The ability to feed energy into a system, or - equivalently - to drive that system with an external input is a fundamental aspect of light-matter interaction. The key concept in many photonic applications is the critical coupling condition: at criticality, all the energy fed to the system via an input channel is dissipated within the system itself. Although this idea was crucial to enhance the efficiency of many devices, it was never considered in the context of systems operating in a non-perturbative regime. In this so-called strong coupling regime, the matter and light degrees of freedom are in fact mixed into dressed states, leading to new eigenstates called polaritons. Here we demonstrate that the strong coupling regime and the critical coupling condition can indeed coexist; in this situation, which we term strong critical coupling, all the incoming energy is converted into polaritons. A semiclassical theory - equivalently applicable to acoustics or mechanics - reveals that the strong critical coupling corresponds to a special curve in the phase diagram of the coupled light-matter oscillators. In the more general case of a system radiating via two scattering ports, the phenomenology displayed is that of coherent perfect absorption (CPA), which is then naturally understood and described in the framework of critical coupling. Most importantly, we experimentally verify polaritonic CPA in a semiconductor-based intersubband-polariton photonic-crystal membrane resonator. This result opens new avenues in the exploration of polariton physics, making it possible to control the pumping efficiency of a system almost independently of its Rabi energy, i.e., of the energy exchange rate between the electromagnetic field and the material transition.
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