M2 Laser Optics Matter

Marc CHENEAU (IOGS) Igor FERRIER-BARBUT (CNRS-IOGS).

Lecture 1: Overview of the course. Reminder of statistical physics. Thermodynamics of ideal gases Bosons, fermions, and the de Broglie wavelength. Lecture 2: Introduction to laser cooling and trapping. Bose-Einstein condensates: Ideal Bose gases. Lecture 3: Weakly-interacting Bose-Einstein condensates at zero temperature: from vanishingly small interactions to Thomas-Fermi regime. Introduction to the second-quantization formalism for bosons and fermions. Lecture 4: Microscopic theory of the Bose gas and Bogoliubov theory. Quantum depletion; superfluidity. Lecture 5: Optical lattices: From one-body to many-body physics. The superfluid to Mott transition. Lecture 6: Degenerate Fermi gases: Ideal Fermi gases. Interacting Fermi gases: Fermi superfluids, BCS theory, BEC-BCS crossover. Lecture 7: Dynamics of correlated quantum systems.

This set of lectures is an introduction to the modern physics of ultracold atoms and to the recently emerged notion of quantum simulators. The lectures start with a reminder of quantum statistical physics and an introduction to laser cooling and manipulation of neutral particles. It provides the students with the necessary elements and tools to address all the topics of the course. The main part of the lectures focus on the microscopic theories of and advanced experiments on Bose-Einstein condensates, degenerate Fermi gases, and optical lattices. Fundamental concepts, such as thermodynamical properties, quasi-particle excitations, quantum depletion, and superfluidity are discussed in detail. Both equilibrium and non-equilibrium phenomena are addressed.

After the lectures, the students will master the most important discoveries in the field of ultracold atoms and quantum simulators of the last decades. They should then be able to read and understand a modern paper of the field of ultracold atoms, and to enter this field with the relevant knowledge.

- Elementary Notion of classical statistical Physics - Elementary Notion of Quantum Physics.

[1] J.L. Basdevant, J. Dalibard, and M. Joffre, Mécanique Quantique (Presse de l’Ecole Polytechnique; Available also in English at Springer, 2006). [2] B. Diu, D. Lederer, and B. Roulet, Physique Statistique (Hermann, Paris, 1996). [3] C.J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, 2008). [4] L.P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon press, Oxford, 2004).

Janvier - Février.

PALAISEAU

Arnaud DUBOIS (IOGS); Emmanuel BEAUREPAIRE (Ecole Polytechnique); Henri BENISTY (IOGS); Cédric BOUZIGUES (Ecole Polytechnique); Nathalie WESTBROOK (IOGS).

? INTRODUCTION TO OPTICAL IMAGING OF BIOLOGICAL MEDIA

? INTRODUCTION TO CELL BIOLOGY

? OPTICAL MICROSCOPY Fluorescence microscopy, confocal microscopy. Full?field imaging techniques. Organic/inorganic fluorophores.

? FLUORESCENCE TECHNIQUES Single?molecule tracking, Fluorescence Recovery After Photobleaching (FRAP), Fluorescence Correlation and Cross?Correlation (FCS, FCCS), Fluorescence lifetime imaging (FLIM), Fluorescence Resonant Energy Transfer (FRET).

? SUPER?RESOLUTION IMAGING Total Internal Reflection Fluorescence microscopy (TIRF), 4? microscopy, Stimulated Emission Depletion microscopy (STED), Stochastic Optical Reconstruction Microscopy (STORM), PhotoActivated Localization Microscopy (PALM).

? OPTICAL TWEEZERS Single molecule manipulation.

? DNA and PROTEIN MICRO?ARRAYS

? NON?LINEAR MICROSCOPY Two?photon excitation fluorescence microscopy, Harmonic generation microscopy; Coherent Anti?Stokes Raman Scattering (CARS) microscopy.

? OPTICAL COHERENCE TOMOGRAPHY.

Course Objectives: To give insights into modern research trends in biophotonics. To provide in particular an overview of the various optical techniques available for biomedical imaging and detection, giving their characteristics and highlighting their advantages and drawbacks.

On completion of the course students should have knowledge of most optical techniques available for imaging and detection in the fields of biology and medicine. The general principles and typical performance of theses techniques should be known.

Basics of ray optics, wave optics, electromagnetism, nonlinear optics and quantum mechanics. Basics of biochemistry. Basics of DNA and proteins.

? P. N. Prasad, Introduction to Biophotonics, Wiley, 2003¬ ? J. R. Lakowicz, Principles of fluorescence spectroscopy, 3rd edition, Springer, 2006 ¬ ? J. Mertz, Introduction to optical microscopy, Roberts & Co. Publishers, 2009¬ ? M. Müller, Introduction to Confocal Fluorescence Microscopy, SPIE Press, 2006¬ ? R. Rigler, H. Vogel (eds.), Single molecules and Nanotechnology, Springer, 2008¬ ? P. Selvin, T. Ha (eds.), Single?Molecule Techniques: A Laboratory Manual , CSH Lab. Press, 2008¬ ? P. R. Selvin, Methods in Enzymology, Vol. 124, Academic Press (1995), p. 300¬ ? W. Drexler, J.G. Fujimoto

Janvier - Février.

PALAISEAU

Isabelle ZAQUINE (Télécom ParisTech, LTCI) Eleni DIAMANTI (LTCI) Damian MARKHAL (LTCI) Romain ALLEAUME (Télécom ParisTech, LTCI).

Syllabus:

- Useful quantum physics notions; - Entangled photon pair sources and single photon detectors; - Teleportation, entanglement swapping; - Cryptography, quantum key distribution systems; - Device independent security; - Quantum state discrimination.

This course aims to give the state of the art in quantum communications
- components and their performance
- examples of protocols
- experimental implementations
- the major challenges of the domain

On completion of the course students should be able to:
- understand the design of quantum communication systems
- understand the major protocols
- calculate key rates in quantum key distribution
- characterize the quality of entanglement of a photon pair source
- identify some major flaws in a quantum communication system design
- contribute to the design of new quantum communication experiments
- contribute to the development of new quantum information protocols.

Basics electromagnetism, quantum physics, quantum optics (field quantization).

There is no comprehensive book on this subject.

Janvier - Février.

PALAISEAU

Olivier DULIEU (LAC, Université Paris Sud) Maxence LEPERS (LAC, Université Paris Sud) Goulven QUEMENER (LAC, Université Paris Sud).

