This study investigates the nonlinear behavior of Rydberg exciton-polaritons in Cu₂O microcavities, revealing strong effective photon-photon interactions (Kerr-like nonlinearity) through the Rydberg blockade and hybridization of excitons and photons. The research demonstrates ultra-fast nonlinear optical responses in Rydberg exciton-polaritons with principal quantum numbers up to n=7, showing a superlinear scaling of the nonlinearity coefficient with n, following a power law of n⁴.⁴±¹.⁸. These results highlight the potential for achieving high Rydberg optical nonlinearities in solid-state systems, paving the way for quantum optical applications and fundamental studies of strongly-correlated photonic states. The study reports a strong and ultra-fast nonlinear optical response for Rydberg exciton-polaritons in a planar Fabry-Perot microcavity with embedded Cu₂O thin crystal. The nonlinear response is found to be comparable or even exceeding the giant optical Kerr-like nonlinearities observed in other polariton platforms, such as GaAs or hybrid perovskites. 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. The ultrafast response is followed by additional nonlinear dynamics on density-dependent timescales of order 100 ps to 2 ns, indicating multiple processes contribute to the nonlinear response. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient. The study also explores the role of Pauli blockade in the nonlinearity, finding that it contributes less significantly compared to the Rydberg-induced blockade. The nonlinear refractive index n₂ is calculated from the Rabi splitting and found to be in the range from 10⁻¹⁷ m²/W to 4×10⁻¹⁵ m²/W for n=3 to n=7. Pump-probe experiments reveal that the Rabi splitting recovers after the pump pulse, indicating the presence of long-lived plasma and excitons. The results show that the nonlinear response is dominated by ultra-fast processes such as Rydberg blockade, while slower processes like Auger recombination can complicate the response. The study also confirms the important role of long-lived 1s states and plasma in the nonlinear response, with the density of these states being significantly higher in continuous wave (CW) excitation than in pulsed excitation. The study concludes that Rydberg polaritons in Cu₂O represent a suitable platform for quantum polaritons with nonlinearities that scale sufficiently strongly with Rydberg exciton quantum number to reach the single polariton nonlinearity. The results demonstrate the potential for achieving higher exciton-polariton nonlinearities through modificationsThis study investigates the nonlinear behavior of Rydberg exciton-polaritons in Cu₂O microcavities, revealing strong effective photon-photon interactions (Kerr-like nonlinearity) through the Rydberg blockade and hybridization of excitons and photons. The research demonstrates ultra-fast nonlinear optical responses in Rydberg exciton-polaritons with principal quantum numbers up to n=7, showing a superlinear scaling of the nonlinearity coefficient with n, following a power law of n⁴.⁴±¹.⁸. These results highlight the potential for achieving high Rydberg optical nonlinearities in solid-state systems, paving the way for quantum optical applications and fundamental studies of strongly-correlated photonic states. The study reports a strong and ultra-fast nonlinear optical response for Rydberg exciton-polaritons in a planar Fabry-Perot microcavity with embedded Cu₂O thin crystal. The nonlinear response is found to be comparable or even exceeding the giant optical Kerr-like nonlinearities observed in other polariton platforms, such as GaAs or hybrid perovskites. 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. The ultrafast response is followed by additional nonlinear dynamics on density-dependent timescales of order 100 ps to 2 ns, indicating multiple processes contribute to the nonlinear response. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient. The study also explores the role of Pauli blockade in the nonlinearity, finding that it contributes less significantly compared to the Rydberg-induced blockade. The nonlinear refractive index n₂ is calculated from the Rabi splitting and found to be in the range from 10⁻¹⁷ m²/W to 4×10⁻¹⁵ m²/W for n=3 to n=7. Pump-probe experiments reveal that the Rabi splitting recovers after the pump pulse, indicating the presence of long-lived plasma and excitons. The results show that the nonlinear response is dominated by ultra-fast processes such as Rydberg blockade, while slower processes like Auger recombination can complicate the response. The study also confirms the important role of long-lived 1s states and plasma in the nonlinear response, with the density of these states being significantly higher in continuous wave (CW) excitation than in pulsed excitation. The study concludes that Rydberg polaritons in Cu₂O represent a suitable platform for quantum polaritons with nonlinearities that scale sufficiently strongly with Rydberg exciton quantum number to reach the single polariton nonlinearity. The results demonstrate the potential for achieving higher exciton-polariton nonlinearities through modifications