Quantum Optics Grad Courses at U. of T.

(last updated 6 September 2006 )

Courses form an incomplete and yet an important aspect of your graduate education, and the graduate curriculum at U. of T. evolves continually in order to try to provide you with the best possible background, both in terms of general "cultural" knowledge of physics and optics and in terms of the specific methods and techniques which are likely to be of use in your own research.

You should choose your courses in consultation with your supervisor, and after studying the course descriptions and getting advice from senior graduate students; in general it is wise to sit in on a range of courses for the first week or two before making your final choices.

On this page, we provide an approximate idea of the sort of programme of study which we believe makes sense for the typical graduate student in quantum optics. This is intended as a guide to help you through the sometimes strange course nomenclature and number schemes, and not as a list of "requirements." (You should note that the course numbers and the official titles which will appear on your transcript occasionally reflect less the present content of the courses than the delays involved in propagating changes through university bureaucracy; when in doubt, speak to the professor teaching the course in question!) After a brief description of the various courses which form a part of the quantum optics programme, we present some ideas of typical schedules.

Please note: This page is not intended to give a complete overview of the many interesting and relevant courses offered by other groups in the department. All quantum optics students take courses from beyond their specialty, both for their own education and interest and also sometimes for use in their own research. For instance, most quantum optics students will take PHY 1850F (Condensed Matter Physics); many take PHY 1500 (Stat Mech), PHY 2301 (Order Parameters), 1810 (Particle Physics), 2403 (Quantum Field Theory), and/or special topics courses offered periodically. In addition, many optics students take courses in ECE, Chemistry, Math, or Computer Science. You should discuss these other course offerings with other students and with your supervisor.

Finally, it is worth pointing out that many students find it profitable to "sit in" on courses even after completing their course requirements for the degree. In particular, this affords an opportunity to be exposed to some "special topics" courses which may not be offered during your first few terms as a graduate student.

Core courses | Preparatory course | QO main sequence | Advanced AMO | Special Topics | Sample Schedule

List of some relevant courses

"Core" courses:

The following Fall-term courses are intended as core preparation for graduate students in all disciplines. While they are not required, most Quantum Optics students should take at least Quantum Mechanics and Electromagnetism, unless they have already had courses at the appropriate level in these disciplines. Many students will find Mathematical Methods to be important preparation, and may also be interested in deepening their knowledge of Statistical Mechanics and Fluid Mechanics.

• PHY 1520F     Quantum Mechanics
• PHY 1510F     Electromagnetism
• PHY 1500F     Statistical Mechanics
• PHY 1530F     Fluid Mechanics  
• PHY 1540F     Mathematical Methods in Physics  

Preparatory course:

Since many undergraduate programmes do not include an advanced optics course, we offer the following cross-listed course:

• PHY 1485F    Modern Optics

One cannot become an expert in quantum optics without a solid grounding in advanced classical optics. This course includes topics such as diffraction theory, the Lorentz model and dispersion relations, gaussian-beam optics, and laser theory (including cavity design, pulsed lasers, et cetera), through to introductory material in semiclassical optics. Students with advanced undergraduate optics backgrounds may be able to skip this course, but should not do so lightly, and certainly not without consulting with their supervisors.

Central QO sequence:

We have a 2-term sequence of quantum-optics-specific courses, both of which are considered core knowledge for our graduate students.

• PHY 2203S    Quantum Optics I
  This Spring-term course will delve into the interaction of light with quantum systems, and introduce some basic ideas about the quantum nature of light itself. It is taught from a largely "experimental" perspective, and is meant to provide an overview of phenomena which are widespread in studies of light-matter interactions (Rabi flopping, nonlinear optics and spectroscopy, quantum interference...), and cover a range of current research topics, ranging from electromagnetically-induced transparency and coherent control to laser cooling and quantum information.
  
• PHY 2204F    Quantum Optics II
  This course deals with the fully quantum-mechanical description of light and matter. Taking a rigorous theoretical approach, it introduces quantization of the electromagnetic field and the fundamentals of quantum electrodynamics. This theory is then applied to the study of resonant fluorescence, photon statistics and the noise properties of light, the Lamb shift, the quantum theory of the laser, et cetera. For advanced students, this course may be taken before PHY2203S, but for most students it will make more sense to take it second.

