Opportunities and Challenges of Solid-State Quantum Nonlinear Optics

Nonlinear interactions between single quantum particles are at the heart of any quantum information system, including analog quantum simulation and fault-tolerant quantum computing. This remains a particularly difficult problem for photonic qubits, as photons do not interact with each other. While engineering light-matter interaction can effectively create photon-photon interaction, the required photon number to observe any nonlinearity is very high, where any quantum mechanical signature disappears. However, with emerging low-dimensional materials, and engineered photonic resonators, the photon number can be potentially reduced to reach the quantum nonlinear optical regime. In this review paper, we discuss different mechanisms exploited in solid-state platforms to attain quantum nonlinear optics. We review emerging materials and optical resonator architecture with different dimensionalities. We also present new research directions and open problems in this field.