Physics 566 Fall 2017

Quantum Optics

University of New Mexico

Department of Physics and Astronomy

 
Instructor: Prof. Ivan H. Deutsch
Lectures: Tues. and Thurs. 2:00-3:15 PM, P&A Room 5

Office Hours: TBA

 
Teaching Assistant: Karthik Chinni

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 information-processing paradigms such as quantum communication and quantum computation.

Topics to be studied include:

- 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)
- 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,

* The Quantum World of Ultra-Cold Atoms and Light: Book 1: Foundations of Quantum Optics - Gardiner and Zoller.

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)

* Introduction to Quantum Optics - Grynberg Aspect, and Fabre,

* Exploring the Quantum: Atoms, Cavities, and Photons - Haroche and Raimond,

* The Quantum Theory of Nonlinear Optics - Drummond and Hillery.

 

Recent books (published within the last 10 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

 

Grading:

* Problem Sets (8-10 assignments) 60%

* Midterm 20%

* Final Project 20%

 

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

 

 


 

Syllabus

 

Phys. 566: Quantum Optics I

I. Classical foundations

            A. Oscillators, interference, and coherence.

            B. Stochastic Processes.

            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.
Jaynes-Cummings model -- Dressed states, Cavity QED.
 

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 and classical statistical optics

            B. Coherent states as quasi-classical states.

            C. Glauber's correlation functions.

            D. Hanbury-Brown and Twiss interferometry and nonclassical light

            E. Bunching, antibunching ,and photon statistics.


 

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

 

 

Aug. 22

Overview of Class.

Quantum and Classical Coherence

Lecture #1

Podcast 1

 

Aug. 24

 

Introduction to Stochastic to Probability

Lecture #2

Podcast 2

 

Aug. 29

No Class

 

 

Aug. 31

 

No Class

 

 

Sep. 5

 

 

Introduction to Stochastic Processes

Podcast 3

 

Sep. 7

 

Lorentz Oscillator and Coherence

Lecture #3

Podcast 4

 

Sep. 12a

 

Coherence and the Density Matrix

Lecture #4

Podcast 5

Sep. 12b

Makeup

 

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

 

Lecture #5

Podcast 6

 

Sep. 14

Continuation

Podcast 7

 

Sep. 19

Magnetic Resonance - Rabi flopping

Lecture #6

Podcast 8

 

Sep. 21

Optical Bloch Equations

Phenomenological decay T1 and T2

Lecture #7

Podcast 9

 

Sep. 26a

 

Introduction to the Master Equation

 

 

Sep. 26b

 

Make up: Laser spectroscopy as magnetic resonance

Two-level atom damped response

 

 

Sep. 28

 

Three-level atoms: Adiabatic elimination

 

 

Oct. 3

 

Raman Transitions and Optical Control of Ground States

 

 

Oct. 5

 

Dark States, Coherent Population Trapping, and EIT

 

 

Oct. 10

Introduction to Quantum Field Theory

 

 

Oct. 12

 

Fall Break

 

 

Oct. 17

Continuation

 

 

Oct. 19

Quantization of the electromagnetic field

 

 

Oct. 24

 

Introduction to Quantized Field - Atom Interactions

 

 

 

 

Oct. 26

 

Continuation

 

 

Oct. 31

 

The Jaynes-Cummings Model

 

 

 

Nov. 2

 

Cavity QED

 

 

Nov. 7

Spontaneous emission

Irreversible decay of an excited state

 

 

Nov. 9

 

Wigner-Weisskopf and the Markoff approximation

 

 

Nov. 14

Photon counting experiments and photon statistics

 

 

Nov. 16

 

Coherent states as quasiclassical states of the electromagnetic field

 

 

Nov. 21

 

Interferometry and coherence: Hanbury-Brown and Twiss

 

 

Nov. 23

 

Thanksgiving

 

 

Nov. 28

Glauber correlation functions

 

 

 

Nov. 24

Classical vs. Nonclassical Light.

Photon statistics

 

 

Dec. 5

 

Introduction to resonance fluorescence

Coherent vs. incoherent photon scattering

 

 

Dec. 7

 

The spectrum of resonance fluorescence: The Mollow triplet

Nonclassical Light: Photon antibunching in resonance fluorescence

 

 


 

 

Problem Sets

Problem Set #1

Problem Set #6

  • Questions
  • Solutions

Problem Set #2

Problem Set #7

  • Questions
  • Solutions

Problem Set #3

Problem Set #8

  • Questions
  • Solutions
Problem Set #4

Problem Set #9

  • Questions
  • Solutions

Problem Set #5

  • Questions
  • Solutions

Problem Set #10

  • Questions
  • Solutions