  We have recently proposed [9], the use of fast-light media to obtain
ultrahigh precision rotation sensing capabilities. The scheme relies on
producing a critically anomalous dispersion, in a suitable dispersive medium,
which is introduced in the arms of a Sagnac interferometer. We present here an
experimental investigation of the anomalous dispersion properties of
bi-frequency Raman gain in rubidium vapor, with the goal of using this medium
for producing the critically anomalous dispersion condition. A heterodyne phase
measurement technique is used to measure accurately the index variation
associated with the dispersion. The slope of the negative linear dispersion (or
group index) is experimentally varied by more than two orders of magnitude
while changing the frequency separation between pump fields, responsible for
producing gain. Using this result, we have identified the experimental
parameters for achieving a null value of the group index, corresponding to the
critically anomalous dispersion condition necessary for enhanced rotational
sensitivity.
