Realization of a gain with electromagnetically induced transparency system using non-degenerate Zeeman sublevels in ⁸⁷Rb

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 interferometric gravitational wave detector (Zhou et al., 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 cold Rb atoms, employing anomalous dispersion at 795 nm. Using the Caves model for a phase insensitive linear amplifier, we show that an enhancement of the sensitivity-bandwidth product by a factor of ∼17 is possible for potentially realizable experimental parameters. While the current LIGO apparatus uses light at 1064 nm, a future embodiment thereof may operate at a wavelength that is consistent with the wavelength considered here.