1. Introduction to ultracold (molecular) gases (3h) 2. Long-range interactions between atoms and molecules (9h) 2.1 Reminder: atomic and molecular quantum numbers 2.2 Calculation of electrostatic energy between two charge distributions 2.3 Long-range interactions in ultracold matter 3. Atomic and molecular collisions and control by electromagnetic fields (9h) 3.1 General features of scattering theory 3.2 Partial waves method 3.3 Magnetic field control of ultracold matter. Formation of Feshbach molecules by magneto-association 3.4 Electric field control of ultracold matter. Controlling long-range interaction between molecules.

Course Objectives:
- Multipolar expansion in Cartesian and spherical coordinates; application of quantum perturbation theory to calculate long-range interactions; examples of their importance for modern research in ultracold gases.
- Theory of ultracold collisions (partial waves). Control of interactions and dynamics with magnetic and electric fields.

Quantum mechanics, basics in atomic and molecular physics.

Janvier - Février.

ORSAY

Marie?Pierre FONTAINE?AUPART (ISMO, Orsay) Lionel POISSON (LIDyL, Saclay) Jérémie CAILLAT (LCPMR, UPMC).

Contenu du cours:

1?Dynamique résolue en temps. Technique Pompe/sonde, conceptualisation, expériences, mécanismes de la relaxation électronique. 2?Spectroscopie résolue en temps à l’échelle atto?seconde : Génération atto?seconde, dynamiques attosecondes: une nouvelle façon de sonder la dynamique. 3? Application aux complexes biologiques Une visite du server laser ATTOLAB et des expériences attenantes sera organisée dans le cadre de ce module.

Ce cours vise à faire découvrir les techniques existantes pour le suivi résolu en temps des dynamiques prenant place au sein de systèmes moléculaires. Nous partirons de résultats expérimentaux pour aborder les phénomènes physiques et chimiques qui gouvernent ces dynamiques. Nous explorerons des phénomènes se déroulant à diverses échelles de temps : de l’atto?seconde pour des processus électroniques, femto/picoseconde pour des processus vibrationnels et des échelles de temps jusqu’à la milliseconde pour les processus biologiques.

Compétences attendues à la fin de l’UE: Compréhension de la physique qui permet de produire ou de sonder un phénomène dépendant du temps dans un système moléculaire. Connaissance de divers processus de relaxation de l’énergie. Connaissance sur l’interaction laser?molécule sous diverses conditions.

Connaissances en physique des lasers et spectroscopie.

H. Zewail, J. Phys. Chem. A 2000, 104, 5660?5694.

Janvier - Février.

ORSAY

P. FERDINAND F. BENABID (XLIM Limoges et Glophotonics) G. BOUWMANS (Lille, IRCICA).

Capteurs à fibres optiques (9h) (P. Ferdinand) L’utilisation des fibres comme capteurs conduit à des dispositifs répandus et très versatiles - avec réseau de Bragg pour le contrôle des déformations, - avec biréfringence, ou avec effets magnéto-optiques, pour la détection le long de la fibre de nombreuses quantités physiques extérieures, dont la température par exemple.

Fibres microstructurées (6h) (F. Benabid, XLIM Limoges et Glophotonics) Les propriétés photoniques remarquables des fibres optiques microstructurées, dites aussi fibres à cristaux photoniques, sont exposées, et des applications avancées sont présentées.

Fibres pour la manipulation et la génération de lumière (6h) (G. Bouwmans, Lille, IRCICA) L’utilisation de phénomènes nonlinéaires dans les fibres, couplé à une meilleure maitrise des formes temporelles des signaux a fait fleurir des approches très riches tant sur le plan de la physique que des applications Ces nouveaux domaines seront expliqués.

L’objectif du cours est de familiariser les étudiants avec les avancées expérimentales et conceptuelles survenues depuis 1995 dans le domaine des fibres optiques et de leurs utilisations passive et active en optique non linéaire et laser.

Bases des télécoms optiques (fibres, modes, débits), base des milieux structurés (notion de bande interdite à 1D), couplage de mode.

Capteurs à fibres optiques : - « Capteurs a fibres optiques et réseaux associés », Pierre Ferdinand (Ed. Lavoisier / Tec & Doc 1999) Voir aussi le "MRS Bulletin" Volume 27, No. 5, May 2002, - Fibres microstructurées : voir le chapitre 11 dans J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, Towards Nanoscale Photonic Devices, 2nd ed. Heidelberg: Springer, 2008. - Nonlinear Fiber Optics (2013, Fifth Edition) A volume in Optics and Photonics , Agrawal, Govind ISBN: 978-0-12-397023-7.

Janvier - Février.

PALAISEAU

Janvier - Février.

PALAISEAU

Pierre MAHOU (Laboratoire d’Optique et Biosciences, CNRS?Ecole Polytechnique) Louis DANIAULT (Laboratoire d’Optique Appliquée, Ecole Polytechnique) Pascal SALIERES (Laboratoire Interactions, Dynamiques et Lasers, CEA-Saclay).

1. Présentation. Propagation d’une impulsion brève. Etirement et compression. Façonnage temporel. 2. Génération, amplification. Caractérisation temporelle, mesure de phase spectrale. 3. Phénomènes non?linéaires : mélange de fréquence, effet Kerr, effet Raman, génération de continuum spectral… 4. Applications : spectroscopie ultrarapide, contrôle cohérent, spectroscopie multidimensionnelle, métrologie des fréquences. 5. Applications : photoablation et micro?usinage, imagerie (microscopie, nanoscopie), génération de rayons X. 6. Génération d’harmoniques d’ordre élevé. 7. Génération et applications d’impulsions attosecondes (10^?18 s).

Les objectifs de ce cours sont de présenter d’une part les propriétés remarquables des impulsions lasers ultrabrèves (sub?picoseconde) et les principes de leur génération, et d’autre part les applications de plus en plus nombreuses dans des domaines très variés : spectroscopie, microscopie, métrologie, nouveaux types de sources de rayonnement, etc…Ce cours introduit les notions et outils nécessaires pour comprendre les phénomènes mis en jeu, ainsi que les techniques expérimentales permettant d’engendrer, amplifier, caractériser et manipuler les impulsions dites « femtosecondes ».

