Coherence and Quantum Entanglement

By Prof. Anand Kumar Jha | IIT Kanpur

Learners enrolled: 637 | Exam registration: 44

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.

Summary

Course Status :	Completed
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Physics
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	22 Jan 2024
End Date :	12 Apr 2024
Enrollment Ends :	05 Feb 2024
Exam Registration Ends :	16 Feb 2024
Exam Date :	28 Apr 2024 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

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

Books and references

1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge university press, New York, 1995).
2. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, New York, 2008).
3. J. W. Goodman, Statistical Optics, (John Wiley and Sons, 2000)
4. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press, New York, USA, 2000).
5. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University Press, Cambridge, 1999).

Instructor bio

Prof. Anand Kumar Jha

IIT Kanpur

Prof. Anand Kumar Jha obtained his 5 years’ integrated MSc in Physics from IIT Kharagpur in 2002 and his PhD from the University of Rochester in 2009. After doing a postdoc for about a year at the University of Rochester, Prof. Jha worked with Intel corporation for about two years and then joined IIT Kanpur as an assistant professor of Physics in 2013. Since 2022, he has been a professor of Physics at IIT Kanpur. Prof. Jha has setup a “quantum optics and entanglement” laboratory at IIT Kanpur and carries out research in the broad areas of classical & quantum coherence, quantum entanglement, and quantum metrology.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: 28 April 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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