30/44 From the energy of NL interactions to hamiltonians, photon correlations obtained from NLO effe

My 2 lectures give an overview of quantum effects (different types of entanglement and squeezing) originating from nonlinear-optical phenomena. In this first lecture, the basic pair creation Hamiltonian, which is responsible for all above-mentioned quantum effects, is derived through macroscopic nonlinear-optical approach taking into account quadratic and cubic nonlinearity. In particular, parametric down-conversion and four-wave mixing/modulation instability are described in detail. Also, seeded versions of these effects are considered. Special accent is made on the number of photons per mode as one of the most important parameters in nonlinear and quantum optics. Further, the generation and properties of entangled photon pairs are described, including: - Hanbury Brown and Twiss interferometry; - Glauber’s correlation functions; - two-photon light and the measurement of the two-photon amplitude.

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Hi i have found an error in 18:00 to 19:00 you tell about solving the equations but d(S)/dt is not equal to Gamma S but maybe equals to S^(dagger), can you help me with this?