A l’issue du cours les étudiants maitrisent les outils nécessaires à la modélisation et à l’utilisation des impulsions courtes, les relations entre durée et spectre, la notion de phase spectrale. Ils connaissent le principe de génération des impulsions brèves et les techniques de caractérisation telles que le FROG ou le SPIDER. Ils ont étudié les applications les plus courantes, et plus en détail la génération d’impulsions attosecondes.

Optique linéaire et non?linéaire, Lasers, Optique de Fourier.

Femtosecond Laser Pulses, Principles and experiments, Claude Rulliere, Ed. Springer, Advanced Texts in Physics, 2005 The Elements of Non?linear Optics, Paul N. Butcher, David Cotter, Cambridge studies in Modern Optics 9, 1991.

Janvier - Février.

PALAISEAU

Rosa TUALLE-BROURI (IOGS) Hans LIGNIER (LAC, Université Paris-Saclay).

I – Quantification du champ électromagnétique - Nature du photon – espace de Fock ? Etats cohérents - Action d’une séparatrice – coalescence de photons - Quadratures ? tomographie quantique ? fonction de Wigner - Problèmes multimodes – interférences à 1 photon

II – Propagation du champ quantique dans les milieux matériels - Amplification paramétrique optique - Génération de vide comprimé – paires EPR - Génération conditionnelle d’états quantiques - Applications: intrication, inégalités de Bell, téléportation, finalité du calcul quantique.

III - Introduction sur le refroidissement - Espace des phases : comparaison classique/quantique - Concept d’entropie: Définition de Boltzmann, de Shannon et de Von Neumann - Evolution

IV – Refroidissement vers le régime ultra-froid - Rappels - Evaporation - Refroidissement avec peu ou sans émission spontanée? - Formation de molécules ultra-froides

V – Refroidissement et ralentissement en régime froid - Refroidissement non-optique - Techniques de décélération.

Objectifs du cours:

- 1ère partie : Rosa Tualle?Brouri : Manipulation d'états quantiques de la lumière:
Les objectifs sont d’étudier l’optique quantique et ses applications. Seront abordés : la nature du photon; l’amplitude et la phase au niveau quantique ; l’intrication ; la propagation du champ quantique dans les milieux matériels ; des notions d’information quantique ; ainsi que les techniques expérimentales associées.

- 2ème partie : Hans Lignier : Manipulation d’atomes, d’ions ou de molécules froides :
Seront abordés : l’action d’un laser sur un atome isolé ; le piégeage de particules ; le passage d’un état quantique à un autre ; le refroidissement ; ainsi que les techniques expérimentales associées à ces thèmes.

A la fin du cours un étudiant doit pouvoir lire, expliquer et évaluer les ordres de grandeurs présents dans les articles récents que ce soit en optique quantique ou en manipulation de particules froides par champs électromagnétiques.

Des pré?requis de base en mécanique quantique sont nécessaires comme par exemple décrits dans le livre Mécanique quantique (Cohen?Tannoudji, Diu, Laloë).

Des notes de cours seront distribuées. STIRAP, RAP : Bruce W. Shore Interaction matière-rayonnement : Jean-Michel Raimond, Paul Berman.

Janvier - Février.

PALAISEAU

Yannick De Wilde (Institut Langevin, ESPCI ParisTech) Samuel Grésillon (Institut Langevin, SU) Ludovic Douillard (CEA).

Syllabus:

- Classical optical microscopy and Scanning electron microscopy. - Atomic force microscopy (AFM). - Scanning tunnelling microscopy (STM). - Theoretical concepts of near?field optics. - Near?field scanning optical microscopy (NSOM) I : near?field probes. - Near?field scanning optical microscopy (NSOM) II : active near?field microscopy. - Near?field scanning optical microscopy (NSOM) III : applications and new trends. - Seminar and Visit of near?field microscopy installations.

The purpose of the course is to provide a detailed description of scanning probe microscopes and electron microscopes, which are the main instruments required to perform nanoscale imaging of various physical properties, to investigate the world of nanoscience and nanotechnology both in academic and industrial research laboratories. The course describes the instruments and the basic principles on which they rely, and explains their modes of operation with illustrative examples.

At the end of the course, the students should have acquired a deep understanding and feel ready to use without apprehension, any of the near?field microscopes described in the course. The latter are the roots of the majority of imaging instruments used in nanoscience, which only differ according to the physical quantities which they probe.

A general background in physics is required to follow the course, mostly oriented towards experimental aspects.

- « Les nouvelles Microscopies – A la découverte du nanomonde », L. Aigouy, Y. De Wilde, Ch. Frétigny, EDITIONS BELIN –COLLECTION ECHELLES (2006). - « Principles of Nano?Optics », L. Novotny and B. Hecht, Cambridge University Press (2006). - « Near Field.

Janvier - Février.

PALAISEAU

- Sensing and imaging with light: Speckle - Roughness and diffraction Measurement of object deformations by Speckle Interferometry Spatial Light Modulators (SLM) Homodyne / Heterodyne sensors

- Optical fibers & telecommunications: Slow and fast lig.

Course based on strong emphasis on hands-on training, which is inseparable from top-level classroom training.
Labwork subjects intend to reflect the most recent advances in research in all areas of modern optics, and in state-of-the-art optical technologies.
The course provides opportunities to perform top-level labwork in instrumental optics (spatial light modulators, phase-shifting interferometer, etc.), optical telecommunications (erbium-doped fibre amplifiers, 10 Gb/s digital transmission), and quantum physics (source of entangled photons, saturated absorption).

On completion of the course students should be able to handle experimental techniques and protocols essential in modern experimental physics.

Http://www.institutoptique.fr/en/Education/Ingenieur-Grande-Ecole/Labwork.

Janvier - Février.

PALAISEAU

Charles BOURASSIN-BOUCHET (IOGS).

Contenu du cours:

- physique de l’interaction lumière X - matière - source synchrotron - optiques et imagerie X - notion d’optique ultrabrève - source harmonique et impulsion attoseconde - laser à électron libre.

L’objectif de ce module est de faire découvrir aux étudiants la physique et l’optique aux très courtes longueurs d'onde (domaine spectral de l'extrême ultraviolet aux rayons X). On s'intéressera aux problématiques des composants optiques, de l'imagerie, des sources de lumière telles que les synchrotrons, les sources à génération d’harmoniques d’ordre élevé pour la génération d'impulsion attoseconde, les lasers à électrons libres et la physique au temps ultracourt.

