Credit: P. Grangier, "Make It Quantum and Continuous", Science (Perspective) 332, 313 (2011)
Office Hours: 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.
Quantum Optics II (Physics 581)

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)
"Recommended" Texts (none required):
* Introduction to Quantum Optics: From the Semiclassical Approach to Quantized Light  Gryberg, Aspect, Fabre
* Quantum Optics  Scully and Zubairy,
* Quantum Optics, by R. Y. Chiao and J. C. Garrision
* Quantum Optics, by M. Fox
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.
Grading:
* Problem Sets (58 assignments) 75%
* Final Project 25%
* Problem sets will be available on the web, about every other week. Generally assignments will be due in class, Wednesdays.
Phys. 581: Quantum Optics II
I. Nonclassical Light
A.
Nonlinear optics and nonclassical light.
B.
Squeezed states.
C.
Homodyne detection.
D. Phase space methods 
Quasiprobability distributions, PGlauber, QHusimi, WWigner functions.
E.
Correlated twin photons.
II. Foundations
A.
Bipartite entanglement.
B.
EPR and Bell’s Inequalities, finite and infinite dimensional systems.
C.
Completelypositive map, Kraus operators, and POVMs.
III. Open quantum systems
A.
Systemreservoir interactions.
B.
BornMarkoff approximation and the Lindblad Master Equation.
C.
Phasespace representation: FokkerPlanck equation.
D.
HeisenbergLangevin equation.
IV. Continuous measurement
A.
Quantum trajectories  different unravelings of the Master Equation.
B.
Quantum MonteCarlo wave functions.
C.
The stochastic Schroedinger equation.
V. Applications in quantum information processing
A.
Quantum communication
B.
Quantum computation
C.
Quantum metrology
Jan. 22 
Review: Coherence,
Particles and Fields

Podcast 1 

Jan. 27 
Review: Nonclassical Light 
Glauber Theory 

Jan. 29 
Continuous variables: Squeezed states, general properties 

Feb. 3

Quadratures, shot noise, and homodyne detection 

Feb. 5 
Introduction to nonlinear optics and the generation of nonclassical light 

Feb.10 
No Lecture
(to be made up)


Feb. 12 
Three Wave Mixing Production
of Squeezed Sates


Feb. 17 
Introduction to Phase Space Representations 

Feb. 19 
Operator Ordering and Quasiprobability
Distributions


Feb. 24 
Quasiprobability functions Wigner (W), Husmi (Q), and Glauber (P) 


Feb. 26 
Tensor product structure and
entanglement 

Feb. 28 
Schmidt decomposition


Mar. 2  Entanglement in quantum optics  particles and waves  
Mar. 4 
Parametric
Conversion I Type I phase matching: Time energy entanglement 

Mar. 9

Parametric Conversion II Spatial mode and polarization entanglement Twomode squeezing and CV entanglement


Mar. 11

Tests of Bells Inequalities in Quantum Optics 

Mar. 1620 
Spring Break 

Mar. 23 
Intro to open quantum systems: Quantum operations, CP maps, Kraus Representation 

Mar. 25 
Irreverisble bipartite systemreservoir interaction. Markov
approximation  Lindblad Master Equation


Mar. 30 
Derivation of the Lindblad Master Equation BornMarkov approximation 

Apr. 1 
Examples of Master Equation Evolution: Damped twolevel atom 

Apr. 6 
Damped Simple Harmonic Oscillator


Apr. 8 
FokkerPlanck Equation and Decoherence 

Apr. 13 
Quantum Trajectories I Measurement theory 

Apr. 15 
Continuation Nonlinear Stochastic Jump Equation 

Aprl. 20

Quantum Trajectories II Quantum MonteCarlo Wave Function Algorithm 

Apr. 22

Quantum Trajectories III Different Unravelings of the Master Equation


Apr. 27

Continuation 

Apr. 29 
The Stochastic Schrodinger Equation. Quantum State Diffusion 

May 4 
QND measurement and and the Stochastic Schrodinger Equation 

May 6.

Continuation 
Problem Set #1 
Problem Set #2

Problem Set #3

Problem
Set #4

Problem
Set #5

Problem
Set #6

Problem
Set #7

Problem
Set #8
