At Toronto, a unique graduate course combines the strengths of systems found elsewhere in the world. We provide a full series of structured lectures, but we also have the assumption that graduate school is the beginning of your career as a practicing scientist -- experimental-physics students, in particular, are usually soon welcomed into the laboratory and are expected to find a way to contribute to the group, while drawing at the same time on the group's expertise and resources. Theoretical-physics students more typically ground themselves in a year of specialized study in their proposed area of research. To accomodate both, as well as a few instances in which the MSc degree is a professional working degree even absent the PhD, Physics at the University of Toronto has MSc-programme options that balance coursework and independent research, while moving things along with a little scheduled pressure.
Though the MSc degree is an important accomplishment, formal admission to the PhD candidacy depends on a qualifying examination given near the end of the second year of graduate studies. The format of this examination is rather like a PhD Proposal Defense employed by some institutions: before a faculty panel, you will describe the work you intend to do for your PhD, and this committee will judge whether you are sufficiently prepared and intellectually capable. In that sense, you 'qualify' to proceed to your thesis research.
Part of being prepared to do research in an area, of course, is to be able to demonstrate that you have educated yourself well enough in the knowledge of your area of research. Part of that is general literacy in your research area, and part of that is familiarity and understanding of the background research in your discipline, on which your work may be based. Therefore, you can expect your panel will ask you questions to probe what you do, and do not know (or understand) about your discipline. Questions can be quite broad, and quite deep, and almost certainly will continue until the perimeters of your knowledge and understanding have been found; that is, quite normally until you are unable to answer satisfactorily.
Your preparation, as your education, will be your own. Your thesis advisor will likely prove very helpful in identifying the specialized background research particular to your proposed PhD research. The courses you've taken, selected with your advisor's approval, should have been very helpful in preparing your broad knowledge of your discipline. Your independent efforts and study will be very important in identifying and learning material that you'll need to proceed with your PhD research.
Scientific Literacy: You should know...
In each research area the basics of scientific literacy will be different, though a broad background in physics and an analytical approach will be important for all. In Quantum Optics, we feel that you can't consider yourself scientifically literate unless you have the following general background. The list below should help guide you to cover most of what you need for this general literacy; you'll very probably need considerably more depth in the area immediately supporting your proposed PhD research, and your advisor may set additional requirements.
EM waves and optics
- Maxwell's equations, wave equation, Helmholtz equation, electric susceptibility,non-local response in time & frequency, dielectric function, dielectric tensor
- Snell's Law, geometrical optics & aberrations, Fresnel reflection
- polarization, birefringence, manipulation of polarization states
- time & frequency domain pictures; Fourier transforms, power spectrum, autocorrelation
- temporal and spatial coherence , Wiener-Khintchine theorem, van Cittert-Zernicke Theorem
- Fresnel & Fraunhofer diffraction theory, gaussian beam optics, optical resonators, optical fibers
- classical atom-models, basic models of optical dispersion: Lorentz model, Drude model, Kramers-Kronig relation, plasma-wave dispersion, photonic band-gap crystals
Texts: e.g., Modern Optics, Fowles; Jackson; Principles of Optics, Born and Wolf; Fourier Optics, Goodman:
- Einstein A and B coefficients, spontaneous & stimulated emission
- Laser theory: semiclassical, single-mode and multi-mode, spatial modes, principles of pulsed and mode-locked operation, principles of single-line operation, basic laser types
- Two-level atoms: Rabi flopping, Bloch sphere, area theorem, broadening mechanisms, T1 & T2, pulse echoes, slowly varying amplitude approximation, cavity QED
Texts: e.g., Lasers, Siegman; Lasers, Milonni and Eberly; Laser Spectroscopy, Wolfgang Demtröder
Basics of QM for optics
- time-dependent & time-independent perturbation theory, adiabatic rapid passage, Fermi's Golden Rule, scattering theory
- symmetries & conservation laws, Heisenberg equations of motion
- dipole matrix elements, selection rules, density matrix formalism
Texts: e.g., Modern Quantum Mechanics, Sakurai; Quantum Mechanics, C. Cohen-Tannoudji, B. Diu and F. Laloë; Quantum Mechanics, Landau & Lifshitz
Atomic physics and condensed-matter physics
- Multi-level atoms: fine & hyperfine splitting, selection rules, Raman transitions,optical pumping, atoms in static fields
- Basics of band structure: Bloch theorem, phonons & photons & polaritons, direct & indirect bandgaps
- Principles of radiation transport: extinction, scattering, opacity
Texts: e.g., Elementary Atomic Structure by G.K. Woodgate, Atomic Physics by C. J. Foot; Ashcroft & Mermin; Kittel; Theory of Atomic Structure and Spectra, Cowan (advanced)
- Quantisation of electromagnetic field: annihilation & creation operators, spont & stimulated emission & relation to A&B coefficients, Hanbury-Brown-Twiss & photon correlations, squeezed states, coherent states
- Quantum interactions of light and matter: Master Equation, Mollow triplet, Autler-Townes doublet, electromagnetically-induced transparency,...
Texts: Loudon; Sargent, Scully, Lamb; Walls & Milburn; Scully & Zubairy
- series expansion, SHG & DFG, symmetries & nonlinear coefficients, self-phase modulation, four-wave mixing, self-focussing, bright & dark solitons, non-perturbative effects, phase conjugation
- parametric conversion, optical parametric oscillators, optical parametric amplification spontaneous parametric down-conversion
- applications: frequency-doubling, autocorrelation measurements, high-order nonlinear spectroscopy, saturated-absorption spectroscopy
Texts: Nonlinear Optics, R.W. Boyd; The Principles of Nonlinear Optics, Y.R. Shen; Quantum Electronics, A. Yariv