The electro-optic effect, where the refractive index of a medium is modified by an electric field, is of central importance in non-linear optics, laser technology, quantum optics and optical communications. In general, electro-optic coefficients are very weak and a medium with a giant electro-optic coefficient would have profound implications for non-linear optics, especially at the single photon level, enabling single photon entanglement and switching. Here we propose and demonstrate a giant electro-optic effect based on polarizable dark states. We demonstrate phase modulation of the light field in the dark state medium and measure an electro-optic coefficient that is more than 12 orders of magnitude larger than in other gases. This enormous Kerr non-linearity also creates the potential for precision electrometry and photon entanglement.
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