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!

Syllabus

Weeks and Topics

1. Fundamentals: Interaction of light fields with atoms
Overview
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

2. Two-level "model" atom: Our model system for a lot of the course
Two Level Atom (Schroedinger Formalism)
Oscillating Dipoles
Bloch Sphere

3. Density matrix and Bloch equations
Density Operator - Density Matrix
Optical Bloch Equations - Dynamics and Steady State
Rabi Frequency, Saturation Parameter, Spontaneous Decay
Lineshape in Fluorescence - Saturation Broadening
Lambert-Beer Law

4. Bloch Vector and Interferometry
Bloch Vector
Ramsey Method
Mach Zehnder Interferometer
Review

5. Quantization of the electromagnetic field
Recap: Quantum Mechanics of Harmonic Oscillator
Ladder Operators, Number Operator
Quantization of the Electromagnetic Field
Hamiltonian of Radiation Field
Energy of Vacuum State

6. Fields in quantized modes
Fock States
Coherent States
Quadrature Operators
Squeezed States, Thermal States

7. Classical and non-classical states of light
Planck's Black Body Radiation Formula
Classical and quantum description of beam splitter
Quantized Mach Zehnder Interferometer
Homodyne / Heterodyne Detection

8. Interferometry with quantized fields
Quantized Light-Atom Interaction
Interaction Hamiltonian
Jaynes Cummings Hamiltonian

9. Quantized fields interacting with matter
Quantum Rabi Oscillations
Vacuum Rabi Oscillations, Collapse & Revivals
Optical Cavities
Elements of Cavity QED

10. Single Mode Quantum Optics
Microwave Cavities and Rydberg Atoms
Seeing a Photon Without Destroying it
Rabi Oscillations in Dressed State Picture
Final Exam

General
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Citación :

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