Ce domaine est en plein essor au niveau local (Synchrotron SOLEIL, station laser X à Paris Sud, ligne de lumière attoseconde au CEA Saclay, Laser intense APOLLON) et également au niveau international (Lithographie EUV, nouvelles sources laser à électrons libres X-FEL aux USA et en Europe)…

Compétences attendues à la fin de l’UE: Avoir une compréhension générale de la physique et de l'optique aux courtes longueurs d'onde et aux temps ultrabrefs.

Physique et optique générale.

David Attwood, Soft X-Rays and Extreme Ultraviolet Radiation (Cambridge University Press) Jens Als-Nielsen and Des McMorrow, Elements of Modern X-ray Physics (Wiley).

Janvier - Février.

PALAISEAU

Emmanuelle DELEPORTE (ENS Paris-Saclay) Patrick BOUCHON (ONERA).

Partie I : Physique des excitons - Excitons dans les semiconducteurs inorganiques - Excitons dans les semiconducteurs organiques - Excitons dans les semiconducteurs hybrides (pérovskites) - Influence de la dimensionnalité des structures sur les effets excitoniques - Influence du champ électrique - Influence du champ magnétique

Partie II : Photodétection A) Jonction P-N B) Photovoltaïque - Filière silicium : principe (jonction P-N), rendements, limitations - Filière organique : principe (couches de transport), rendements, limitations - Filière pérovskite : principe, rendements, limitations - Filière tandem : principe, rendements, limitations C) Photodétecteurs quantiques - Détecteurs Photoconductifs - Détecteurs à puits quantique - Détecteurs à avalanche - Bruit de détection - Détectivité

Partie III : Photoémission - Guides d’ondes - Physique de l’oscillation laser - Lasers à semiconducteurs (interbande et intersousbande) - Optiques non linéaires des structures quantiques.

L’objectif de ce cours est d’étudier les effets excitoniques existant dans les différents types de semiconducteurs ainsi que dans les hétérostructures de semiconducteurs. Ces effets excitoniques sont à l’origine des dispositifs photoniques aujourd’hui largement utilisés tels que les cellules photovoltaïques, les lasers et les détecteurs quantiques. Contrôler les effets excitoniques est un enjeu majeur pour améliorer les performances des dispositifs et en développer de nouveaux.

Physique quantique et physique statistique quantiques de base : spin, systèmes à 2 niveaux, perturbations indépendantes du temps, perturbations dépendant du temps (règle d’Or de Fermi), distribution de Fermi-Dirac.

Janvier - Février.

PALAISEAU

Jean-Pierre HERMIER (UVSQ).

1. Study of 7 articles (1 per session) 2. General analysis 3. Detailed analysis of the results and discussion.

Course Objectives:
1. Analyze recent experiments in the field of nanophysics.
2. Methodology: document analysis (general structure of an article, detailed analysis, overview).
3. Provide an overview of the scientific publishing field.
4. Enlighten and illustrate concepts addressed in other courses through articles.

On completion of the course students should be able to:
- Analyze a scientific paper in detail,
- Identify quickly the key points of a publication.

General concepts in nanophysics and nanophotonics. Key concepts for each paper will be shortly presented at the beginning of each session.

Janvier - Février.

PALAISEAU

Patrick GEORGES (Laboratoire Charles Fabry, Palaiseau) Xavier DELEN (Institut d'Optique Graduate School, Palaiseau).

Contenu du cours (copie des transparents distribués):

- Rappel historique, différents types de lasers, marché des lasers, lasers à gaz - Diodes laser de puissance - Lasers solides pompés par lampes - Lasers solides pompés par diodes de puissance - Conversion de fréquence par effets non linéaires - Lasers à impulsions ultra-courtes (différentes techniques de verrouillage de modes, oscillateurs femtosecondes à saphir dopé au titane, amplification à dérive de fréquence, présentation des chaînes laser femtosecondes commerciales basse et haute cadence, accordabilité par effet paramétrique optique, nouveaux lasers femtosecondes pompés directement par diodes) - Caractérisation spatiale et temporelle d'un faisceau laser - Applications des lasers à impulsions ultra-courtes (spectroscopie non linéaire résolue en temps, microscopie de fluorescence, generation d’impulsions attosecondes, micro-usinage athermique, chirurgie refractive de l’oeil).

L’objectif de ce cours est de présenter un état de l’art des différents types de systèmes lasers, continus ou impulsionnels (jusqu’aux lasers femtoseconde) émettant de l’ultraviolet à l’infrarouge. On insistera sur les différentes technologies mises en place récemment en s’appuyant sur des exemples concrets de lasers (souvent commerciaux). On étudiera les solutions technologiques innovantes de lasers à solides pompés par diode récemment mises en place pour améliorer ces performances. Pour chaque type de lasers, des exemples d’applications de ces sources seront présentés. Les techniques de caractérisation spatiale et temporelle sont présentées.

Compétences attendues à la fin de l’UE :
- comprendre les solutions techniques mises en œuvre dans un système laser (régime continu ou impulsionnel)
- analyse d'articles scientifiques sur la technologie laser
- faire une analyse critique des choix scientifiques et techniques mis en œuvre dans les systèmes laser
- définir une architecture de système laser pour atteindre une bande de longueur d'onde spécifique, une puissance moyenne ou une énergie, une durée d'impulsion
- comprendre la fiche technique d’un système laser
- choisir le système laser le plus approprié pour une application spécifique
- faire une revue scientifique et technique d'une technologie laser spécifique.

Cours en Physique des Lasers, Lasers à Semi-Conducteurs, Optique Non Linéaire, Polarisation, Acousto-optique, Electro-optique.

“Lasers” A Siegman, Stanford University“, (University Science Books, (1986) ISBN 978-0-935702-11-8, “Solid-State lasers Engineering” W. Koechner, Springer 6th Edition ISBN-10: 038729094X ISBN-13: 978-0387290942.

Janvier - Février.

PALAISEAU

Fabien BRETENAKER (ENS Paris-Saclay) Marc HANNA (IOGS) Frédéric DRUON (IOGS) Thierry RUCHON (CEA).

