Controlling the group velocity of light is a valuable resource for quantum and classical optical processing and high performance sensor technologies. In this context, slow-light (SL) and the associated steep dispersion have been proposed to increase the sensitivity of certain types of interferometers. Here, we show that the interaction of two intensity-balanced light beams in a SL medium can be used to detect Doppler shifts with extremely high sensitivity. By using this effect in a liquid crystal light-valve, we have been able to measure Doppler shifts as low as 1 μHz with an integration time of only 1 s. The shot noise limited sensitivity inversely depends on the steepness of the beam-coupling dispersive response. This method allows for remote sensing of very slowly moving objects with a linear response over 5 orders of magnitude.
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