Enhanced sensitivity in electromagnetically induced transparency (EIT) can be obtained by the use of noise correlation spectroscopy between the fields involved in the process. Here, we investigate EIT in a cold ($< 1$ mK) rubidium vapor and demonstrate sensitivity to detect weak light-induced forces on the atoms. A theoretical model is developed and shows good agreement with our measurements, enabling the attribution of the observed effects to the coupling of the atomic states to their motion. The effects remain unnoticed on the measurement of the mean fields but are clearly manifest in their correlations.
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