We theoretically predict the interaction between polaritonic excitations arising from the coupling of a cavity photon mode with bound to continuum intersubband transitions in a doped quantum well. The resulting exciton bound by photon exchange, recently demonstrated experimentally, exhibits a binding energy that can be continuously tuned by varying the cavity frequency. We show that polariton-polariton interactions, originating from both Coulomb interactions and Pauli blocking, can be dramatically enhanced by reducing the exciton binding energy, thereby increasing the effective Bohr radius along the growth (vertical) direction. This regime is reminiscent of Rydberg atoms, where weak binding leads to strong quantum interactions. Our predictions indicate that this physics can give rise to giant quantum optical nonlinearities in the mid and far infrared, a spectral region that remains largely unexplored in quantum optics and offers exciting opportunities for both fundamental studies and applications.

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• Polaritons
• Quantum optics
• Doped semiconductors
• Quantum cavities
• Quantum wells
• Cavity resonators