Microscopic Maxwell equations

This lecture covers the fundamentals of nonlinear optics and photonics for quantum computing, discussing natural and synthetic qubits, microwave and electron phenomena, trapped ions, neutral atoms, superconducting loops, silicon quantum dots, and topological qubits. It explains the generation of new frequency components in nonlinear media, the importance of phase matching for constructive interference, and the realization of effective photon-photon interactions. The lecture also delves into stimulated vs. spontaneous processes, photon counting detection, coherent states, and vacuum fluctuations. Key elements of linear optics, including microscopic Maxwell's equations, Fourier transform, macroscopic Maxwell's equations in a medium, wave propagation in anisotropic crystals, and the effects of dispersion and diffraction on laser pulses and beams, are discussed in detail.