Physics 581 Spring 2020

Quantum Optics II

Credit: P. Grangier, "Make It Quantum and Continuous", Science (Perspective) 332, 313 (2011)


University of New Mexico

Department of Physics and Astronomy

Instructor: Prof. Ivan H. Deutsch
Lectures: Mon. and Wed. 11:00am-12:15pm, P&A Room 1160

Office Hours: TBA

Teaching Assistant: Maneul Muñoz

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.

Quantum Optics II (Physics 581)

- 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:


General Information


"Recommended" Texts (none required):

* Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light - Gryberg, Aspect, Fabre

* Quantum Optics - Scully and Zubairy,

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

* Quantum Optics, by M. Fox


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.




* Problem Sets (5-8 assignments) 75%

* Final Project 25%


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




Tentative Syllabus


Phys. 581: Quantum Optics II

I. Nonclassical Light

            A. Nonlinear optics and nonclassical light.

            B. Squeezed states.

            C. Homodyne detection.

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

            E. Correlated twin photons.

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.


IV. Continuous measurement

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

            B. Quantum Monte-Carlo wave functions.

            C. The stochastic Schroedinger equation.


V. Applications in quantum information processing

            A. Quantum communication

            B. Quantum computation

            C. Quantum metrology



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

 Jan. 22

Review: Coherence, Particles and Fields

Lecture #1

Podcast 1

 Jan. 27

 Review: Nonclassical Light - Glauber Theory


Jan. 29

 Continuous variables:

Squeezed states, general properties

Feb. 3

Quadratures, shot noise, and homodyne detection

 Feb. 5

Introduction to nonlinear optics and the generation of nonclassical light


No Lecture
(to be made up)

 Feb. 12

Three Wave Mixing Production of Squeezed Sates

 Feb. 17

Introduction to Phase Space Representations 

 Feb. 19

Operator Ordering and Quasiprobability Distributions

Feb. 24

Quasiprobability functions Wigner (W), Husmi (Q), and Glauber (P)

 Feb. 26

 Tensor product structure and entanglement

 Feb. 28

Schmidt decomposition

Mar. 2 Entanglement in quantum optics - particles and waves

Mar. 4

Parametric Conversion I
Type I phase matching:
Time energy entanglement

Mar. 9

Parametric Conversion II

Spatial mode and polarization entanglement

Two-mode squeezing and CV entanglement


Mar. 11


Tests of Bells Inequalities in Quantum Optics

 Mar. 16-20

Spring Break

Mar. 23 Intro to open quantum systems:
 Quantum operations, CP maps, Kraus Representation

Mar. 25

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation


Mar. 30

 Derivation of the Lindblad Master Equation Born-Markov approximation

Apr. 1

 Examples of Master Equation Evolution:

Damped two-level atom

 Apr. 6

Damped Simple Harmonic Oscillator



Apr. 8

Fokker-Planck Equation and Decoherence


Apr. 13

 Quantum Trajectories I

Measurement theory


Apr. 15



Nonlinear Stochastic Jump Equation


Aprl. 20


 Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Apr. 22

Quantum Trajectories III

Different Unravelings of the Master Equation



Apr. 27



 Apr. 29

The Stochastic Schrodinger Equation.

Quantum State Diffusion

 May 4

QND measurement and and the Stochastic Schrodinger Equation

May 6.




Problem Sets

Problem Set #1

Problem Set #2

  • Questions

Problem Set #3

  • Questions
Problem Set #4
  • Questions
Problem Set #5
  • Questions
Problem Set #6
  • Questions
Problem Set #7
  • Questions
Problem Set #8
  • Questions