Introduction to Quantum Optics

This course is about the quantum mechanics of light. Classically, light consists of electromagnetic waves, which are fully described by Maxwell's equations. On the quantum level, however, this description has to be extended to introduce the concept of the photon.

Quantum Optics is about how light is described in terms of photons, and how the interaction of photons with matter such as atoms can be understood. We will see that, on the one hand, things that we take as a given in a classical description can be naturally derived in the quantum optical context from fundamental principles. On the other hand, the quantum descriptions allows for novel types of light with properties that can not occur with a purely classical description.

Quantum optics also predicts some very counter-intuitive effects such as an optical coupling to empty vacuum - which can be experimentally tested and have actually been confirmed in laboratories around the world!

Semiclassical Light-Atom Interaction

• Introduction, Overview of classical, semiclassical and q.m. models
• Interaction Hamiltonian of charged particle with e.m. field
• Time Dependent Perturbation Theory
• Transition Rates
• Fermi-Golden Rule
• Two-level atom
• Oscillationg dipoles
• Bloch sphere
  
• Density Operator - Density Matrix
• Optical Bloch Equations
• Rabi Frequency, Saturation Parameter, Spontaneous Decay
• Lineshape in Fluorescence - Saturation Broadening
• Lambert-Beer Law
  
• Bloch Vector
• Ramsey Method
• Mach Zehnder Interferometer

Quantization of the Electromagnetic Field

• Quantized Modes
• Recap: Quantum Mechanics of Harmonic Oscillator
• Ladder Operators, Number Operator
• Quadrature Operators
• Quantization of the EM Field
• Hamiltonian of Radiation Field
• Energy of Vacuum State
• Fock States
• Coherent States
• Squeezed States, Thermal States
• Planck's Black Body Radiation Formula

Beam Splitters and Interferometers

• Beam Splitter
• Classical description of beam splitter
• QM description of beam splitter
• Quantized Mach Zehnder Interferometer
• Homodyne / Heterodyne Detection

Quantized Light-Atom Interaction

• Interaction Hamiltonian
• Jaynes Cummings Hamiltonian
• Quantum Rabi Oscillations
• Vacuum Rabi Oscillations, Collapse & Revivals

Elements of Cavity QED

• Optical Cavities
• Microwave Cavities and Rydberg Atoms
• Seeing a Photon Without Destroying it
• Rabi Oscillations in Dressed State Picture