong pulse experiences in a Kerr medium.