Quantum Theory of Light





Quantum Mechanics







James Clerk Maxwell ingeniously showed that electric and magnetic fields are both generated and altered by each other. This revolutionary discovery led to a novel and unique branch of physics, named electrodynamics. Electrodynamics successfully explains numerous physical phenomena, but ​is incapable of describing several empirical effects, such as the photo-electric and Compton effects, and also resulted in theultraviolet catastrophe. Max Planck, in an attempt to describe blackbody radiation, considered a discrete spectrum, i.e. an energy wavepacket, instead of a continuous spectrum for electromagnetic radiation. His theory, i.e. quantisation of energy, successfully described the radiation from a blackbody, and later on, was used by Albert Einstein to describe the photoelectric effect. This was a starting point for the development of one mankind’s best theories: Quantum Mechanics. Numerous ingenious scientists helped and contributed to both quantum formalism and quantum foundations since its inception. Here, in this course, we will focus on the quanta of light, i.e. photons, and its features, the way that they are generated, manipulated and detected. During the course, we will learn how the field quantisation leads to understanding unique effects such as Lamb shift, spontaneous emission, and spontaneous parametric down-conversion. Classical and non-classical light (Coherent, Thermal, Fock, and Squeezed) sources and their photon statistics will be discussed in detail. The action of different optical elements in the quantum regime, and seminal quantum optics experiments (e.g., Hanbury-Brown Twiss, EPR, Bell’s inequality, Hong-Ou-Mandel, induced coherence) will be reviewed during the course.

Completing this course will help you:

Who is the course for?

This course is suitable for graduate students in physics (optics) who are familiar with advanced quantum mechanics, electrodynamics, and nonlinear optics. Quantum optics, in the current form, has been developed over the last 100 years, and thus, it is impossible to learn all these developments historically. Thus, the contents are chosen selectively for the graduate programme by the faculty of science. Note that light-matter interaction will not cover during this course.

Main Textbooks

The course will be based on two books; (1) The Quantum Theory of Light by Rodney Loudon, and (2) Quantum Optics by Marlan O. Scully (Texas A & M University) and M. Suhail Zubairy (Quaid-i-Azam University). Chapters 1, 3, 4, 5, 6, and 9 of The Quantum Theory of Light and Chapters 1, 2, 3, 4, 18, 20, and 21 of Quantum Optics will be covered during this course. In addition, whenever is needed proper research articles will be discussed for the course. 

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Learning Path

Electromagnetic fields, Maxwell’s equations as well as the link to Riemann-Silberstein vector will be explored and discussed. Field quantisation will be introduced, and corresponding Hamiltonian, mode annihilation and creation operators for EM field will be derived.

Video #1: 2 Hours and 31 Minutes

Paraxial wave equation and the field propagation (time-evolution of the field) in a dispersive medium will be studied. Transverse quantisation, associated modes in different coordinates as well as X-pulses will be introduced.

Fock states, quantum beats, Lamb shift and Planck distribution will be discussed.  

Video #2: 2 Hours and 30 Minutes

Harmonic oscillator and phase space will be introduced. We will briefly discuss the radiation from a classical current and introduce coherent and squeezed states. Uncertainty relations for both states will be derived and their statistics will be shown. Finally, mathematical tools to perform photon statistic will be introduced. 

Video 2 Hours and 50 Minutes 

The action of optical elements, such as mirror, beam-splitter, wave-plates, lenses, etc at the quantum regime will be reviewed. After this, we review their action on the classical and non-classical lights.

Video 2 Hours and 50 Minutes 

Different quasiprobability distributions, such as Glauber–Sudarshan P, Husimi Q and Wigner W representations will be discussed for several cases.

Video 2 Hours and 50 Minutes 


Midterm and Final Exams

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Missed Midterm

The only valid reasons for missing the midterms are:

(1) Sickness confirmed by the note from a physician(s). The note has to be dated on the date of the test or before it, and has to clearly indicate that student was sick on the date of the test; (2) Serious injury and/or hospitalization – the note from the hospital will be needed; (3) Representing university as an athlete, scholar or researcher.

Contact me ASAP

I will need to have Xerox-copy of the doctor’s note, stapled to the brief letter explaining your situation. Your name, student number, date of the test etc. should be stated clearly in your letter. I will decide on the form of the supplementary evaluation after all of the students who missed the test have contacted me.