The study investigates the nonlinear optical properties of Rydberg exciton-polaritons in Cu₂O microcavities. Rydberg excitons, highly excited bound electron-hole states with large Bohr radii, exhibit strong optical nonlinearity due to their interaction and coupling to light. The researchers achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) through the Rydberg blockade phenomenon and the hybridization of excitons and photons forming polaritons in Cu₂O-filled microresonators. Under pulsed resonant excitation, the polariton resonance frequencies are renormalized due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the observed scaling of the polariton nonlinearity coefficient as ∝ n⁴.⁴±1.⁸ for principal quantum numbers up to n = 7. This high principal quantum number is essential for realizing high Rydberg optical nonlinearities, paving the way for quantum optical applications and fundamental studies of strongly-correlated photonic (polaritonic) states in a solid-state system. The study also reports strong and ultra-fast nonlinear optical responses, with the nonlinearity scaling highly superlinearly with the principal quantum number. The nonlinear indices n₂ are found to be in the range from 10⁻¹⁷ m²/W to 4 × 10⁻¹⁵ m²/W for n = 3 to n = 7. Single-pulse experiments reveal picosecond rise and fall times for the nonlinearity, followed by additional dynamics on density-dependent timescales of order 100 ps to 2 ns. Theoretical models are developed to explain the observed experimental behavior, considering contributions from Rydberg and Pauli blockade. The study concludes that Rydberg polaritons in Cu₂O are a suitable platform for quantum polaritonics with nonlinearities scaling strongly with Rydberg exciton quantum numbers, reaching single-polariton nonlinearity.The study investigates the nonlinear optical properties of Rydberg exciton-polaritons in Cu₂O microcavities. Rydberg excitons, highly excited bound electron-hole states with large Bohr radii, exhibit strong optical nonlinearity due to their interaction and coupling to light. The researchers achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) through the Rydberg blockade phenomenon and the hybridization of excitons and photons forming polaritons in Cu₂O-filled microresonators. Under pulsed resonant excitation, the polariton resonance frequencies are renormalized due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the observed scaling of the polariton nonlinearity coefficient as ∝ n⁴.⁴±1.⁸ for principal quantum numbers up to n = 7. This high principal quantum number is essential for realizing high Rydberg optical nonlinearities, paving the way for quantum optical applications and fundamental studies of strongly-correlated photonic (polaritonic) states in a solid-state system. The study also reports strong and ultra-fast nonlinear optical responses, with the nonlinearity scaling highly superlinearly with the principal quantum number. The nonlinear indices n₂ are found to be in the range from 10⁻¹⁷ m²/W to 4 × 10⁻¹⁵ m²/W for n = 3 to n = 7. Single-pulse experiments reveal picosecond rise and fall times for the nonlinearity, followed by additional dynamics on density-dependent timescales of order 100 ps to 2 ns. Theoretical models are developed to explain the observed experimental behavior, considering contributions from Rydberg and Pauli blockade. The study concludes that Rydberg polaritons in Cu₂O are a suitable platform for quantum polaritonics with nonlinearities scaling strongly with Rydberg exciton quantum numbers, reaching single-polariton nonlinearity.