Estimation of temporal separation of slow light pulses in atomic vapors by weak measurement

We show how two circular polarization components of a linearly polarized pulse, propagating through a coherently driven dilute atomic vapor, can be well resolved in time domain by weak measurement. Slower group velocity of one of the components due to electromagnetically induced transparency leads to a differential group delay between the two components. For low number density, this delay may not be large enough to temporally resolve the two components. We show how this can be enhanced in terms of mean time of arrival of the output pulse through a post-selected polarizer. We demonstrate the idea with all the analytical and numerical results, with a specific example of alkali atoms.