## Physics 673: Quantum Optics and Nonlinear Optics |

Tuesday, 14:00-15:15, SS 115 (Social Sciences)

Thursday, 14:00-15:15, SS 115 (Social Sciences)

This course was held during fall 2004 at the University of Calgary. It covers the fundamentals of quantum and nonlinear optics. The foundations of quantum optics include quantization of the electromagnetic field and many-particle theories, interaction between atoms and photons, few-level models for atoms, open quantum systems and density matrix, and electromagnetically induced transparency. Lecture notes are available here .

Maxwell's Equations and Gauge Fields Maxwell's Equations Scalar Potential and Vector Potential Gauge transformations Multipole Expansion Electrodynamics in Dielectric Media Derivation of macroscopic Maxwell equations Plane Waves Elements of classical optics

Quantum Field Theory of Light - QED Many-Particle Theory of Quantum Mechanics Fock Space and Number Representation Creation and Anihilation Operators The Field Operator Second Quantization Summary of the construction of a many-particle theory Quantization in Coulomb Gauge

Coherent States Classical and Quantum Mechanical Interference Remarks on the Quantization Procedure for other Gauges

Quantum Mechanics of Atoms: a short Review The Hydrogen Atom, Parity Fine structure and spin Hyperfine structure

The Interaction between Atoms and Light Minimal Coupling Derivation of Minimal Coupling Gauge Invariance of Minimal Coupling

The Power-Zienau-Woolley Transformation The Basic Idea The Complete Transformation

Dipole approximation and dipole coupling Selection rules for atoms

The two-level model for atoms Derivation of two-level systems Representation of operators Coupling between a two-level atom and the electromagnetic field

Rabi oscillations and Landau-Zener transitions Landau-Zener transitions

Dressed States Dressed states in a cavity

Models with few levels, dark states, Raman transitions Dark States Raman transitions

Adiabatc theorem, STIRAP Application of the adiabatic theorem to dark states

Incoherent Interaction and Density Matrix Density Matrix Formalism Liouville Equation, Superoperators Reduced density matrix, Zwanzig's Master Equation Reduced Density Matrix, Projection Superoperators Zwanzig's Master Equation

Spontaneous Emission Spontaneous emission cancellation through interference

Electromagnetically induced transparency The Maxwell-Bloch equations Index of refraction for a two-level atom Electromagnetically induced transparency and dark states

Photonic band gaps Nonlinear Optics Appendices Green's function Angular momentum algebra Addition of two angular momenta Tensor operators and Wigner-Eckart theorem Addition of three angular momenta Matrix elements for composed systems

Distributions

Bibliography Index

Claude Cohen-Tannoudji, Jacques Dupont-Roc, and Gilbert Grynberg,
*Photons and
atoms : introduction to quantum electrodynamics* (1989).
In this book the
fundamental equations of non-relativistic QED are
thoroughly explained.

D.P. Craig and T. Thirunamachandran,
*Molecular quantum electrodynamics : an introduction
to radiation-molecule interactions* (1997). Despite its title
it is also very useful for atoms. A cheap (15 €) alternative to the
first book.

Claude Cohen-Tannoudji, Jacques Dupont-Roc, Gilbert Grynberg,
*Atom-photon
interactions : basic processes and applications* (1992).
A very good book dealing with the fundamental
techniques to describe the interaction of atoms with light.
Includes dressed states, resolvent method, master equations.

M.O. Scully and M.S. Zubairy, *Quantum Optics* (1997). A very nice
introduction which also covers electromagnetically induced
transparency.

Leonard Mandel and Emil Wolf,
*Optical coherence and quantum optics* (1995).
One of the most comprehensive and complete texts on quantum optics.
Gives a good survey of most techniques and topics.