  It is known that cross-correlation between the random intensity fluctuations
of two lasers forming electromagnetically-induced transparency (EIT) exhibits a
transition from correlation to anticorrelation. We study the linewidth behavior
of this transition and have found the linewidth is below the (effective)
coherence lifetime limit and is only limited by competing noises. We
established a numerical model which reveals the linewidth dependence on laser
linewidth and laser power. Our experiments using lasers with different
linewidth showed results in qualitative agreement with the model. This result
is useful for quantum optics using EIT, and may also have applications in
spectroscopy and precision measurements.
