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, Tuesdays.
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.
III. Continuous measurement
A. Quantum trajectories – different unravelings of the Master Equation.
B. Quantum MonteCarlo wave functions.
C. The
stochastic Schrödinger equation.
IV. Fundamental Paradigms of quantum optics
A. Cavity QED (from atoms to superconductors)
B. Ion
traps.
C. Cold
neutral atom ensembles.
D.
Correlated photons and squeezed states.
V. Applications in quantum information processing
A. Quantum communication
B. Quantum
computation
C. Quantum
metrology
Aug. 23 
Review: Particles, Waves, Coherence, Density Matrix 

Aug. 25 
No Lectue: Travel 
Review 
Aug. 30 
Review: Quantum Fields, Nonclassical Light  Glauber Theory


Sept. 1 
Continuation 

Sept. 6 
Continuous variables: Squeezed states, general properties


Sept. 8 
Continuation 

Sept. 13 
Quadratures, shot noise, and homodyne detection 

Sept. 14 
Introduction to nonlinear optics and the generation of nonclassical light 

Sept. 15 
Production of Squeezed Sates Parametric Downconversion 

Sept. 20 
Quasiprobability functions Wigner (W), Husmi (Q), and Glauber (P)


Sept. 22 
Continuation


Sept. 27 
Continuation


Sept. 29 
Tensor product structure and entanglement


Oct. 4 
Schmidt decomposition


Oct. 6 
Entanaglement in quantum optics  particles and waves


Oct. 11

Twin photon pairs and twomode squeezing


Oct. 12

Tests of Bells Inequalities in Quantum Optics


Oct. 13 
Fall Break 

Oct. 18

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

Oct. 20 
Irreverisble bipartite systemreservoir interaction. Markov approximation  Lindblad Master Equation


Oct. 25 
Continuation 

Oct. 27 
Examples of Master Equation Evolution: Damped twolevel atom, damped SHO


Nov. 1 
Continuation


Nov. 3 
FokkerPlanck Equation and Decoherence 

Nov. 8 
HeisenbergLangevin formulation of open quantum systems Fluctuationdissipation 

Nov. 10 
Continuation 

Nov. 15 
Quantum Trajectories I Measurement theory 

Nov. 17 
Quantum Trajectories II Quantum MonteCarlo Wave Function Algorithm 

Nov. 22 
Continuation 

Nov. 24 
Thanksgiving 

Nov. 29 
Quantum Trajectories III Different Unravelings of the Master Equation


Dec. 1 
Continuation


Dec. 6 
The Stochastic Schrodinger Equation. Quantum State Diffusion 

Dec. 8 
QND measurement and and the Stochastic Schrodinger Equation. CaseStudy: Spin Squeezing 
Problem Set #1

Problem Set #2

Problem Set #3

Problem
Set #4

Final Project