1. Matter-light interaction; Equations of the single-frequency laser 2. Single frequency laser in steady-state regime 3. Inhomogeneous line broadening 4. Transient and Q-switched operation 5. Noise properties of lasers 6. Mode-locking and ultrashort pulses 7. Optical resonators: ray matrices, Gaussian beams, cavity stability 8. Advanced topics in ultrafast optics : carrier-envelope phase and attosecond pule generation.

The course starts with a semi-classical description of light-matter interaction, and establishes Maxwell-Bloch equations. The rate equation approximation is used to provide operational principles of the single frequency laser. Starting from this description, transition broadening mechanisms, dynamical regimes, and noise properties of lasers are described. The spatial aspects are then examined, using paraxial transfer matrices to describe cavity stability and beam propagation. Finally, ultrafast lasers using mode-locking are studied along with related subjects such as the propagation and characterization of femtosecond pulses and attosecond pulse generation.
On completion of the course students should be able to: understand and be able to describe the physical principles underlying laser operation in a wide variety of regimes.

Undergraduate knowledge of electromagnetism and quantum mechanics. A first course in lasers helps, but is not required.

Lecture notes written by Fabien Bretenaker.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

François HACHE (Ecole Polytechnique) Isabelle ZAQUINE (Télécom ParisTech) Marie-Claire SCHANNE-KLEIN (Ecole Polytechnique).

I - INTRODUCTION TO NONLINEAR OPTICS Basics of nonlinear optics Physical origins of the optical nonlinearities

II - NONLINEAR WAVE EQUATIONS Derivation of Maxwell’s equations Nonlinear susceptibilities Nonlinear wave equations

III - 2nd ORDER NONLINEARITIES Manley-Rowe relations 2nd Harmonic Generation Phase matching in uniaxial crystal. Quasi-phase matching in materials Frequency Mixing, Optical parametric amplification and oscillation Spontaneous parametric down conversion Sources of entangled photons based on SPDC

IV - MICROSCOPIC THEORY of the NONLINEAR OPTICAL RESPONSE Notion of polarizability and local field factor Liouville equation: perturbation approach with the density matrix formalism Calculation of the linear susceptibility Calculation of X(2) Calculation of the third-order nonlinear response function for resonant configurations Introduction to the 2D spectroscopy

V - 3rd ORDER NONLINEARITIES Four-wave Mixing Optical Kerr effect Raman Scattering Brillouin Scattering 2 photons Absorption.

Since the laser has been invented, optics opened a new dimension entering the nonlinear world with already numerous applications to light sources and optical processing of information. This course will introduce the students to this domain and enable them to fully master its innovative aspects. It describes the physics of the nonlinear interaction between light and matter from a perturbation approach and shows its consequences on the propagation of optical waves. Its describes in detail the second and third order non linear effects rich in applications.
On completion of the course students should be able to: understand and be able to describe the physical principles underlying various nonlinear interactions.

Undergraduate knowledge of electromagnetism (linear regime, optical properties of anisotropic media…). A first course in nonlinear optics helps, but is not required.

F. Hache, Optique non linéaire, CNRS-EDPSciences, Savoirs actuels, 2016. Lecture notes available at http://paristech.iota.u-psud.fr/site.php?id84 Robert W. Boyd, Nonlinear Optics, 4th Edition, Elsevier Ed BUTCHER, PAUL N. / COTTER, DAVID, The Elements of Nonlinear Optics , Cambridge University Press.1993. F. Sanchez, Optique non line?aire, Ellipses, 1999.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Eric CHARRON.

Several “Hands-on” exercise sessions are provided during this course, as well as two homework problems. Final grades will be based on the two homework assignments (20% each), and on a final exam (60%). Collaboration, limited to two students, on each homework assignment is allowed.

SYLLABUS: I – Time-Dependent Quantum Dynamics II – Phase-space representation of Quantum Mechanics III – Approximate solutions of the time-dependent Schrödinger equation IV – Numerical Methods in time-dependent quantum dynamics V – Molecular Dynamics in the Femtosecond (10-15 s) regime VI – Attosecond (10-18 s) Processes and Strong Field Physics.

This course, with hands-on exercise sessions, will provide a unified treatment for the understanding of quantum dynamical processes taking place in laser-matter interaction, with a particular emphasis on non-linear interactions and on ultra-short processes taking place in atoms and molecules. This will include quantum interferences between indistinguishable pathways, multiple pulse spectroscopy, control of atomic and molecular dynamics, interpretation of spectra and of scattering cross sections in terms of time correlation functions and in terms of potential energy surfaces, femtosecond and attosecond physics, time dependent processes in cold atom physics and finally, strong field non-linear physics. All phenomena will be introduced and explained from a time-dependent quantum mechanical perspective.

On completion of the course, students will gain a good understanding of several theoretical and numerical methods used to describe laser-matter interaction in nowadays explicitly time-dependent experiments. The everlasting development of new laser sources and of controlled time-dependent magnetic fields renders this knowledge a pre-requisite in today’s research in atomic, molecular and optical physics.

Quantum Mechanics courses of L3 and/or M1 level.

Quantum Physics: Introduction to Quantum Mechanics: A Time-Dependent Perspective, D. J. Tannor ; Quantum Mechanics, vol. 1 & 2, C. Cohen-Tanoudji, B. Diu, F. Laloë ; Quantum Mechanics, L. I. Schiff.

Atomic & Molecular Physics: Atomic Physics, C. J. Foot ; Molecular Quantum Mechanics, P. W. Atkins, R. S. Friedman ; Coherent Dynamics of Complex Quantum Systems, V. M. Akulin.

Septembre - Octobre - Novembre - Décembre.

ORSAY

Pascal PARNEIX (ISMO) Cyril FALVO (ISMO).

Chapter 1: Introduction to the intramolecular dynamics ? Born?Oppenheimer approximation ? Quantum yield ? Non?adiabatic couplings ? Time?dependent and time?independent quantum approaches ? Statistical limit and irreversibilty Chapter 2: Electronic energy relaxation in the statistical limit ? Internal conversion ? Intersystem conversion Chapter 3: Vibrational Energy relaxation ? Intramolecular Vibrational Redistribution ? Fragmentation, Isomerisation and IR radiative relaxation ? Classical and quantum vibrational density of states ? Canonical and microcanonical properties of a large molecular system ? Isomer superposition model for a complex potential energy surface ? Transition State Theory Chapter 4: Molecular spectroscopy and linear response theory ? Optical response and auto?correlation function ? Fluctuation?dissipation theorem ? Classical approximation Chapter 5: Molecules coupled to an environment ? Bath as stochastic process, Kubo theory ? Bath as harmonic oscillators, cummulant Gaussian expansion.

