Fig. 3: Scaling of the dressed state frequency with atom number.

Position of the upper dressed state as a function of atom number in each spin state for a spin-balanced gas, with Δ_c > 0 and Δ_a = 0. Orange circles show experimental data and light blue diamonds are obtained from the ab initio theory calculation accounting for all the high-order cavity modes. The lines describe an analytical model with two atomic states and the TEM₀₀ cavity mode only. The dashed lines are fits of both experimental data (orange) and theory calculation (light blue) with g_eff as a free parameter (see text). The purple solid line is the expected scaling for g_eff = g = 2π × 0.339 MHz. Error bars are given by the statistical fluctuations over 10 realizations.