peak, while the blue detuned peak shows no threshold over the measurement range. It is also evident from Fig. \[atnogrid\](b) and Fig. \[atnogrid\](c) that the agreement with the VRS calculation starts degrading at the larger values of $N_c$, which coincides with the tendency towards saturation of the red detuned peak height.

![Change in emission from the cavity when the atom number coupled to the cavity is varied. (a) These graphs show cavity emission spectrum for different atom numbers. $\Delta_{ca} = \omega_c - \omega_a $ is detuning of empty cavity resonance from atomic transition and V is signal detected on PMT. (b) Red dots with error bars show the change in peak separation of the cavity emission with $N_c$. Blue empty squares are corresponding VRS ($2g_0 \sqrt{N_c}$) values. $\Delta_{BR}$ - The frequency separation between red and blue detuned peaks (c) Variation in the height of red and blue detuned peaks. In the range of measurement, the red peak shows a threshold behaviour with atom number whereas the blue peak does not. $V_{max}$ - Maximum voltage generated by PMT for the red and blue detuned peaks. Total intensity of all cooling laser beams is 36 mW/cm$^2$ for all the measurements.[]{data-label="atnogrid"}](At_no_dependence.pdf){width="15cm"}

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