ABOUT THE COURSE :This course is for PhD and advanced undergraduate students as well for researchers who want to gain a solid understanding of the concept of coherence as well as its applications in modern quantum optics and quantum information technologies. The course will have two main parts. The first part will discuss the concept of coherence associated with waves and one-particle systems. In the second part, we will transition into quantum entanglement by building the idea of a two-photon system and the associated concept of two-particle coherence. Course content: 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. Quantum Entanglement: Basics of nonlinear optics, Two-photon ?eld 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, applications of quantum entanglement: Quantum Cryptography, Quantum Teleportation, Quantum Imaging.INTENDED AUDIENCE : Senior-UG/PG/PhD students and researchers in Physics, Optics, Electrical Engineering and Computer Science. PREREQUISITES : At least an undergraduate level quantum physics course and some background in Optics.INDUSTRY SUPPORT : Could be relevant for Optics industry. Also, this could be potentially highly relevant for industries based on quantum technologies involving photonics. As part of the upcoming national quantum mission, such companies will see a big boost.
Coherence and Quantum Entanglement
Indian Institute of Technology Kanpur and NPTEL via Swayam
This course may be unavailable.
Overview
Syllabus
Week 1 :Main differences between classical and quantum mechanics; Intro to coherence; Stochastic Processes: some essential concepts
Week 2 :The Joint probability function used in classical optics; Second-order coherence theory (Temporal) ; Temporal correlations: some essential mathematical concepts
Week 3 :Quantifying the temporal correlations; Second-order coherence theory (Spatial); Spatial correlations: some essential mathematical concepts ; Angular correlation function
Week 4 :Quantifying the spatial correlations; Propagation of Correlation;; Second order coherence theory (Angular); Angular correlations: some essential mathematical concepts; Quantifying the angular correlations. Second-order coherence theory (polarization);
Week 5 :Quantifying the polarization correlation; Visibility of Polarization Interference; Degree of Polarization Coherent Mode Representation of Optical Fields
Week 6 :Review of Quantum Mechanics; quantum Mechanical Correlation Functions; An example: one-photon interference in Michelson interferometer
Week 7 :Intro to quantum entanglement; Basics of Nonlinear Optics; Second-Order Nonlinear Optical Effects; Parametric down-conversion; Temporal two-Photon State Produced by Parametric Down-Conversion
Week 8 :Phase-matching in Parametric Down-Conversion; Temporal two-photon interference; Deriving the two-photon interference law; One Photon Interference Effects with Entangled photons; Some example of two-photon interference effects
Week 9 :Two-Photon State Produced by Parametric Down-Conversion: Spatial; Two-Photon Interference: Spatial; Quantum Measurements
Week 10 :Can the quantum mechanical description of physical reality be considered complete? Hidden Variable Interpretation of Quantum Mechanics.
Week 11 :Bell Inequalities; Entanglement Verification
Week 12 :Entanglement Quantification and connection between coherence and entanglement; Quantum Cryptography; Quantum Teleportation
Week 2 :The Joint probability function used in classical optics; Second-order coherence theory (Temporal) ; Temporal correlations: some essential mathematical concepts
Week 3 :Quantifying the temporal correlations; Second-order coherence theory (Spatial); Spatial correlations: some essential mathematical concepts ; Angular correlation function
Week 4 :Quantifying the spatial correlations; Propagation of Correlation;; Second order coherence theory (Angular); Angular correlations: some essential mathematical concepts; Quantifying the angular correlations. Second-order coherence theory (polarization);
Week 5 :Quantifying the polarization correlation; Visibility of Polarization Interference; Degree of Polarization Coherent Mode Representation of Optical Fields
Week 6 :Review of Quantum Mechanics; quantum Mechanical Correlation Functions; An example: one-photon interference in Michelson interferometer
Week 7 :Intro to quantum entanglement; Basics of Nonlinear Optics; Second-Order Nonlinear Optical Effects; Parametric down-conversion; Temporal two-Photon State Produced by Parametric Down-Conversion
Week 8 :Phase-matching in Parametric Down-Conversion; Temporal two-photon interference; Deriving the two-photon interference law; One Photon Interference Effects with Entangled photons; Some example of two-photon interference effects
Week 9 :Two-Photon State Produced by Parametric Down-Conversion: Spatial; Two-Photon Interference: Spatial; Quantum Measurements
Week 10 :Can the quantum mechanical description of physical reality be considered complete? Hidden Variable Interpretation of Quantum Mechanics.
Week 11 :Bell Inequalities; Entanglement Verification
Week 12 :Entanglement Quantification and connection between coherence and entanglement; Quantum Cryptography; Quantum Teleportation
Taught by
Prof. Anand Kumar Jha
