Generation of hyperentangled photon pairs in the time and frequency domain on a silicon photonic chip.

Multi-dimensional entangled photon states represent an important resource in quantum communication networks. Specifically, hyperentangled states presenting simultaneous entanglement in several degrees of freedom (DoF) stand out for their noise resilience and information capacity. In this work, we demonstrate the generation of hyperentangled photon pairs in the time and frequency-bin domain by spontaneous four-wave mixing from the coherent driving of two integrated silicon microresonators. We demonstrate entanglement in each DoF by proving the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than 27 standard deviations (STDs) in each reduced space. Genuine hyperentanglement is then assessed from the negativity of a hyperentanglement witness, which is verified by more than 60 STDs. These results mark the first, to the best of our knowledge, demonstration of time-frequency bin hyperentanglement in an integrated silicon photonic device.