Physics 566 Fall 2004

Quantum Optics

(Tues. and Thurs. 5:30-6:45, PandA Room 5)


University of New Mexico

Department of Physics and Astronomy


Instructor: Prof. Ivan H. Deutsch

Office Hours: MW 11:00-12:00, PandA room 24

Click here for: Deutsch-group Homepage
Grader: Animesh Datta


Quantum optics is a broad and varied subject which 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. In the last couple of decades, quantum optics has developed into the natural arena for experimental tests on the foundations of quantum mechanics, 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 cryptography and quantum computation.
This course will develop the theoretical tools necessary to analyze these problems, including the optical Bloch equations, density matrix equation and representations (master equation, Langevin, Fokker Planck) , quantum trajectories and continuous measurement, and the quantization of the electromagnetic field. These theoretical methods will be applied to contemporary research problems including:
* Laser spectroscopy and coherent control
* Coherence in multilevel atom systems
* Nonclassical light
* Cavity QED
* Atomic traps
* Two photon interferometry


On this page:




Quantum Optic map (pdf download)




General Information


"Recommended" Texts:

* "Atom-Photon interactions"- Cohen-Tannoudji,

* "Quantum Optics" - Scully and Zubairy,

* "Quantum Optics" - Walls and Milburn

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 ten years)

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

* 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

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

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

Old standards

* 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 (7 assignments) 70%

· Final Projects 30%


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




Tentative Syllabus


I Foundations

A. Review of Quantum Mechanics: Hilbert space, operators, states, time evolution.

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

C. Simple Harmonic Oscillator.


II. 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.

C. Resonance fluorescence -- Mollow triplet


VI Nonclassical light

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

B. Coherent states as quasi-classical states.

C. Phase space methods - Quasiprobability distributions, P,Q, Wigner functions.

D. Squeezed states.

E. Theory of partial coherence -- Glauber's correlation functions.

F. Photon antibunching and resonance fluorescence.

G. Jaynes-Cummings model -- Dressed states, collapse and revival.


V Theory of dissipation in quantum mechanics

A. System reservoir interaction.

B. Derivation of the Linblad master equation in the Born-Markov approximation.

C. Damped two-level atom and simple harmonic oscillators.

D. Heisenberg formulation - Langevin equations.


VII Theoretical methods for open quantum systems

A. Formal theory of the density operators.

B. Quantum trajectories -- Unraveling the master equation.

C. Measurement theory and decoherence.


VIII Experimental paradigms

A. Cavity QED

B. Ion Traps

C. Optical Lattices

D. Parametric down conversion and correlated photon interferometry



Lecture Schedule

Aug. 24

Overview of Class:

Review of Quantum mechanics

Lecture #1

Aug. 26

 The density operator

(review from Phys 492)

Lecture #1b

Aug. 31

Two level systems - Paul algebra, Bloch-sphere

Lecture #2

Sep. 2

Magnetic Resonance - Rabi flopping

Lecture #3

Sep. 7

Optical Bloch Equations (I)

Laser spectroscopy as magnetic resonance

Lecture #4

Sep. 9

Optical Bloch Equations (II) 

Phenomenological decay T1 and T2

Lecture #5

Sep. 14

Introduction to quantum field theory

Review of SHO algebra

Lecture #6

Sep. 16

Quantization of the electromagnetic field

Sep. 21

Spontaneous emission -Wigner-Weiskoff

Lecture #8

Sep. 23

Are there photons?

Photon counting experiments and photon statistics

Coherent states as quasiclassical states

Lecture #9

Sep. 28

Phase space methods - Operator ordering

Lecture #10

Sep. 29

Make up

Quasiprobability theory-

Wigner, Glauber-P, Q functions

Sept. 30

On Travel


Oct. 5

 Interferometry and coherence: Hanbury-Brown Twiss

Lecture #12


Special Supplement:

Glauber Les Houches Lectures (1964) - "Quantum Theory of Coherence"





Oct. 7

Glauber correlation functions:

Optical coherence and photon statistics

Lecture #13

Oct. 12
On Travel
Oct. 14
Fall break

Oct. 19

Nonclassical Light:

Resonance fluorescence and twin photon generation

Lecture #14

Oct. 21

Squeezed states: general properties
Oct. 26
Squeezed states: production and detection

Oct. 28

 Interaction of atoms and quantized field - Jaynes Cummings vs. irreversable

Lecture #17


Irreverisble bipartite system-reservoir interaction.

Lecture #18

Nov. 4

Tensor products, marginal denisty opertor, entanglement


Nov. 9

Born-Markoff derivation of Linblad Master Equation

Nov. 11

Examples - Damped two-level atom, damped SHO.

Rate Equations.

Lecture #20

Nov. 16

Fokker-Plank Equation.

Damping, diffusion, and decoherence

Lecture #21

Make up

Heisenberg-Langevin equations.

Lecture #22


Resonance Fluorescence: Mollow Triplet

Lecture #23

supplement Molmer1

Nov. 23

Quantum Trajectories - quantum jump picture.

Lecture #24

supplement Molmer2

Nov. 25

Monte-Carlo wave function simulation.

Lecture #25

supplement Molmer3

Nov. 30

Different unravelings of the master equation.

Example - Coherent population trapping.

Lecture #26

supplement Molmer4

Dec. 2

Measurement theory -- POVMs

Superoperators -- Krause representation

Lecture #27

Dec. 7

Quantum trajectories -- Formal theory..

Dec. 9

The Stochastic Schroedinger Equation.

Continuous measurement - quantum state diffusion

Lecture #29




Problem Sets

Problem Set #1

 Problem Set #5

 Problem Set #2

Problem Set #6

Problem Set #3

 Problem Set #7

Problem Set #4

Problem Set #8






Final Project



As a final project for the class, you will review an experiment in quantum optics. The goal is to understand how the particular system works and the physics that is explored in the experiment. Possible topics are shown below. Your topic must meet my approval.


Target Dates:

- Submission of abstract of project: Nov. 4

- Approval: Nov. 5

- Due Dec. 7



A. Laser spectroscopy

1. Electromagnetically Induced Transparency (EIT).

2. Lasing without inversion.

3. "Fast" and "slow" light.


B. Atom cooling and trapping

1. Ion traps

2. Optical Molasses and Magneto-Optic Trap (MOT).

3. Optical lattices.

4. Atom interferometry.


C. Cavity QED

1. Microwaves and Rydberg atoms.

2. Optical Cavity QED.

3. Modification of spontaneous emission for atoms in cavities.

4. VCELS and cavity QED in solids.

5. Micromasers (with atoms) / microlasers (in solids).


D. Nonclassical light

1. Photon anti bunching and resonance fluorescence.

2. Production of squeezed states via four-wave mixing, parametric oscillation,

second harmonic generation.

3. Correlated two-photon production via parametric downconversion.


E. Quantum Information Processing

1. Nonclassical atomic motion engineering with trapped ions.

2. Quantum computing with trapped ions.

3. Quantum computing with cavity QED.

4. Quantum computing in optical lattices.

5. Quantum state tomography and state measurement.


F. Quantum Measurement Foundations

1. Quantum nondemolition measurement.

2. Quantum jumps and the "Quantum Zeno Effect".

3. Continuous measurement and quantum feedback.

4. Decoherence and the quantum-classical transition - theory and experiment.


Final Project Publication
Electronic Journal - Reviews of Quantum Optics, Vol. 1, 1999