My talk will cover the use of nonlinearity in quantum optics to design quantum-limited amplifiers or generate entanglement. In the first part, I will discuss a new design for microwave degenerate parametric amplifiers (DPAs) that uses kinetic inductance to overcome limitations caused by high-order nonlinearities from Josephson junctions. The resulting DPA exhibits phase-sensitive gains of up to 40 dB, operating close to the quantum noise limit, and provides new opportunities for sensitive microwave measurements. In the second part of my talk, I will discuss entanglement generation in silicon-based Topologically insulate Floquet defect mode resonance (FDMR) systems. Our study leverages a resonance effect in the bulk of an FDMR to demonstrate enhanced entangled photon pair generation. We achieve second-order cross correlation of photon pairs 300 times higher than without resonance, thanks to a wavelength-tunable FDMR with Q-factors up to 10^5 and FSR ~5 nm. Our results provide new insights into generating and manipulating entanglement in quantum systems, which has important implications for quantum communication and computation.