Physics 581 Fall 2016

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: Tues. and Thurs. 2:00-3:15 PM, P&A Room 5

Office Hours: Wed. TBA

Teaching Assistant: Ezad Shojaee

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, Tuesdays.




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.


III. Continuous measurement

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

            B. Quantum Monte-Carlo wave functions.

            C. The stochastic Schrödinger equation.


IV. Fundamental Paradigms of quantum optics

            A. Cavity QED (from atoms to superconductors)

            B. Ion traps.

            C. Cold neutral atom ensembles.

            D. Correlated photons and squeezed states.


V. Applications in quantum information processing

            A. Quantum communication

            B. Quantum computation

            C. Quantum metrology



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


Aug. 23


Review: Particles, Waves, Coherence, Density Matrix

Lecture 1

Podcast 1


Aug. 25


No Lectue: Travel


Lecture 15 - QO I


Aug. 30


Review: Quantum Fields, Nonclassical Light - Glauber Theory


Lecture 16 - QO I

Podcast 2


Sept. 1



Podcast 3


Sept. 6


Continuous variables: Squeezed states, general properties


Lecture 2

Podcast 4


Sept. 8


Podcast 5


Sept. 13

Quadratures, shot noise, and homodyne detection

Podcast 6


Sept. 14

Introduction to nonlinear optics and the generation of nonclassical light

Lecture 3

Podcast 7


Sept. 15

Production of Squeezed Sates

Parametric Downconversion

Podcast 8


Sept. 20


Quasiprobability functions

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


Lecture 4a

Podcast 9


Sept. 22




Podcast 10


Sept. 27




Podcast 11


Sept. 29


Tensor product structure and entanglement


Lecture 5

Podcast 12


Oct. 4


Schmidt decomposition


Podcast 13


Oct. 6


Entanaglement in quantum optics - particles and waves


Lecture 6

Podcast 14


Oct. 11



Twin photon pairs and two-mode squeezing


Podcast 15


Oct. 12



Tests of Bells Inequalities in Quantum Optics


Phys521 Lecture 26

Podcast 16


Oct. 13


Fall Break



Oct. 18



Intro to open quantum systems:

Quantum operations, CP maps, Kraus Representation

Lecture 7

Caves Lecture

Podcast 17


Oct. 20


Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation


Lecture 8

Podcast 18


Oct. 25



Podcast 19


Oct. 27


Examples of Master Equation Evolution:

Damped two-level atom, damped SHO


Lecture 9

Podcast 20


Nov. 1




Podcast 21


Nov. 3


Fokker-Planck Equation and Decoherence

Podcast 22


Nov. 8


Heisenberg-Langevin formulation of open quantum systems


Lecture 10

Podcast 23


Nov. 10



Podcast 24


Nov. 15

Quantum Trajectories I

Measurement theory

Lecture 11

Molmer 1

Podcast 25


Nov. 17

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Lecture 12

Molmer 2

Podcast 26


Nov. 22




Molmer 3

Molmer 4

Podcast 27



Nov. 24





Nov. 29


Quantum Trajectories III

Different Unravelings of the Master Equation


Lecture 13

Podcast 28


Dec. 1




Podcast 29


Dec. 6

The Stochastic Schrodinger Equation.

Quantum State Diffusion

Lecture 14

Podcast 30


Dec. 8

QND measurement and and the Stochastic Schrodinger Equation.

Case-Study: Spin Squeezing

Lecture 15

Podcast 31




Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Final Project