Spectral engineering of cavity-protected polaritons in an atomic ensemble

Multiple quantum emitters coupled to a single cavity mode appear in many situations, including quantum technologies and polaritonic chemistry. The ideal case of identical emitters is modelled in terms of symmetric states, and understood in terms of polaritons. In the practically relevant case of an inhomogeneous frequency distribution, this simple picture breaks down and new features emerge. Here we observe the transition from a disordered regime to a polaritonic one with only two resonances, using the high degree of control in a strongly coupled cold-atom system where the ratio between coupling strength and frequency inhomogeneities can be tuned. The polaritons are much narrower than the frequency distribution, as predicted in the context of cavity protection. We find that the concentration of photonic weight of the coupled light–matter states is a key parameter for this transition and demonstrate that a simple parameter based on the statistics of transmission count spectra provides an experimental proxy for this theoretical quantity. Moreover, we realize a dynamically modulated Tavis–Cummings model to produce a comb of narrow polariton resonances protected from disorder, with potential applications to quantum networks.