the measurements in this figure is 36 mW/cm$^2$.[]{data-label="fano"}](fano_plus_narrowing_vrs.pdf){width="15cm"}

Gain mechanism
==============

The phenomenon of gain in probe beam when two-level atoms are strongly driven by another drive laser is well known. B. R. Mollow was first to predict such gain mechanism [@mollow_stimulated_1972] using semi-classical arguments and phenomenologically including atomic decay rates. Haroche *et.al* [@haroche_theory_1972] also did similar calculations during the same year. This was later observed in an experiment with sodium beam by Wu *et.al* [@wu_observation_1977]. Grynberg *et.al* [@grynberg_central_1993] later calculated the cross-section for such gain using microscopic perturbation theory. They showed that in the presence of a strong laser the atomic states get dressed, and the gain arises because of multi-photon processes between the dressed states. In the case where the driving laser is red detuned, this type of gain occurs only when the frequency of probe is to the red side of the drive laser frequency. For blue detuned peak such multi-photon processes lead to loss due to absorption. The mechanism for the gain here is similar to the work discussed above, with the additional consideration that the cavity-atom collective strong coupling regime introduces certain differences discussed below.

In the regime defined by collective strong coupling, weak probe 