Physics 566 Fall 2013

Quantum Optics I

University of New Mexico

Department of Physics and Astronomy

Instructor: Prof. Ivan H. Deutsch
Lectures: Tues. and Thurs. 5:15-6:30 PM, P&A Room 184

Office Hours: Wed. 10:00-11:00, Room 23

Teaching Assistants: Bob Keating and Xiaodong Qi

Problem Session: Mon. 2:00-3:00, Room 5

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 information-processing 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
- Atom-photon coupling and atomic coherence
- The quantum electromagnetic vacuum
- Nonclassical light and photon statistics
- Quantum optical particles and waves (discrete and continuous variables)

Quantum Optics II (Physics 581)
- 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)


On this page:



Quantum Optics map (pdf download)




General Information


"Recommended" Texts (none required):

* Atom-Photon interactions- Cohen-Tannoudji,

* Quantum Optics - Scully and Zubairy,

* Quantum Optics, by R. Y. Chiao and J. C. Garrision


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.


Other Texts:

Recent books (published within the last 5 years)

* Statistical Methods in Quantum Optics 1 and 2, by H. J. Carmichael

* Quantum Noise, by C. Gardiner (also Handbook of Stochastic Methods)

* Quantum Optics, An Introduction, by M. Fox

* Introductory Quantum Optics by C. Gerry and P. Knight

* Fundamental of Quantum Optics, by J. R. Klauder and E. C. G. Sudarshan

* Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence by M. Orszag

* Introduction to Quantum Optics: From Light Quanta to Quantum Teleportation by H. Paul and I. Jex

* Fundamentals of Quantum Optics and Quantum Information by P. Lambropoulos and D. Petrosyan

* Modern Foundations Of Quantum Optics by Vlatko Vedral


Older standards

* Elements of Quantum Optics, by P. Meystre and M. Sargent

"Quantum Optics" - Walls and Milburn

* Photons and Atoms: Introduction to Quantum Electrodynamics, by Claude Cohen-Tannoudji et al.

* Optical Coherence and Quantum Optics, by L. Mandel and E. Wolf

* Lasers, by P. Milonni and J. H. Eberly

* Optical Resonance and Two-Level Atoms , by Allen and J. H. Eberly

* Quantum Statistical Properties of Radiation, by W. H. Louisell

* Quantum Properties or Radiation, R. Loudon

* Laser Theory, by H. Haken



* Problem Sets (8-10 assignments) 50%

* Midterm 25%

* Final Project 25%


* Problem sets will be available on the web, about every week. Generally assignments will be due in class, Tuesdays.




