above a critical number of atoms ($N_c \sim 20 \times 10^3$) as seen Fig. \[atnogrid\](a) and grows rapidly to dominate the blue detuned peak for atom number $N_c \sim 33\times 10^3$. In addition, from Fig. \[atnogrid\](a) the peaks are seen to broaden as $N_c$ increases.

Fig. \[atnogrid\](b) shows change in peak separation when $N_c$ is changed, as the cavity length is changed to scan across the atomic resonance frequency. Blue dots in Fig. \[atnogrid\](b) show corresponding vacuum Rabi splitting (VRS) calculated for the same number of atoms and cavity parameters, when the cavity is on atomic resonance, and external weak probe light scans the atom-cavity system. From this close agreement between the measured frequency split and the VRS calculation we can see that the observed split depends on $g_0\sqrt{N_c}$, similar to VRS and hence we conclude that the observed splitting and the atom-cavity collective strong coupling are very closely related. However, this is the case only beyond a certain atom number in the cavity mode. Below a critical value of $N_c$, the red-detuned peak disappears while the blue detuned peak persists, as seen in Fig. \[atnogrid\](c). Here a clear threshold is seen in the measured heights of the red detuned 