Physics 566 Fall 2021

Quantum Optics

biphoton

University of New Mexico

Department of Physics and Astronomy

 
Instructor: Prof. Ivan H. Deutsch
Lectures: Tuesday, Thursday 9:30am-10:55am, PAÍS Room 1140

Problem Session: Mondays 11:00-12:00  (Zoom)

 
Teaching Assistant:  Sivaprasad Omanakuttan

TA Problem Session: Wednesdays 11:00-12:00 (room 2500)

 


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 the basic interaction of photons and matter 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. The theoretical and experimental tools of quantum optics have helped to ignite the "second quantum revolution" and the development of Quantum Information Science (QIS), with applications in quantum computation and communication.


This class is the first in a two-semester sequence.  Over the course of the year, 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:


 

map of quantum optics

 


 

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.

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

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

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 Standard  Texts:

* Quantum Properties or Radiation, R. Loudon

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

• Quantum Optics by  Walls and Milburn

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

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

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

* Modern Foundations Of Quantum Optics by Vlatko Vedral

 

Additional Resources

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

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

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

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


 

Grading:

* Problem Sets (10 assignments) 80%

* Final Project 20%

 

* Problem sets will be available on the web, about every week. Generally assignments will be due Tuesdays, 5:00pm, in the TA's maiilbox.

 

 


 

Syllabus

 

Phys. 566: Quantum Optics I

I. Classical foundations

            A. Oscillators, interference, and coherence.

            B. Lorentz oscillator model.

 

II. Quantum foundations

            A. Density matrix and coherence.

            B. Two level systems -- Qubits, 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.



VI. Quantum-Optical Coherence and Nonclassical Light

            A. Photon counting statistics and classical statistical optics

            B. Coherent states as quasi-classical states.

            C. Glauber's correlation functions.

            D. Bunching, antibunching, and photon statistics.

            E. Squeezed states if light.
   


 


Lectures
Lecture notes in pdf.   Podcasts for Lectures:  Microsoft Stream


 

 

 Aug. 24

Overview of Class.

Quantum and Classical Coherence

Lecture #1

 

Aug. 26

Coherence and the Density Matrix

Lecture #2

 

Aug. 31

Continuation


Sep. 2

Qubits -- Paul algebra, Bloch-sphere, SU(2)

Lecture #3

Sep. 7 Continuation

 
Sep. 9

Magnetic Resonance - Rabi flopping 


Sep. 14

Continuation

Sep. 16


Two-level atoms and Lorentz Oscillator

Lecture #5

 

Sep. 21

Optical Bloch Equations

Phenomenological decay T1 and T2

Lecture #6

Sep. 23

Introduction to the Master Equation

 Sep. 28


Two-level atom damped response

Laser rate equations

Lecture #7


Sep. 30

Three-level atoms: Adiabatic elimination Raman Transitions and Optical Control of Ground States


Oct. 5

Dark States, Coherent Population Trapping, and EIT


 Oct. 7

Introduction to Quantum Field Theory


 Oct. 12

Quantization of the electromagnetic field


Oct. 14


Fall Break


Oct. 19

Quantized Field - Atom Interactions

 

Oct. 21

The Jaynes-Cummings Model and Cavity QED

 Oct. 26


Continuation



Oct. 28


Spontaneous emission: Wigner-Weisskopf and the
Markov approximation

 

Nov. 2


Stochastic Processes
Photon counting experiments and photon statistics


 Nov. 4 

Continuation

Nov. 9 

Coherent states as quasiclassical states of the electromagnetic field
  Nov. 11

Continuation

 

Nov. 16

Statistical Optics.
Interferometry and coherence: Hanbury-Brown & Twiss


Nov. 18

Glauber correlation functions

Classical vs. Nonclassical Light


Nov. 23 

 

 Continuous variables:

Squeezed states, general properties

 




Nov. 25


Thanksgiving



Nov. 30

Quadratures, shot noise, and homodyne detection



Dec. 2



Introduction to nonlinear optics and the generation of nonclassical light




Dec. 7



Continuation



Dec. 9


Three Wave Mixing Production of Squeezed States

 


 

 

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

Problem Set #10

  • Questions
  • Solutions

 

Final Project