Office Hours: TBA
Problem Session: TBA
Quantum
optics is a broad and varied subject that deals with the study, control,
and manipulation of quantum coherence associated with electromagnetic
fields. This includes nonclassical optical media, the basic interaction
of photons and atoms, and the nonclassical nature of the electromagnetic
field itself. Quantum optics is the natural arena for experimental
tests of the foundations of quantum mechanics and measurement,
especially in the context of open, nonequilibrium quantum systems. Most
recently, developments in theory and experiment have led to the
possibility of applying the coherent control of quantum optical systems
to perform completely new informationprocessing paradigms such as
quantum communication and quantum computation.
Topics
to be studied include:
 Quantum and classical coherence
 Atomphoton coupling and atomic coherence
 The quantum electromagnetic vacuum
 Nonclassical light and photon statistics
 Quantum optical particles and waves (discrete and continuous
variables)
 Foundations of entanglement and quantum maps
 Open quantum systems and decoherence
 Quantum trajectories and continuous measurement
 Fundamental paradigms in quantum optics (cavity QED, ion and neutral
atom traps, entangled light)
 Applications in quantum information science (quantum communication,
computation, metrology)
Quantum Optics map (pdf download)
"Recommended" Texts (none required):
* AtomPhoton interactions CohenTannoudji,
* Quantum Optics  Scully and Zubairy,
* The Quantum World of UltraCold Atoms and Light: Book 1: Foundations of Quantum Optics  Gardiner and Zoller.
We will not be following any of these texts directly . They all have strengths in different areas and are good to have on your bookshelf.
Other Texts:
Recent books (published within the last 5 years)
* Introduction to Quantum Optics  Grynberg Aspect, and Fabre,
* Exploring the Quantum: Atoms, Cavities, and Photons  Haroche and Raimond,
* The Quantum Theory of Nonlinear Optics  Drummond and Hillery.
Recent books (published within the last 10 years)
* Statistical Methods in Quantum Optics 1 and 2, by H. J. Carmichael
* Quantum Noise, by C. Gardiner (also Handbook of Stochastic Methods)
* Quantum Optics, An Introduction, by M. Fox
* Introductory Quantum Optics by C. Gerry and P. Knight
* Fundamental of Quantum Optics, by J. R. Klauder and E. C. G. Sudarshan
* Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence by M. Orszag
* Introduction to Quantum Optics: From Light Quanta to Quantum Teleportation by H. Paul and I. Jex
* Fundamentals of Quantum Optics and Quantum Information by P. Lambropoulos and D. Petrosyan
* Modern Foundations Of Quantum Optics by Vlatko Vedral
Older standards
* Elements of Quantum Optics, by P. Meystre and M. Sargent
"Quantum Optics"  Walls and Milburn
* Photons and Atoms: Introduction to Quantum Electrodynamics, by Claude CohenTannoudji et al.
* Optical Coherence and Quantum Optics, by L. Mandel and E. Wolf
* Lasers, by P. Milonni and J. H. Eberly
* Optical Resonance and TwoLevel Atoms , by Allen and J. H. Eberly
* Quantum Statistical Properties of Radiation, by W. H. Louisell
* Quantum Properties or Radiation, R. Loudon
* Laser Theory, by H. Haken
Grading:
* Problem Sets (810 assignments) 60%
* Midterm 20%
* Final Project 20%
* Problem sets will be available on the web, about every week. Generally assignments will be due in class, Thursdays.
Phys.
566: Quantum Optics I
I. Classical foundations
A.
Oscillators, interference, and coherence.
B.
Stochastic Processes.
C.
Lorentz oscillator model.
II. Quantum foundations
A.
Density matrix and coherence.
B.
Two level systems  Pauli algebra, Blochsphere, magnetic resonance.
C.
Quantum simple harmonic oscillator.
III. Optical resonance for two level atoms
A.
Atomphoton interaction in electric dipole approximation.
B.
Pseudospin formulation, Rabi flopping.
C.
Density matrix formulation.
D.
Phenomenological damping  master equation and rate equations.
IV. The electromagnetic vacuum
A.
Quantization of the electromagnetic field.
B.
Spontaneous emission and WignerWeisskopf theory.
C.
JaynesCummings model 
Dressed states, Cavity QED.
V. Three level quantum coherence
A.
Raman resonance.
B.
Dark states and EIT.
C.
Slow light, fast light, and polaratons.
VI. QuantumOptical Coherence
A.
Photon counting statistics and classical statistical optics
B.
Coherent states as quasiclassical states.
C.
Glauber's correlation functions.
D.
HanburyBrown and Twiss interferometry and nonclassical light
E.
Bunching, antibunching ,and photon statistics.
Aug. 22 
Overview of Class.
Quantum and Classical Coherence 

Aug. 24 
Introduction to Stochastic to Probability 

Aug. 29 
No Class 

Aug. 31 
No Class 

Sep. 5

Introduction to Stochastic Processes 

Sep. 7 
Lorentz Oscillator and Coherence 

Sep. 12a 
Coherence and the Density Matrix 

Sep. 12b Makeup 
Two level atoms  Paul algebra, Blochsphere, SU(2)


Sep. 14 
Continuation


Sep. 19 
Magnetic Resonance  Rabi flopping 

Sep. 21 
Continuation 

Sep. 26a 
Optical Bloch Equations Phenomenological decay T1 and T2


Sep. 26b 
Make up: Introduction to the Master Equation 

Sep. 28 
Twolevel atom damped response Laser rate equations 

Oct. 3 
Threelevel atoms: Adiabatic elimination 

Oct. 5 
Raman Transitions and Optical Control of Ground States 

Oct. 10 
Dark States, Coherent Population Trapping, and EIT 

Oct. 12 
Fall Break 

Oct. 17

Introduction to Quantum Field Theory 

Oct. 19 
Continuation 

Oct. 24 
Quantization of the electromagnetic field


Oct. 26 
Introduction to Quantized Field  Atom Interactions 

Oct. 31 
The JaynesCummings Model and Cavity QED 

Nov. 2 
Spontaneous emission: WignerWeisskopf and the Markoff approximation


Nov. 7 
Spontaneous emission: Heisenberg Picture: Radiation Reaction 

Nov. 9 
Photon counting experiments and photon statistics


Nov. 14 
Coherent states as quasiclassical states of the electromagnetic field 

Nov. 16 
Continuation 

Nov. 21 
Interferometry and coherence: HanburyBrown and Twiss


Nov. 23 
Thanksgiving 

Nov. 28 


Nov. 30 
Classical vs. Nonclassical Light


Dec. 5 
Photon statistics Introduction to resonance fluorescence Coherent vs. incoherent photon scattering 

Dec. 7 
The spectrum of resonance fluorescence: The Mollow triplet Nonclassical Light: Photon antibunching in resonance fluorescence

Problem Set #1

Problem Set #6

Problem Set #2 
Problem Set #7

Problem Set #3

Problem Set #8

Problem
Set #4

Problem Set #9

Problem Set #5

Problem Set #10

Final Project