Course Objectives:
Understanding the intramolecular dynamics in large excited molecule or cluster
Understanding the effect of vibronic couplings on the intramolecular dynamics
Exploring the different relaxation pathways for a large molecule
Effect of an environment on the molecular optical response

On completion of the course students should be able to identify the coupling operators and the molecular parameters which influence the intramolecular dynamics. They should be able to identify the effect of the intramolecular dynamics on the spectral features. They should be able to use some simple or more refined models for theoretically describing the intramolecular dynamics. From the illustration of experiments proposed in the course, they should be able to identify some typical experimental set?up for studying complex intramolecular dynamics.

Quantum mechanics : Mécanique quantique (Tomes I et II), Claude Cohen?Tannoudji, Bernard Diu, Franck Laloë, Editor: Hermann Molecular physics : Molecular quantum mechanics, Peter Atkins and Ronald Friedman, Editor: Oxford University Press Statistical physics : Elements de physique statistique, Bernard Diu, Danielle Lederer and Bernard Roulet, Editor: Hermann.

Radiationless transitions in polyatomic molecules, Emile S. Medvedev, Vladimir I. Osherov, Editor: Springer?Verlag Energy landscapes: Applications to clusters, biomolecules and glasses, David Wales, Editor: Cambridge university press Statistical physics of nanoparticles in the gas phase, Klauss Hansen, Editor: Springer Principles of nonlinear optical spectroscopy, Shaul Mukamel, Editor: Oxford university press Statistical Physics II, R. Kubo, M. Toda and N. Hashitsume, Editor: Springer?Verlag Statistical Mechanics, D. A. McQuarrie, Editor: Harper&Row.

Septembre - Octobre - Novembre - Décembre.

ORSAY

David CLEMENT (IOGS) Vincent JOSSE (IOGS).

Reminder on coherent propagation of light in optical systems Introduction to the theory of optical coherence and statistical optics Temporal and spatial coherence of optical waves with statistical approach and field correlators Description of the photo?detection process Measurement setups of optical coherence and its application to modern research Speckle phenomenon – general understanding of the main statistical properties Application of speckle phenomena to imaging through a diffusive medium Properties of “subjective” speckle field: from coherent to incoherent imaging.

The class aims at introducing the modern theory of coherence of light and describe applications in connection to current research. Two different topics are considered. The first part of the course (D. Clément) is dedicated to general coherence properties (temporal and spatial) are reviewed in close relation with ideas developed in the context of quantum optics (as field correlator and photo-detection process). The second part of the course (V. Josse) is dedicated to laser speckle phenomena, which is related to spatial coherence properties of the light when propagating to a random scattering medium. An important objective of this part is to introduce the modern field of research of wave propagation and how to use spatial coherence to implement innovative imaging techniques in complex media. In particular a seminar will be given by K. Vynck (LP2N, Bordeaux) on current research topic.
On completion of the course students should be able to: use statistical tools to accurately describe and understand optics and light sources ; use master concepts of second order coherence and their applications to current research and technology; describe and calculate speckle patterns and its properties; understand basic principle of recent concept of imaging through complex media.

Fresnel and Fraunhoffer diffraction theory Application of diffraction theory to simple imaging systems, Fourier filtering Basic mathematics on random variables.

Textbooks/bibliography: - Introduction to Fourier optics, Goodman Joseph W. [prerequisites on diffraction and Fourier filtering] - Statistical Optics, Goodman Joseph W. [prerequisites on random variables: Chapter 2] - Fundamentals of photonics, Bahaa E. A. Saleh, Malvin Carl Teich [Chapter 10] - Speckle phenomena in optics, Goodman Joseph W. - Introduction to the Theory of coherence of and Polarization of Light, E. Wolf A recent review (will be available on course webpage): Light field in complex media: Mesoscopic scattering meets wave control, Review of Modern Physics, 89, 015005 (2017).

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Antoine BROWAEYS (IOGS) David CLEMENT (IOGS).

- Basics of atomic physics - Phenomenological models of light-atom interaction (Lorentz and Einstein models) - Semi-classical approach of light-atom interaction (interaction Hamiltonian, Rabi oscillations, relaxation processes) - Time-evolution of the de.

The course describes the interaction of photons and atoms in different fields of physics and the manipulation of ensemble of atoms with laser beams. It starts with a microscopic description of the interaction between a classical light field and a quantum atom and then it extends the description to ensemble of atoms thanks to the density matrix and Optical Bloch Equations (OBE). Applications of this microscopic description include the radiation pressure force and optical dipole potentials, laser cooling of atomic and molecular gases, slow light and Electromagnetically Induced Transparency (EIT). The course will proceed with the treatment of systems in contact with Markovian reservoirs and the derivation of the Master Equation from which OBEs are obtained. The alternative approach of the Monte-Carlo wave-function for dissipative processes will be presented as well. Finally the Bloch-Maxwell equations for the propagation of light in optically thick media will be introduced, along with applications (i.e. fast/slow light, photon echo or quantum memories).
On completion of the course students should be able to understand and to describe the interaction of laser light with an atom and with an ensemble of atoms in various situations.

- Classical electromagnetism (Maxwell equations, macroscopic polarization and susceptibility, …) - Basics of quantum mechanics (Schrodinger equation, bra and ket, two-level systems, Rotating Wave Approximation, …) - Fourier transforms and linear different.

- “Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light”, G. Grynberg, A. Aspect, C. Fabre – Cambridge Univ. Press, 2010 (in particular the first chapters describe the semi-classical approach and the Optical Bloch Equations.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Jacqueline BLOCH (C2N) Jean-Sébastien LAURET (ENS Paris-Saclay).

I- Optical processes in a two level system: II- Quantum description of the dielectric constant: III- Effect of the dimensionality: IV- Exciton V- Exciton in molecular materials / Defect centers VI- Introduction to the second quantification VII- Quantum dots: Carrier confinement, Spectrum of emission, radiative cascade VIII- Quantum dots in cavity: IX- Quantum wells in cavity: X- Cavity polaritons: quantum fluids of light.