Advanced AMO courses:

Quantum optics is a part of the broader area of Atomic, Molecular, and Optical (AMO) Physics, and one cannot be an educated quantum optician without a good knowledge of the basics of AMO in general. We offer two courses, in alternate years, to cover two of the topics we believe are most essential for your education as optical physicists:

• PHY 2202S    Atomic and Molecular Physics  (was offered in Spring 2006, as PHY2206, and will be in subsequent even-numbered years) 
  Atomic physics is not only an important discipline in its own right, but is also essential background for a variety of other areas of physics, ranging from laser physics to condensed matter and plasma physics to molecular spectroscopy and atmospheric physics. Furthermore, the concepts and techniques involved in the application of quantum mechanics to atoms and molecules have broad applicability to the description of other quantum systems and their interactions with the electromagnetic field. It is in this spirit that we will attempt to discuss the fundamentals of a variety of issues in atomic, molecular, and optical physics.
• PHY 2208S    Nonlinear Optics  (to be offered in Spring 2007 and subsequent odd-numbered years)  Nonlinear optics is the discipline in physics in which the electric polarization density of the medium is studied as a nonlinear function of the electromagnetic field of the light. Being a wide field of research in electromagnetic wave propagation, nonlinear interaction between light and matter leads to a wide spectrum of phenomena, such as optical frequency conversion, optical solitons, phase conjugation, and Raman scattering. In addition, many of the analytical tools applied in nonlinear optics are of general character, such as the perturbative techniques and symmetry considerations, and can equally well be applied in other disciplines in nonlinear dynamics. The concepts of nonlinear optics are central to most modern research in quantum optics; in particular, there is no experimentally observable consequence of the difference between the classical and quantum theories of light until nonlinearities of some sort are taken into account!

Special-topics courses:

In order to provide a deeper exposure to how research progresses in reality, and to the latest topics in quantum optics, we will offer one or two "special topics" most years. The subjects will typically draw on the research expertise of our own or visiting faculty members, and be accessible to all quantum optics students. In 2006-2007, we have one:

• PHY 2205S    Special Topics in Quantum Optics I : Bose-Einstein Condensation and Ultra-Cold Quantum Gases (course number still subject to change)
  This course will cover the basic concepts important to the creation and study of cold quantum gases. Not just for the specialist, this background material is (in my opinion) a "best of" list of topics from statistical mechanics, atomic physics, hydrodynamics, quantum optics, nonlinear optics, and solid state physics. Students will be expected to write a report on a current topic of study in the field, and the goal of the lectures will be to provide background necessary to understand the current literature.
• Click here for some previously offered special-topics courses

Sample course schedules

A typical entering student should expect to take 3 or 4 semesters to complete his or her coursework at U of T, depending both on level of preparation and on the choice of M.Sc. option. Students with a strong previous background in quantum optics may be able to complete all of their coursework in 2 semesters. Below we give hypothetical schedules for students planning to complete the programme in 4,3, or 2 semesters. In all cases, it is expected that students will take some courses from outside of quantum optics, and these should be chosen based on interest and on consultation with your research supervisor; we do not specify them here.

	4-semester plan	3-semester plan	2-semester plan
Fall 1	1520 QM	1520 QM	2204 QO-II
	1510 EM and/or 1540 MM	1485 MO	1485 MO
	1485 MO	[poss. 1510 EM / 1540 MM]	[poss. 1510 EM / 1540 MM]
	[poss. others (e.g. 1850,1500)]	others (e.g., 1850,1500)	others (e.g., 1850,1500,2403)
Spring 1	2203 QO-I	2203 QO-I	2203 QO-I
	2206/2208 AMP/NLO	2206/2208 AMP/NLO	2206/2208 AMP/NLO
		2205/2208 Special Topic	2205/2208 Special Topic
			other (e.g. 2301)
Fall 2	2204 QO-II	2204 QO-II
		poss. others (e.g., 1850,1500,2403)
Spring 2	2208/2206 NLO/AMP	(sit in on NLO/AMP and/or Spec.Top's)	(sit in on NLO/AMP and/or Spec.Top's)
	2205/2208 Special Topic

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