Objectives of the course
The official course Text book is Quantum optics by Mark Fox. Below is a list of the chapters to be studied in this course and in each chapter, the sub-sections are marked either RED, BLUE or GREEN.

Where RED = Important, BLUE = Interesting.

The student should know all the details and derivations for the sections marked "Important". For the sections marked "Interesting" the student should be familiar with the main results and should be able to apply them to problems, but the student is not expected to reproduce any derivations. If part of an important subsection is not important this part is then listed separately.

Part I: Introduction and background

1. Introduction

2. Classical optics

Maxwell's equations, electromagnetism, polarization, diffraction, and interference.

2.1 Maxwell's equations.
2.2 Diffraction and Interference.
2.3 Coherence
2.4 Nonlinear Optics

 

3. Quantum mechanics

Formalism of quantum mechanics, quantization, and harmonic oscillator.

3.1 Formalism of Quantum Mechanics.
3.2 Quantized States in Atoms.
3.3 Harmonic oscillator
3.4 Stern-Gerlach experiment
3.5 Band theory of solids

 

4. Radiative Transitions in atoms

Radiative transition rates, selection rules, the width and shape of spectral lines, and lasers.

4.1 Einstein coefficients.
4.2 Radiative transition rates.
4.3 Selection rules
4.4 Width and shape of transition lines
4.5 Line broadening in solids
4.6 Optical properties of semiconductors
4.7 Lasers

 

Part II: Photons

5. Photon statistics

Photon counting statistics, poissonian, super-poissonian, sub-poissonian photon statistics, theory photon detection, and shot noise in photodiodes.

5.2 Photon-counting statistics.
5.3 Poissonian photon statistics.
5.4 Classification of light
5.5 Super-poissonian light
5.6 Sub-poissonian light
5.7 Degradation of statistics by losses
5.8 Theory of photodetection
5.9 Shot noise in photodiodes

5.10 Observation of sub-Poissonian

 

6. Photon antibunching

Interferometer, Hanbury Brown-twiss experiments, photon bunching and antibunched light.

6.1 Introduction.
6.2 HBT experiment.
6.3 second order correlation
6.4 HBT with photons
6.5 Bunching and antibunching
6.6 Experimental demonstration
6.7 Single photon sources

 

7. Coherent states and squeezed light

Light as a quantum harmonic oscillator, coherent light, number-phase uncertainty and squeezed states.

7.1 Light as classical harmonic oscillator.
7.2 Light as classical harmonic oscillator.
7.3 Light as quantum SHO.
7.4 Vacuum field.
7.5 Coherent states.
7.6 Shot noise.
7.7 Squeezed states.

7.8 Detection of squeezed light.
7.9 Generation of squeezed light.
7.10 Quantum noise in amplifiers

 

8. Photon number states

Number state representation, quantum theory of Hanbury Brown-twiss experiments.

8.1 Operator solution of SHO.
8.2 Number state representation.
8.3 Photon number states.
8.4 Coherent states.
8.5 Quantum theory of HBT experiment.

 

Part III: Atom--photon interactions

9. Resonant light--atom interactions

Two-level atom approximation, coherent superposition states, and damping, and Rabi oscillations.

9.2 Preliminary concepts.
9.3 Time-dependent SE.
9.4 Weak field limit.
9.5 Strong filed limit.
9.6 Bloch sphere.

 

10. Atoms in cavities

Optical cavities, atom-cavity coupling, and strong coupling.

10.1 Optical cavities.
10.2 Atom-cavity coupling.
10.3 Weak coupling.
10.4 Strong coupling.
10.5 Applications.

 

11. Cold atoms

Laser cooling, and Bose-Einstein.

11.1 Introduction.
11.2 Laser cooling.
11.3 Bose-Einstein condenstaion.
11.4 Atom lasers

 

Part IV: Tests of quantum mechanics

12. Single photon operation

Photon polarization superposition state, measurement, and quantum state tomography

 

13. Entangled states

Generation of photon polarization entangled states, entanglement detection

 

14 Bell Inequality

Bell, CHSH inequality, experimental violation of Bell inequality