Credit: P. Grangier, "Make It Quantum and Continuous", Science (Perspective) 332, 313 (2011)
Office Hours: Wed. 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 Schrödinger equation.
V. Applications in quantum information processing
A. Quantum communication
B. Quantum
computation
C. Quantum
metrology
Jan. 17 
Review: Particles, Waves, Coherence, Density Matrix 

Jan. 22 
Review: Quantum Fields 

Jan. 24 
Review: Nonclasiscal Light  Glauber Theory


Jan. 29 
Continuous variables: Squeezed states, general properties 

Jan. 31 
Quadratures, shot noise, and homodyne detection


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

Feb. 7 
Three Wave Mixing Production of Squeezed Sates 

Feb. 12 
On Travel: No Lecture 

Feb. 14 
On Travel: No Lecture 

Feb. 19 
Introduction to Phase Space Representations


Feb. 21 
Continuation 

Feb. 26 
Continuation 

Feb. 28

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

MAKEUP Mar. 1 
Tensor product structure and entanglement


Mar. 5 
Schmidt decomposition


Mar. 7 
No Lecture  Travel to March Meeting


Mar, 1216

Spring Break 

Mar. 19

Entanglement in quantum optics  particles and waves 

Mar. 21

Parametric Conversion I Type I phase matching: Time energy entanglement 

Mar. 22 MAKEUP

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

Mar. 26 
Tests of Bells Inequalities in Quantum Optics 

Mar. 28 
Intro to open quantum systems: Quantum operations, CP maps, Kraus Representation


Mar. 29 MAKEUP

Irreverisble bipartite systemreservoir interaction. Markov approximation  Lindblad Master Equation 

Apr. 2 
Derivation of the Lindblad Master Equation BornMarkov approximation


Apr. 4 
Examples of Master Equation Evolution: Damped twolevel atom 

Apr. 9 
Damped Simple Harmonic Oscillator


Apr. 11 
FokkerPlanck Equation and Decoherence 

Apr. 16 
Quantum Trajectories I Measurement theory 

Apr. 18 
Continuation Nonlinear Stochastic Jump Equation 

Aprl. 19 MAKEUP

Quantum Trajectories II Quantum MonteCarlo Wave Function Algorithm 

Apr. 23 
Quantum Trajectories III Different Unravelings of the Master Equation


Apr. 25

On Travel: No Lecture 

Apr. 30 
Continuation 

May 2 
The Stochastic Schrodinger Equation. Quantum State Diffusion



QND measurement and and the Stochastic Schrodinger Equation 
Problem Set #1 
Problem Set #2 
Problem Set #3 
Problem
Set #4

Problem
Set #5
