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The paradigm of $N$ quantum emitters coupled to a single cavity mode appearsin many situations ranging from quantum technologies to polaritonic chemistry.The ideal case of identical emitters is elegantly modeled in terms of symmetricstates, and understood in terms of polaritons. In the practically relevant caseof an inhomogeneous frequency distribution, this simple picture breaks down andnew and surprising features appear. Here we leverage the high degree of controlin a strongly coupled cold atom system, where for the first time the ratiobetween coupling strength and frequency inhomogeneities can be tuned. Wedirectly observe the transition from a disordered regime to a polaritonic onewith only two resonances. The latter are much narrower than the frequencydistribution, as predicted in the context of ''cavity protection''. We findthat the concentration of the photonic weight of the coupled light-matterstates is a key parameter for this transition, and demonstrate that a simpleparameter based on statistics of transmission count spectra provides a robustexperimental proxy for this theoretical quantity. Moreover, we realize adynamically modulated Tavis-Cumming model to produce a comb of narrow polaritonresonances protected from the disorder, with potential applications to quantumnetworks.

Spectral Engineering of Cavity-Protected Polaritons in an Atomic Ensemble with Controlled Disorder