Quantum optics and quantum information

PHYS-454

Media

24, Sideband cooling

06.05.2021, 14:08

26, Rydberg Atoms 2

12.05.2021, 08:02

Damped harmonic oscillator 1

22.03.2023, 11:29

12, Lindblad equation

19.03.2021, 17:56

17, Introduction to quantum computing

24.06.2022, 19:09

3, Bipartite systems - Entanglement

28.02.2021, 12:52

7, Evolution of density matrices

12.03.2021, 13:23

2, Reminders on harmonic oscillators

18.02.2021, 15:56

25, Rydberg Atoms 1

12.05.2021, 08:02

1, Reminders on the two-level system

18.02.2021, 15:56

13, Optical Bloch Equations

27.03.2021, 16:31

Quantum Trajectories 1

22.03.2023, 15:26

Quantum Trajectories 2

26.03.2023, 22:24

9, Evolution of density matrices

16.03.2021, 09:17

23, Sideband cooling

06.05.2021, 14:08

Damped harmonic oscillator 2

22.03.2023, 11:31

6, Quantum Measurements

07.03.2021, 21:00

20, Mechanical effects of light

30.04.2021, 20:31

10, Lindblad equation

19.03.2021, 17:56

16, Introduction to quantum computing

24.06.2022, 19:08

11, Linblad equation

19.03.2021, 17:56

27, Rydberg Atoms 3

12.05.2021, 08:02

Quantum Trajectories 3

26.03.2023, 22:25

5, Quantum Measurements

07.03.2021, 20:59

4, Bipartite systems - Entanglement

28.02.2021, 12:53

21, Mechanical effects of light

30.04.2021, 20:33

8, Evolution of density matrices

12.03.2021, 13:23

22, Mechanical effects of light

06.05.2021, 14:08


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Quantum Optics and Quantum Information


Welcome to the lectures on quantum optics and quantum information !


In this course, you will learn the operation principles of quantum machines, as they are nowadays developed in laboratories and in the emergent quantum tech industry. The focus will be both on the basic concepts, and an in-depth description of some of the most prominent examples using atoms and photons.

This course has a strong synergy with the lecture PHYS-464: Solid state systems for quantum information by Prof. Scarlino.

Lectures

The lecture format will be hybrid: recorded videos, available on weekly basis, will convey the theoretical content and discuss in depth the concepts, in a 'blackboard' style on the iPad, with the notes made available.

Discussion and exercises

A four-hours slot is available on Thursdays from 14:15 to 18:00 in CE 1 100 for discussions and exercises. The discussion part will review in an informal way the content of the current week course, and answer all the questions concerning the concepts.
Exercises are the most important part of the weekly schedule, putting you in position to get familiar with the concepts and apply them to models close to actual quantum machines. For some of the exercises you will be asked to run small guided simulations with Python. Simply follow the link provided for each week to open both the exercise sheet and the corresponding python notebooks.

Paper clubs and presentations

In order to link the lectures and exercises to the frontier of research, several exercises classes will be dedicated to paper reading and discussions. Paper discussions will occur in small groups of ~10 students with one assistant, to favor discussions. Papers will be allocated in advanced and presented by one person in each group. A joint event with Prof. Scarlino's class will take place at the end of the semester. 

Prerequisites

This lecture follows PHYS-453 Quantum Electrodynamics and Quantum Optics given in the fall semester. The topics are largely independent, even though a few notions will be only very superficially described in order to avoid repetitions. This includes among other topics the field quantization, light-matter interactions, phase-space methods and photon detection. These are covered in many textbooks, such as Grynberg-Aspect-Fabre, or Scully. References on specific topics can be given upon request.




Lecture 1: Introduction

Quantum devices, reminders (two-level systems, harmonic oscillators)

Bibliography:

  • S. Haroche and J.M. Raimond Exploring the quantum,  Chapter 3

Lecture 2: Bi-partite systems, entanglement, density matrices

Bipartite systems, Schmidt decomposition, density matrices, entanglement entropy

Bibliography:

  • J. Preskill: Lecture notes Chap. 2
  • M. Nielsen and I.L. Chuang Quantum computation and Quantum information Chap 2

Video : Entanglement

Lecture 3: Quantum measurements

Generalized measurements, POVMs

Bibliography:

  • J. Preskill Lecture notes Chap 3
  • M. Nielsen and I.L. Chuang, Quantum computation and quantum information, Chap 2 and 8

Video: Quantum measurements 1
Video: Quantum measurements 2


Lecture 4: Evolution of density matrices

Super-operators, quantum channel examples

Bibligraphy:

  • S.Haroche and J.M. Raimond, Exploring the quantum, Chap 4
  • J. Preskill Lecture notes Chap 3
  • M. Nielsen and I.L. Chuang, Quantum computation and quantum information, Chap 2 and 8


Paper club 1 – 20.03.2025

This week's exercise session is a paper club. We will read 3 papers. There are no videos nor exercise sheets this week, but everybody has to read carefully one of the three papers.

You have received an email telling you which group you belong to. For this week, students of group 1 are presenting a paper, students of groups 2 and 3 are questioning the presenters. Presentations will last 35 minutes, followed by a 10 minutes-long discussion and a short break.

For the organization, everyone should register in this link, by putting his/her name in the presenter or questionner box (depending on which group you belong), for one of the three papers.

How to structure a presentation:
  • the first 15 minutes should be dedicated to the context and motivation of the paper (why should we care?)
  • the next 10-15 minutes should be dedicated to the results themselves
  • the last part should present the limitations and perspectives
How to prepare a question:
  • read the paper carefully including the technical aspects.
  • be critical on the data presentation, techniques used, conclusions drawn
  • search for an answer to your criticims in the paper and in case you do not find a good answer there, it means it is a good question!


