Physics 581 Spring 2022

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 11:00am-12:15pm, P&A Room 1160

Office Hours: TBA

Teaching Assistant: Sivaprasad Omanakutan

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:  Microsoft Stream

 Jan. 18

Review: Coherence, Particles and Fields

Lecture #1

 Jan. 20

 Review: Nonclassical Light - Glauber Theory


Jan. 25

 Continuous variables:

Squeezed states, general properties

Lecture #2
Jan. 27

Quadratures, shot noise, and homodyne detection

 Feb. 1

Introduction to nonlinear optics and the generation of nonclassical light

Lecture #3


Three Wave Mixing Production of Squeezed States

 Feb. 8


 Feb. 10

Introduction to Phase Space Representations 

Lecture #4

 Feb. 15

Operator Ordering and Quasiprobability Distributions

Feb. 17

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

 Feb. 22

 Tensor product structure and entanglement Schmidt decomposition

Lecture #5
 Feb. 24 Continuation

Mar. 1

Mar. 3

EPR, Bell's Inequalities, and tests in Quantum Optics
Lecture #6

Mar. 8

Entanglement in quantum optics - particles and waves

Spontaneous Parametric Conversion
and Time-Energy Entanglement

Mar. 10

Spatial mode and polarization entanglement

Two-mode squeezing and CV entanglement

Mar. 14-18

Spring Break

Mar. 22 Intro to open quantum systems:
 Quantum operations, CP maps, Kraus Representation
Lecture #7
Mar. 24

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation
Lecture #8


Mar. 29

Derivation of the Lindblad Master Equation Born-Markov approximation

Mar. 31

No Class

 Apr. 5

Examples of Master Equation Evolution:

Damped two-level atom

Lecture #9


Apr. 7

 Damped Simple Harmonic Oscillator


Apr. 12



Apr. 14

Quantum Dynamics in Phase Space

Fokker-Planck Equation, Heisenberg -Langevin Equations

Lecture #10


Aprl. 19


Quantum Trajectories I

Measurement theory

Lecture #11
Apr. 21

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Lecture #12


Apr. 26


Quantum Trajectories III

Different Unravelings of the Master Equation

Lecture #13

 Apr. 28

Lecture #14

 May 3

The Stochastic Schrodinger Equation.

Quantum State Diffusion

Lecture #15

May 5


QND measurement and and the Stochastic Schrodinger Equation
Lecture #16


Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Problem Set #5

 Final Project