Physics 581 Spring 2023

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: Tuesday and Thursday 2:00-3:15pm, PAIS Room 1160

Office Hours: TBA

Teaching Assistants: I.A. Gunter and M. Raza

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 Thursdays in TA mailbox.




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 Bellís 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




Lecture notes in pdf.   Podcasts for Lectures on YouTube

 Jan. 16

Review: Coherence, Particles and Fields

Discrete and Continuous variables

Lecture #1

Podcast #1

 Jan. 18

Squeezed states, general properties

Lecture #2

Podcast #2


Jan. 23

Podcast #3
Jan. 25

Quadratures, shot noise, and homodyne detection

Podcast #4

Jan. 30

Introduction to nonlinear optics and the generation of nonclassical light

Lecture #3

Podcast #5


Three Wave Mixing Production of Squeezed States

Podcast #6

 Feb. 6

Introduction to Phase Space Representations

Lecture #4

Podcast #7

 Feb. 8

Wigner Function

Podcast #8

 Feb. 13

Operator Ordering and Quasiprobability Distributions  Wigner (W), Husumi (Q), and Glauber (P)
Podcast #9

Feb. 15


Podcast #10

 Feb. 20

Introduction to Entanglement
Tensor product structure

Lecture #5

Podcast #11
Feb. 22
Entanglement - Schmidt Decomposition
EPR, Bell's Inequalities

Lecture #6

Podcast #12
Feb. 27

Entanglement in quantum optics - particles and waves

Spontaneous Parametric Conversion
and Time-Energy Entanglement

Podcast #13

Feb. 29

Podcast #14

Mar. 5

No lecture -- To me made up

Mar. 7

Spatial mode and polarization entanglement

Two-mode squeezing and CV entanglement

Podcast #15

Mar. 11-15

Spring Break

Mar. 19
Intro to open quantum systems:
 Quantum operations, CP maps, Kraus Representation
Lecture #7

Podcast #16
Mar. 21

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation

  Lecture #8

Podcast #17


Mar. 26

Derivation of the Lindblad Master Equation Born-Markov approximation
Podcast #18

Mar. 28


Podcast #19

 Apr. 2

Examples of Master Equation Evolution:

Damped two-level atom

Lecture #9

Podcast #20


Apr. 4

  Damped Simple Harmonic Oscillator

Quantum Dynamics in Phase Space  
Lecture #10
Podcast #21


Apr. 9

Quantum Trajectories I

Introduction to Quantum Trajectories

Lecture #11
Moelmer 1
Podcast #22


Apr. 11

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Lecture #12
Moelmer 2
Podcast #23


Aprl. 16


Quantum Trajectories III

Different Unravelings of the Master Equation

Lecture #13
Moelmer 3
Podcast #24
Apr. 18

Application - Coherent Population Traopping
Podcast #25


Apr. 23


No Lecture

 Apr. 25

No Lecture

 Apr. 30

Quantum Trajectories III

The Stochastic Schrodinger Equation.

Continuous measurement

Lecture #14
Moelmer 4
Podcast #26

May 2

Continuous Measurement

Lecture #15
Podcast #27

 May 7

Master Equation in Phase Space

Fokker-Planck Equation and Decoherence

Lecture #16

May 9


The Quantum-to-Classical Transition


Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Problem Set #5

Problem Set #6:  EXTRA CREDIT

FINAL Project