A nonlinear process occurs inside nonlinear optical crystals where one photon with higher energy ω_p and wavevector k_p is spontaneously down-converted into two photons with lower energy ω_s,ω_i and wavevectors k_s k_i. In this process both energy and momentum are conserved, i.e., ω_p=ω_s+ω_i k_p=k_i+k_s. In periodically (and a-periodically) poled nonlinear crystals PPKTP, APPKTP the lack of momentum and other photon properties can be controlled by engineering the poling periods of the nonlinear crystals k_p=k_i+k_s+k_G. The mismatch of the income and outcome photon’s momentum is compensated by a reciprocal lattice vector of the crystal. This nonlinear SPDC process allows the generation of high efficient single photons, correlated photons and entangled photons. These photons are important for several applications such as quantum key distribution, squeezed light, quantum computing, quantum super-resolution detection and imaging etc.
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