Coherence and Quantum Entanglement: Lecture # 16 (Phase matching in parametric down-conversion)

This is the 16th lecture of the course "Coherence and Quantum Entanglement (PHY690G)." In this lecture we study the phase matching in parametric down-conversion.

Course Objectives: This course is for PhD and advanced undergraduate students who wish to have a solid understanding of the concept of coherence and its applications in quantum entanglement. The course has two main parts. The first part, which covers about 1/3rd of the course, discusses the concept of coherence. The other part discusses Quantum Entanglement in detail.

Course content:
(1) Coherence: Spectral properties of stationary random processes, Wiener-Khintchine theorem, Angular spectrum representation of wavefields, Introduction to the second-order coherence theory, Propagation of coherence, The van Cittert-Zernike theorem, Coherent mode representation of sources and fields.

(2) Quantum Entanglement: Basics of nonlinear optics, Two-photon field produced by parametric down-conversion, EPR paradox, Bell inequalities and its experimental violations, Quantum theory of higher-order correlations, Two-photon coherence and two-photon interference effects. Two-photon entanglement in the following variables: time-energy, position-momentum, and angle-orbital angular momentum; Introduction to Quantum Information: Quantum Cryptography, Quantum Dense Coding, Quantum Teleportation, Quantum Imaging.