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.

 

 

Grading:

* 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

 


 

Lectures
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

 

Continuation

 

Podcast 9

 

 

Feb. 26

 

Continuation

 

Podcast 10

 

 

Feb. 28

 

 

Quasiprobability functions

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

 

Podcast 11

 

MAKE-UP

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

MAKEUP

 

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

 

Podcast 17

 

 

Mar. 28

 

Intro to open quantum systems:

Quantum operations, CP maps, Kraus Representation

 

 

Lecture #7

Caves Notes

Podcast 18

 

 

Mar. 29

MAKEUP

 

 

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation

 

Lecture #8

Podcast 19

 

 

Apr. 2

 

Derivation of the Lindblad Master Equation

Born-Markov approximation

 

 

Podcast 20

 

 

Apr. 4

 

Examples of Master Equation Evolution:

Damped two-level atom

 

Lecture #9

Podcast 21

 

 

Apr. 9

 

Damped Simple Harmonic Oscillator

 

 

Podcast 22

 

 

Apr. 11

Fokker-Planck Equation and Decoherence

 

Podcast 23

 

 

Apr. 16

 

Quantum Trajectories I

Measurement theory

Lecture 11

Molmer 1

Podcast 24

 

Apr. 18

 

Continuation

Nonlinear Stochastic Jump Equation

 

Podcast 25

 

 

Aprl. 19

MAKEUP

 

 

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

Lecture 12

Molmer 2

Podcast 26

 

Apr. 23

 

Quantum Trajectories III

Different Unravelings of the Master Equation

 

 

Lecture 13

Molmer 3

Molmer 4

Podcast 27

 

 

 

Apr. 25

 

On Travel: No Lecture

 

 

Apr. 30

Continuation

Lecture 14

Podcast 28

 

May 2

The Stochastic Schrodinger Equation.

Quantum State Diffusion

 

Podcast 29

 

 

QND measurement and and the Stochastic Schrodinger Equation

Lecture 15

Special Notes

 

 


 

Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4
Problem Set #5