The course aims at describing light-matter interaction in condensed matter systems in close connection with on-going state of the art research. It focuses on semiconductor nanostructures and their use to tailor light matter interaction, realize sources of quantum light and explore quantum fluids of light. The course starts with the description of light-matter interaction using a semi-classical approach (classical light – quantum description of matter). The processes of absorption and emission of light is described as well as their dependence on the dimensionality. The notion of excitonic states is then discussed. The second part of the course is dedicated to cavity quantum electrodynamics (CQED) using condensed matter quantum emitters embedded in integrated high finesse cavities. The properties of quantum dots (fermionic systems behaving as artificial atoms) and their use as bright sources of quantum light will be discussed. Then we will discuss how quantum wells in microcavities provide a platform for the exploration of quantum fluids of light.
On completion of the course, the student will have a deep background on the light-matter interaction in condensed matter, and will have the basis concerning the current issues on CQED with condensed matter quantum emitters.

- Solid State Physics (M1) or the 3h pre-requesite course of LOM master (see website) - Quantum physics (M1) - Electromagnetism (L3).

- G. Bastard “Wave mechanics applied to Semiconductor heterostructures” - PY Yu & M. Cardona: “Fundamental of semiconductors” - Y. Toyozawa: “Optical processes in Solids” - M. Fox: “Optical properties of Solids”.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Laurence PRUVOST (Université Paris Saclay) Fabienne GOLDFARB (Université Paris Saclay).

Le cours complète le cours de mécanique quantique de type L3 ou M1. Son objectif est d’appréhender des méthodes fondamentales, analytiques ou semi-analytiques, pour traiter des problèmes classiques de mécanique quantique.

Cours 1 : Puits carré avec une barrière infinie.
Cours2 : Méthode d’approximation semi-classique WKB.
Cours3 : Couplage discret-continuum.
Cours 4 : Ensemble de N particules identiques. Théorie du champ moyen. Equation de Gross-Pitaevski.
Cours 5 et 6: Atome en interaction avec un champ quantique. Théorie de l’atome habillé.

The aim of the next lectures is to introduce some tools to model the behaviour of quantum opened systems. A common thread will be here the modelization of dissipation and fluctuations due to spontaneous emission : we will see that the introduction of these new tools makes it possible to see different phenomena, which are not visible with the usual closed system models. The approaches developed here are quite general and can be used in many different cases.

Cours 7: Irreversibility in closed systems
Cours 8: Interaction with a reservoir
Cours 9: Heisenberg-Langevin approach.

Le niveau requis intègre les enseignements de mécanique quantique de L3 et M1. Plus particulièrement il est demandé de connaitre • l’équation de Schrodinger, en particulier à une dimension. • L’oscillateur harmonique • L’atome à deux niveaux en interaction avec une onde laser dans l’approximation des grandes longueurs d’ondes. (ce point pourra être vu dans un autre cours proposé au M2).

• Mecanique quantique C Cohen-Tannoudji, B Diu, F Laloe, Hermann • Photons et atomes - Introduction à l'électrodynamique quantique , C Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, InterEditions/Editions du CNRS • Theoretical atomic physics, H Friedrich, Springer • Quantum Optics, M. O. Scully and M. S. Zubairy, Cambridge • Physique quantique , M. Le Bellac, CNRS édition.

Septembre - Octobre - Novembre - Décembre.

ORSAY

Niloufar SHAFIZADEH ( DR-CNRS-ISMO) Jean-Hugues FILLION (Professeur UPMC-LERMA).

Chapitre I- Les bases pour comprendre la structure moléculaire Chapitre II- Structure électronique d’une molécule diatomique Chapitre III- La molécule avec spin électronique -Interaction spin-orbite Chapitre IV- Structure vibrationnelle et rotationnelle d’une molécule diatomique Chapitre V- Interaction molécule- rayonnement Chapitre VI- Moment de transition pour une transition dipolaire électrique à un photon et puis plusieurs photons.

The purpose of this course is to teach the student how to analyze and extract information from a molecular spectrum. Molecular spectra bring quasi directly fundamental information on the structure and geometry of molecules, their potential energy surfaces and, the coupling between different internal angular momenta. These days molecular spectroscopy is a direct and powerful tool to determine the composition and physical properties (for example temperature) of inaccessible environments such as planetary atmospheres, molasses of cold molecules or the heart of a motor or rocket engine.
In this course will detail:
*The models which describe the molecular electronic, vibrationnal and rotationnal wave functions and their symmetries .
*The approximations which allow to describe the nuclear motion in molecules (vibration and rotation).
*The coupling between the orbital angular momentum and the rotational angular momentum
*The selection rules which allow the interaction between the radiation and the molecules
This option is a direct approach for describing the electronic structure of isolated molecules

On completion of the course, the students will be able to analyse a molecular spectrum and extract from it informations on the molecular structure, geometry and the energy levels of the system.

Element of Quantum Mechanic.

*Gerhard Herzberg Molecular Spectra and Molecular Structure volume 1,2,3 *Hollas Spectroscopie Dunod Paris 1998 *Emile Biémont Spectroscopie Moléculaire édition de boeck 2008 *Hélène Lefevre-Brion and Robert Field Spectra and dynamics of diatomic molecules Elsevier Academic Press 2004 *Edmonds Angular Momentum in Quantum Mechanics (Princeton University Press Princeton 1974 *R.N Zare Angular Momentum Undrestanding Spatiale Aspects in Chemistry and Physics Wiley –Interscience publication 1987 *Condon and Shortley The Theory of Atomic Spectra *Jeffrey Steinfeld Molecules And Radiation: An

Septembre - Octobre - Novembre - Décembre.

ORSAY

Henri BENISTY (IOGS) Christophe SAUVAN (IOGS).

Propagation of waves in periodic media is at the heart of many physical phenomena, to start with the formation of bands for electrons in solids. This course addresses the same issue in optics. We start, in particular, with the notion of Bloch modes in optical artificial materials, that is materials structured at sub-wavelength scale. Thanks to the recent progresses in nanofabrication methods, such materials are massively investigated nowadays. By analogy with electrons, we introduce the forbidden photonic band gap and also the idea of artificial materials. These latter lead in particular to the possibility of artificially synthesizing materials that display properties otherwise not found in nature. Theoretical notions such as density-of-states (DOS), light-line ( aka light cone), slow light, etc. are systematically illustrated by applications that have arisen from recent nanophotonics literature. The course is illustrated by a few training sessions (~3 x 1.5h) aimed at rackling with some more depth fundamental concepts.