Lecture 5: Lindblad equations

Markovian evolution and Lindblad equation, fundamental exemples: optical Bloch equations, damped harmonic oscillator

Bibliography:

  • S. Haroche and J.M. Raimond Exploring the quantum Chap 4
  • J. Preskill Lecture notes chap 3
  • D.F. Walls and G.J. Milburn, Quantum Optics Chap 6


Lecture 6: Optical Bloch equations and damped oscillator

Two fundamental examples of open quantum systems. Formulation, stationary solutions, interpretation and extensions

Bibliography:

  • D.F. Walls and G.J. Milburn, Quantum Optics Chap 10
  • S. Haroche and J.M. Raimond, Chap 4.4


Lecture 7 : Quantum trajectories

Stochastic Schrödinger equation, interpretation, Monte-Carlo wave-function algorithm, weak continuous measurements, quantum state diffusion

Bibliography:

  • H. Wiseman and G. Milburn, Quantum measurement and control, chap 4
  • H. Carmichael, An open systems approach to quantum optics, chap 7 section 5, chap 8
  • See also the online lectures of Prof. Ivan Deutsch https://youtu.be/qZEdTt5B7Zo and following.

Lecture 8: Mechanical effects of light

Motional effects on light-matter interactions, Doppler shifts, semi-classical forces on the two-level atom, Doppler cooling.

Bibliography:

  • H. Metcalf and P. van der Straten, Laser cooling and trapping, chap3
  • D. Guéry-Odelin and C. Cohen-Tannoudji, Advances in atomic physics, chap 11
  • More advanced presentation: C. Gardiner and P. Zoller, The Quantum World of Ultra-Cold Atoms and Light, Book II, Chap 15

Paper club 2 – 01/05/2023

The 2nd paper club is held on 17th April, following the same organization of Paper Club 1. We will read 3 papers. There are no videos nor exercise sheets this week, but everybody has to read carefully one of the three papers.

For Paper Club 1, you had received an email telling you which group you belong to. For this week, students of group 2 are presenting a paper, students of groups 1 and 3 are questioning the presenters. Presentations will last 35 minutes, followed by a 10 minutes-long discussion and a short break.

For the organization, everyone should register in this link, by putting his/her name in the presenter or questionner box (depending on which group you belong to), for one of the three papers.

How to structure a presentation:
  • the first 15 minutes should be dedicated to the context and motivation of the paper (why should we care?)
  • the next 10-15 minutes should be dedicated to the results themselves
  • the last part should present the limitations and perspectives
How to prepare a question:
  • read the paper carefully including the technical aspects.
  • be critical on the data presentation, techniques used, conclusions drawn
  • search for an answer to your criticims in the paper and in case you do not find a good answer there, it means it is a good question!

Lecture 9: Sideband Cooling

Resolved sideband spectrum, sideband cooling.


Bibliography:

  • C. Gardiner and P. Zoller, The Quantum World of Ultra-Cold Atoms and Light, Book II, Chap 15

Extra material: Introduction to quantum computing

For students who never had an introduction to quantum information processing.
DiVincenzo criteria, quantum circuits, exemple: quantum teleportation

Bibliography:


Lecture 10: Rydberg atoms

Reminders on the hydrogen-like atoms, scaling with principal quantum number. Dipole-dipole interaction, van der Waal forces, Rydberg blockade. 2-qubit gates, quantum simulation of spin models

Bibliography:



Lecture 9 : Trapped ions

Trapped ion systems, geometric phase gate, Cirac-Zoller gate, Mølmer-Sørensen gate

Bibliography:

  • C. Gardiner and P. Zoller, The Quantum World of Ultra-Cold Atoms and Light, Book II, Chap 15
  • S.Haroche and J.M. Raimond, Exploring the quantum, Chap 8

Paper Club 3 – 22/05/2022

The last paper club of the semester will be a joint paper club with the class of Prof. Scarlino, to see and discuss together the different platforms for quantum

Please register below for one of the papers as a presenter or questionner.

Each presentation should be about 30 minutes long, followed by roughly 10 minutes discussion. Keep in mind that part of the audience didn't attend the Quantum Optics class, please take care in preparing a proper introduction so that the paper presentation could be enjoyed by everyone.

Lecture 9: spin ensembles

Dicke operators and states, coherent spin states for spin ensembles. Introduction to quantum metrology, Fisher information and quantum limits. Collective light-matter coupling, Tavis-Cummings model.

Note: the quantum  metrology section is a complement, and will not be part of the requirements for the exam

Bibliography:

  • S. Haroche and J.M Raimond, Exploring the Quantum Part 4.7
  • H. Wiseman and G. Milburn, Quantum measurement and control, Chap 2
  • L. Pezze and A. Smerzi, Quantum theory of phase estimation. arXiv:1411.5164

Lecture 13 : Digital quantum simulation

Introduction, Lloyd algorithm, Jordan-Wigner representation

Bibliography:

Lecture 14 : Analog quantum simulation

ultracold gases, Bose-Einstein condensation, introduction to optical lattices and Feshbach resonances.

Bibliography


Exam :

Written exam 16.06.2023 from 15:15 to 18:15

Room GC A3 30
The exam consists in a written set of exercises to be solved in 3 hours.

All written documents are allowed, including printouts lecture notes, books or exercise solutions, but no internet connectable devices. I will bring printouts of the lecture notes, and also a copy of the following books: Haroche and Raimond, Chuang and Nielsen, Gardiner and Zoller. These will be available during the exam (in case several people request it at the same time, we will organize slots of 5 minutes max per person).

Grading will be done as follows: all exercises are corrected and the exam grade is calculated from the best of the exercises. The other exercises give a few bonus points (up to 0.5 out of 6).