Physics 581 Spring 2018

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. 12:30-1:45 PM, P&A Room 5

Office Hours: Wed. TBA

Teaching Assistant: Karthik Chinni

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 Schrödinger equation.


V. Applications in quantum information processing

            A. Quantum communication

            B. Quantum computation

            C. Quantum metrology



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


Jan. 17


Review: Particles, Waves, Coherence, Density Matrix

Lecture #1

Podcast 1


Jan. 22


Review: Quantum Fields

Podcast 2


Jan. 24


Review: Nonclasiscal Light - Glauber Theory


Podcast 3


Jan. 29


Continuous variables: Squeezed states, general properties


Lecture #2

Podcast 4



Jan. 31


Quadratures, shot noise, and homodyne detection



Podcast 5



Feb. 5


Introduction to nonlinear optics and the generation of nonclassical light


Lecture #3

Podcast 6



Feb. 7

Three Wave Mixing

Production of Squeezed Sates


Podcast 7



Feb. 12


On Travel: No Lecture



Feb. 14


On Travel: No Lecture



Feb. 19

Introduction to Phase Space Representations



Lecture #4

Podcast 8



Feb. 21




Podcast 9



Feb. 26




Podcast 10



Feb. 28



Quasiprobability functions

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


Podcast 11



Mar. 1


Tensor product structure and entanglement



Lecture #5

Podcast 12



Mar. 5


Schmidt decomposition



Podcast 13



Mar. 7


No Lecture -- Travel to March Meeting




Mar, 12-16


Spring Break


Mar. 19


Entanglement in quantum optics - particles and waves


Lecture #6

Podcast 14



Mar. 21


Parametric Conversion I

Type I phase matching: Time energy entanglement


Podcast 15



Mar. 22



Parametric Conversion II

Spatial mode and polarization entnaglement

Two-mode squeezing and CV entanglement


Podcast 16




Mar. 26


Tests of Bells Inequalities in Quantum Optics



Mar. 28


Intro to open quantum systems:

Quantum operations, CP maps, Kraus Representation



Mar. 29







Apr. 2


Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation


Apr. 4




Apr. 9


Examples of Master Equation Evolution:

Damped two-level atom, damped SHO




Apr. 11

Fokker-Planck Equation and Decoherence



Apr. 16


Heisenberg-Langevin formulation of open quantum systems




Apr. 18


Quantum Trajectories I

Measurement theory





Aprl. 19








Apr. 23


Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm




Apr. 25


On Travel: No Lecture



Apr. 30

Quantum Trajectories III

Different Unravelings of the Master Equation



May 2

The Stochastic Schrodinger Equation.

Quantum State Diffusion



May 3


QND measurement and and the Stochastic Schrodinger Equation.

Case-Study: Spin Squeezing





Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Problem Set #5
  • Questions