Physics 566 Fall 2010

Quantum Optics

University of New Mexico

Department of Physics and Astronomy

Instructor: Prof. Ivan H. Deutsch
Lectures: Tues. and Thurs. 5:30-6:45 PM, P&A Room 5

Office Hours: Fridays 11-12, room 23

Click here for: Deutsch-group Homepage
Teaching Assistants: Leigh Norris and Ben Baragiola
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 (none required):

* "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 5 years)

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

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

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

* 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

* 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%

* Take Home Midterm 25%

* Final Project 25%


* Problem sets will be available on the web, about every week. Generally assignments will be due in Leigh Norris's mailbox at 3:00 PM Fridays.




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.



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

Aug. 24

Overview of Class:

Review of Quantum mechanics

Lecture #1


Aug. 26
The Density Matrix

Lecture #1b


Aug. 31

Two level systems - Paul algebra, Bloch-sphere

Lecture #2


Sep. 2

Magnetic Resonance - Rabi flopping (I)

Lecture #3


Sep. 7

Magnetic Resonance - Rabi flopping (II)

Continuation Lect 3


Sep. 9

Optical Bloch Equations (I)

Laser spectroscopy as magnetic resonance

Sep. 14

Optical Bloch Equations (II) 

Phenomenological decay T1 and T2

Lecture #5


Sep. 16

Optical Bloch Equations (III) 

Two-level Atomic Response

Lecture #5b


Sep. 21

Introduction to Quantum Field Theory

Lecture #6


Sep. 23

Introduction to Quantum Field Theory (Ii)


Sep. 28
Quantization of the electromagnetic field

Sep. 30

Spontaneous emission: Wigner-Weisskopf
Oct. 5

Are there photons?

Photon counting experiments and photon statistics

Lecture #9



Coherent states as quasiclassical states

Oct. 12

Phase space methods in Quantum Mechanics

Lectures #10


Oct. 14

Fall Break




Wigner, Glauber-P, Q functions

Lecture #11


Oct. 21

 Interferometry and coherence: Hanbury-Brown Twiss

Lecture #12



Special Supplement:

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





Oct. 26

Glauber correlation functions:

Optical coherence and photon statistics

Lecture #13


Oct. 28

Nonclassical Light:

Photon Antibunching, Resonance fluorescence

Lecture #14


Nov. 2

Nonlinear Optics and Nonclassical Light:

Parametric Downconversion and two-photon interferometry

Nov. 4

Squeezed states - General properties

Nov. 9

Squeezed states - Production and detection

Nov. 11

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

Lecture #17


Nov. 16

Open Quantum Systems

Tensor products, marginal density opertor, entanglement

Nov. 18

Quantum Opertations, POVMs, Krause representation

Lecture #19


Nov. 22

Make Up

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation

Lecture #20



Nov. 23

Examples of Master Equation Evolution:

Damped two-level atom, damped SHO

Nov. 25

supplement Molmer1

supplement Molmer2

supplement Molmer3

supplement Molmer4

Nov. 30

Quantum Trajectories I

Introduction to measurment theory

Master equation: quantum jump picture

Dec. 2

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Lecture #23


Dec. 7


Multilevel Quantum Jumps


Dec. 9

Quantum Trajectories III

Different Unravelings of the Master Equation


Additional Topics:

Stochastic Schrödinger Equation

Continuous Measurement

Lecture #29

Lecture #30




Problem Sets

Problem Set #1

Problem Set #4

 Problem Set #2

 Problem Set #5

Problem Set #3

 Problem Set #6


Problem Set #7


Final Project