Extremely large optical Kerr non-linearities (n 2 ) and (n 4 ) were measured in two closed degenerate two-level transitions in the caesium D 2 line when a probe and a coupling laser simultaneously probed and coupled the hyperfine structure in an atomic beam. The magnitude of the measured non-linearities in both transitions were found to be a function of the coupling laser intensity and of the probe detuning from the two-photon resonance. In a figure of merit, the ratio between the non-unitarian part of the refractive index and the absorption coefficient measured in conditions of electromagnetically induced transparency showed a maximum value for a probe detuning of 160 kHz from the two-photon resonance and resulted in being 10 5 times larger than in the absence of the coupling laser field. The Kerr effect is a non-linear effect which couples the changes in the refractive index of a material to the intensity of an applied electric field. Kerr non-linearities correspond to the refractive part of the third order susceptibility in optical media and play a crucial role in non-linear optics for the generation of optical solitons, frequency conversion, polarisation phase gates, quantum logic, ... (see [1] and references therein). In recent years various schemes for generating large Kerr non-linearities were proposed and implemented: optical fibres fabricated with novel glass materials [2], microcavities at room temperature [3], thin films [4], and atomic coherence [5].In this publication, partly stimulated by the current research into gravitational-waves, we want to transfer the information acquired in studying the dispersion of closed two-level systems [6] and the associated giant Kerr effect to concepts which are closer to those used in the development of future gravitational wave detectors. It is expected that the coming generations of earth-based interferometers for the detection of gravitational waves will -at some point -be limited by quantum noise. The insertion of media exhibiting a non-negligible Kerr u Fax: +49 (0)511 762 2784, E-mail: Luca.Spani.Molella@aei.mpg.de effect under the action of the applied electric field in the interferometer cavities is one of the methods suggested to beat the standard quantum limit and thus to improve the performance of future detectors [7]. Furthermore, some of us have experimentally demonstrated that a transparent Kerr medium inside a cavity drastically changes the properties of the cavity [8].It has been demonstrated that in the proximity of a twophoton resonance responsible for electromagnetically induced absorption (EIA [9, 10]) or electromagnetically induced transparency (EIT [11,12]) within the caesium D 2 line, giant Kerr non-linearities can be measured [13]. These results have been obtained in a caesium cell, where the maximum linear absorption did not exceed 60%. However, a characterisation of the Kerr effect and of the corresponding medium absorption is needed to estimate the potential efficiency of such a non-linear medium inside a large interferometer. In...