Realization of Gain with Electromagnetically Induced Transparency System with Non-degenerate Zeeman Sublevels in $^{87}$Rb

TL;DR

This paper demonstrates how to realize a gain electromagnetically induced transparency (GEIT) system using non-degenerate Zeeman sublevels in $^{87}$Rb atoms, enabling enhanced quantum noise sensitivity-bandwidth product for future gravitational wave detectors.

Contribution

It proposes a realistic implementation of the GEIT system with $^{87}$Rb atoms and analyzes its potential to significantly improve detector sensitivity.

Findings

Achieves a sensitivity-bandwidth enhancement factor of ~17.

Shows feasibility of using $^{87}$Rb atoms at 795nm for negative dispersion.

Validates the use of the Caves model for quantum noise estimation.

Abstract

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.