Fig. 5: Cavity mode occupation of the coupled spin-photon system.

Occupation number distribution P(n_ph) of the cavity photon at different values of the interlayer exchange coupling J_D at fixed light-matter coupling λ including the observable correction arising from the downfolding derived in Supplementary Note 2. The results for L = 32 shown here are converged to the thermodynamic limit as is visible in the inset, showing the average occupation 〈n_ph〉 as a function of the exchange coupling ratio J_D/J around the critical point \({J}_{D}^{c}\) (vertical line). J is the intralayer exchange coupling. P(5) and P(7) are finite but vanishingly small so that they do not show on the logarithmic axis. The error bars represent the standard deviation of the data.