Office Hours: Wed. 10:0011:00, Room 23
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.
In this year long course will develop the tools necessary to analyze these
problems and apply them to contemporary research problems. Topics to be
studied include:
Quantum Optics I (Physics 566)
 Quantum and classical coherence
 Atomphoton coupling and atomic coherence
 The quantum electromagnetic vacuum
 Nonclassical light and photon statistics
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.
D. Quantum
filtering theory.
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
Jan. 21 
Review: Quantum Optics, Coherence, and Quantum Fields 

Jan. 23 
Continuous variables: Squeezed states, general properties 

Jan. 28 
Quadratures, shot noise, and homodyne detection 

Jan. 30 
Introduction to nonlinear optics and the generation of nonclassical light


Feb. 4 
Linear optics, threewave mixing 
No Podcast  Sorry 
Feb. 6 
Production of Squeezed Sates Parametric Downconversion 

Feb. 11 
Quasiprobability functions Wigner (W), Husmi (Q), and Glauber (P) 

Feb. 13 
Continuation 

Feb. 18 
Tensor product structure and entanglement 

Feb. 20 
No lecture  SQuInT 

Feb. 25 
Continuation 

Feb. 26 
Entanglement and different degrees of freedom 

Feb. 27

Entanaglement in quantum optics  particles and waves Twin photon pairs and twomode squeezing 

Mar. 6 
Continuation 

Mar. 11

Test of Bell's Inequalities in Quantum Optics 

Mar. 13 
Intro to open quantum systems: Quantum operations, CP maps, Kraus Representation 

Mar. 1721 
Spring Break 

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

Mar. 27 
Continuation


Apr. 1 
Makeup 

Apr. 5 
Examples of Master Equation Evolution: Damped twolevel atom, damped SHO 

Apr. 8 
Continuation 

Apr. 10 
FokkerPlanck Equation and Decoherence 

Apr. 15 
HeisenbergLangevin formulation of open quantum systems Fluctuationdissipation 

Apr. 17 
Quantum Trajectories I Master equation: quantum jump picture


Apr. 22 
Quantum Trajectories II Quantum MonteCarlo Wave Function Algorithm


Apr. 24 
Quantum Trajectories III Different Unravelings of the Master Equation


Apr. 29 
Continuation


May 1 
Quantum Trajectories IV Quantum State Diffusion 

May 6 
Continuous Measurement  The Stochastic Schrödinger Equation 

May 8 
Case study  Spin squeezing 
Problem Set #1

Problem Set #2

Problem Set #3

Problem
Set #4