Tentative Syllabus


Phys. 566: Quantum Optics I

I. Classical foundations

            A. Oscillators, interference, and coherence.

            B. Simple harmonic oscillators, quadratures, and Fourier analysis.

            C. Lorentz oscillator model.


II. Quantum foundations

            A. Density matrix and coherence.

            B. Two level systems -- Pauli algebra, Bloch-sphere, magnetic resonance.

            C. Quantum simple harmonic oscillator.


III. Optical resonance for two level atoms

            A. Atom-photon interaction in electric dipole approximation.

            B. Pseudo-spin formulation, Rabi flopping.

            C. Density matrix formulation.

            D. Phenomenological damping -- master equation and rate equations.


IV. The electromagnetic vacuum

            A. Quantization of the electromagnetic field.

            B. Spontaneous emission and Wigner-Weisskopf theory.

            C. Resonance fluorescence -- Mollow triplet.

            D. Jaynes-Cummings model -- Dressed states.


V. Three level quantum coherence

            A. Raman resonance.

            B. Dark states and EIT.

            C. Slow light, fast light, and polaratons.


VI. Quantum-Optical Coherence

            A. Photon counting statistics -- Mandel's formula.

            B. Theory of partial coherence - Classical statistical optics

            C. Coherent states as quasi-classical states.

            D. Glauber's correlation functions.

            E. Hanbury-Brown and Twiss interferometry.

            F. Bunching, antibunching ,and photon statistics.


Phys. 581: Quantum Optics II

I. Nonclassical Light

            A. Phase space methods -- Quasiprobability distributions, P-Glauber, Q-Husimi, W-Wigner functions.

            B. Nonlinear optics and nonclassical light.

            C. Squeezed states.

            D. Homodyne detection.

            E. Correlated twin photons.

            F. Photon interferometry.


II. Foundations

            A. Bipartite entanglement.

            B. EPR and Bell’s Inequalities, finite and infinite dimensional systems.

            C. Completely-positive map, Kraus operators, and POVMs.


III. Open quantum systems

            A. System-reservoir interactions.

            B. Born-Markoff approximation and the Lindblad Master Equation.

            C. Phase-space representation:  Fokker-Planck equation.

            D. Heisenberg-Langevin equation.


III. Continuous measurement

            A. Quantum trajectories – different unravelings of the Master Equation.

            B. Quantum Monte-Carlo 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



Notes in .pdf, Video in .mp4 (Quicktime).

Aug. 20

Overview of Class.

Quantum and Classical Coherence

Lecture #1

Podcast 1

Aug. 22

Oscillators, Quadratures, and Fourier Analysis

Lecture #2

Podcast 2

Aug. 27

Lorentz Oscillator Model

Lecture #3

Podcast 3

Aug. 29

Lorentz Oscillator Model Continued:

Radiation Reaction and the Classical Theory of

Resonance Fluorescence

Podcast 4

Sep. 3

Two level atoms -- Paul algebra, Bloch-sphere, SU(2)

Lecture #4

Podcast 5

Sep. 5


Podcast 6

Sep. 10

Magnetic Resonance - Rabi flopping

Lecture #5

Podcast 7

Sep. 12


Podcast 8

Sep. 17

Laser spectroscopy as magnetic resonance

Coherence and the Density Matrix

Lecture #6

Podcast 9

Sep. 19


Podcast 10

Sep. 24

Optical Bloch Equations (I)

Phenomenological decay T1 and T2

Lecture #7

Podcast 11


Sep. 26



Podcast 12


Oct. 1

Optical Bloch Equations (II) 

Two-level atom damped response

Lecture #8

Podcast 13


Oct. 3


Three-level atoms: Adiabatic elimination

Lecture #9

Podcast 14


Oct. 8

Dressed States and Raman Transitions

Podcast 15


Oct. 10


Fall Break




Dark states, Coherent Population Trapping,

Electromagnetically Induced Transparency

Lecture #10

Podcast 16

Oct. 17

Introduction to Quantum Field Theory

Lecture #11

Podcast 17


Oct. 22



Podcast 18


Oct. 24


Midterm Exam



Oct. 29

Quantization of the electromagnetic field

Lecture #12

Lecture 12 Supplement

Podcast 19


Oct. 31

Introduction to Quantize Field - Atom Interactions

The Jaynes-Cummings Model

Lecture #13

Podcast 20


Nov. 5




Podcast 21


Nov. 7


Spontaneous emission: Wigner-Weisskopf

Lecture #14

Podcast 22


Nov. 12


Wigner-Weisskopf 2:

Schrödinger picture: Single photon spontaneous wavepackets

Heisenberg picture: Radiation reaction vs. vacuum fluctations


Podcast 23


Nov. 14


Photon counting experiments and photon statistics

Coherent states as quasiclassical states

Lecture #15

Podcast 24


Nov. 19




Podcast 25


Nov. 21


Interferometry and coherence: Hanbury-Brown and Twiss



Lecture #16

Glauber Les Houches

Aspect HBT Talk

Podcast 26

Nov. 26

No Class -- On Travel


Nov. 28



Dec. 3


Glauber correlation functions:

Podcast 27

Dec. 5

Snow Day

Dec. 9


Photon statistics and bunching

Podcast 28

Dec. 10


Introduction to resonance fluorescence

Coherent vs. incoherent photon scattering

Lecture #17

Podcast 29

Dec. 11

The spectrum of resonance fluorescence: The Mollow triplet

Nonclassical Light: Photon antibunching in resonance fluorescence


Podcast 30




Problem Sets

Problem Set #1

Problem Set #6

Problem Set #2


Problem Set #7

Problem Set #3

Problem Set #8

Problem Set #4

Problem Set #9

Problem Set #5


Final Project