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 Thursdays in TA mailbox.
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. 18 
Review:
Coherence, Particles and Fields


Jan. 20 
Review: Nonclassical
Light  Glauber Theory 

Jan. 25 
Continuous variables: Squeezed states, general properties 
Lecture #2 
Jan. 27

Quadratures, shot noise, and homodyne detection 

Feb. 1 
Introduction to nonlinear optics and the generation of nonclassical light 
Lecture #3 
Feb.3 
Three Wave Mixing Production of Squeezed States 

Feb. 8 
Continuation


Feb. 10 
Introduction to Phase Space
Representations 
Lecture #4 
Feb. 15 
Operator
Ordering and Quasiprobability Distributions


Feb. 17 
Quasiprobability functions
Wigner (W), Husumi (Q), and
Glauber (P) 

Feb. 22 
Tensor product structure
and entanglement Schmidt decomposition 
Lecture #5 
Feb. 24  Continuation 

Mar. 1 
Continuation 

Mar. 3 
EPR, Bell's Inequalities, and tests in Quantum Optics 
Lecture #6 
Mar. 8

Entanglement in quantum optics 
particles and waves
Spontaneous Parametric Conversion and TimeEnergy Entanglement 

Mar. 10

Spatial mode and polarization
entanglement
Twomode squeezing and CV entanglement 

Mar. 1418 
Spring Break 

Mar. 22  Intro to open quantum systems: Quantum operations, CP maps, Kraus Representation 
Lecture #7 
Mar. 24 
Irreverisble bipartite systemreservoir interaction. Markov
approximation  Lindblad Master Equation

Lecture #8 
Mar. 29 
Derivation of the Lindblad Master Equation BornMarkov approximation 

Mar. 31 
No Class


Apr. 5 
Examples of Master Equation Evolution: Damped twolevel atom 
Lecture #9 
Apr. 7 
Damped Simple Harmonic Oscillator 

Apr. 12 
Decoherence 

Apr. 14 
Quantum Dynamics in Phase Space FokkerPlanck Equation, Heisenberg Langevin Equations 
Lecture #10 
Aprl. 19

Quantum Trajectories I
Measurement theory 
Lecture #11 
Apr. 21

Quantum Trajectories II Quantum MonteCarlo Wave Function Algorithm 
Lecture #12 
Apr. 26

Quantum
Trajectories III
Different Unravelings of the Master Equation 
Lecture #13 
Apr. 28 
Continuation 
Lecture #14 
May 3 
The Stochastic Schrodinger Equation. Quantum State Diffusion

Lecture #15 
May 5

QND measurement and and the Stochastic Schrodinger Equation 
Lecture #16 
Problem Set #1 
Problem Set #2 
Problem Set #3 
Problem Set #4

Problem Set #5
