  Previously, we had proposed an optically-pumped five-level Gain EIT (GEIT)
system, which has a transparency dip superimposed on a gain profile and
exhibits a negative dispersion suitable for the white-light-cavity
signal-recycling (WLC-SR) scheme of the interferometeric gravitational wave
detector [Phys. Rev. D. 92, 082002 (2015)]. Using this system as the negative
dispersion medium (NDM) in the WLC-SR, we get an enhancement in the quantum
noise (QN) limited sensitivity-bandwidth product by a factor of ~18. Here, we
show how to realize this GEIT system in a realistic platform, using
non-degenerate Zeeman sublevels in alkali atoms. Specifically we choose
$^{87}$Rb atoms, which produce the negative dispersion around 795nm. The
current LIGO operates at 1064nm but future LIGO may operate at a wavelength
that is consistent with this atomic system. We present a theoretical analysis
for the susceptibilities of the system. To account for the QN from the GEIT
system, it is necessary to use the master equation (ME) approach. However, due
to the number of energy levels involved, applying the full ME approach to this
system is very complex. We have also shown earlier, in the reference cited
above, that under GEIT condition, the net enhancement in the
sensitivity-bandwidth product, as predicted by the ME, is close to that
predicted by applying the Caves model for a phase-insensitive linear amplifier.
Therefore we here use the Caves model for the QN from the NDM and this
simplified numerical model shows that the enhancement of the
sensitivity-bandwidth product as high as 17 is possible.