This course intends to introduce:
1) Fundamentals of electromagnetism of nanostructures,
2) applications of artificial optical nanostructures, and eventually
3) Combination of these optical structures with basic structures for electronic confinement (quantum well and quantum dots) for enhanced light matter interaction (Purcell effect, etc.).

Basics of waves, diffraction, guiding, semiconductors.

Lecture notes available at : http://paristech.iota.u-psud.fr/site.php?id348 [1] H. Benisty, J.-M. Gérard, R. Houdré, J. Rarity, and C. Weisbuch, Eds., Confined Photon Systems : Fundamentals and Applications (Lecture Notes in Physics. Heidelberg: Springer, 1999 [2] J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals, Towards Nanoscale Photonic Devices. Heidelberg: Springer, 2005 [3] H. Benisty and C. Weisbuch "Photonic crystals," in Progress in Optics. vol. 49, E. Wolf, Ed., ed Amsterdam: Elsevier, 2006, pp. 177-315 [4] A. Yariv, Quantum

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Denis GREBENKOV (Ecole Polytechnique).

Lecture 1: Brown's experiment; probability as lack of information about the detailed classical dynamics; central limit theorem, Gaussian propagator and its properties; diffusion equation; passage from micro- to macro-dynamics Lecture 2: Langevin equation as a microscopic description; Fourier/Laplace transform as methods of solution; standard examples for overdamped limit (Brownian motion and Ornstein-Uhlenbeck processes); naive derivation of the Fokker-Planck equation; Ito's formula; forward and backward equations Lecture 3: Generalized Langevin equation; friction memory kernels; anomalous behavior; hydrodynamic effects; Lecture 4: Fluctuation-dissipation theorem; ergodicity Lecture 5: Continuous Time Random Walks as an alternative model for anomalous diffusion; fractional diffusion equation; weak ergodicity breaking Lecture 6: Application to biophysics: optical trapping, FRAP (fluorescence recovery after photobleaching), FCS (fluorescence correlation spectroscopy) The lectures will be complemented by practical works.

Introduction to non-equilibrium statistical physics; presentation of modern problems, physical principles and mathematical methods for analysis of various diffusive processes; illustration of these concepts for several biophysical applications.

On completion of the course students should be able to describe and analyze various natural phenomena governed by non-equilibrium statistical physics.

Basic statistical physics, basic mathematical physics, basic probability course.

P. L. Krapivsky, S. Redner, E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, 2010).

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

- Sensing and imaging with light: Speckle - Roughness and diffraction Measurement of object deformations by Speckle Interferometry Spatial Light Modulators (SLM) Homodyne / Heterodyne sensors

- Optical fibers & telecommunications: Slow and fast lig.

Course based on strong emphasis on hands-on training, which is inseparable from top-level classroom training.
Labwork subjects intend to reflect the most recent advances in research in all areas of modern optics, and in state-of-the-art optical technologies.
The course provides opportunities to perform top-level labwork in instrumental optics (spatial light modulators, phase-shifting interferometer, etc.), optical telecommunications (erbium-doped fibre amplifiers, 10 Gb/s digital transmission), and quantum physics (source of entangled photons, saturated absorption).

On completion of the course students should be able to handle experimental techniques and protocols essential in modern experimental physics.

Http://www.institutoptique.fr/en/Education/Ingenieur-Grande-Ecole/Labwork.

Janvier - Février.

PALAISEAU

Timothée NICOLAS (Ecole polytechnique).

1. Introduction. Interest for plasmas; plasmas in nature and in laboratories; plasmas for thermonuclear controlled fusion; classification of plasmas. 2. Basic notions. Debye length; coupling parameter; electron and ion plasma frequencies; binary collisions and coulomb logarithm. 3. Fluid description and kinetic theory. Distribution functions; mean fields and Vlasov-Maxwell equations; collisional kinetic equation; fluid quantities and fluid equations; closure of fluid equations. 4. Fluid theory of plasma waves. Electrostatic waves in cold plasmas; ion acoustic waves; electromagnetic waves; propagation in inhomogeneous plasmas; BKW approximation. 5. Kinetic theory of electron plasma waves. Landau damping. 6. Trapping of particles in longitudinal waves. Motion of a particle in a finite amplitude wave; circulating and trapped particles; separatrix; wave-particle interaction. 7. Nonlinear waves in plasmas. Ponderomotive force; parametric instabilities of laser beams in plasmas.

This course aims to give an introduction to plasma physics. A particular attention will be given to plasmas created by lasers, as the Saclay area hosts two of the most powerful and energetic lasers in the world, and as the corresponding local scientific community is recognized as being at the top international level.

On completion of the course students should be able to understand the main characteristics of plasma physics, its specificity with regards to other fields of physics; distinguish the main waves propagating in a plasma, and caculate their dispersion relation and their phase velocity; have an insight in the dynamical and nonlinear aspects of plasma physics.

Classical electrodynamics (e.g., Jackson’s text book).

J.-M. Rax, Physique des plasmas, Dunod 2005 (in french).

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

Antoine BROWAEYS (IOGS) Chris WESTBROOK (IOGS).

1. Blackbody radiation according to Planck, Einstein and Bose. Quantization of the harmonic oscillator 2. Quantization of the electromagnetic field. Number states, coherent states, thermal states, squeezed states 3. Interaction with atoms: dipole approximation, perturbation solution for both a classical and a quantum field. Einstein's A and B coefficients revisited 4. Spontaneous emission in vacuum and in a cavity, Fermi's 2nd golden rule. Weisskopf Wigner approach. 5. Photo-electric effect for classical and quantum fields. Theory of photon detection. Action of a beam splitter. 6. Theory of photon detection for multiple photons and multiple frequencies, Hong Ou Mandel Effect 7. Quantum coherence, Hanbury Brown Twiss effect. 8. Non-linear quantum optics, single photon sources, squeezing. 9. Interferometry, noise and entanglement 10. Other topics: teleportation, quantum information, the Jaynes-Cummings model, non-destructive photon detection.

Course Objectives:
- Give a simple introduction to quantization of the electromagnetic field and its interaction with an atom
- Show how some typical optics problems are treated using quantized fields: the photo-electric effect, light detection, shot noise (the standard quantum limit), coherence, the Hanbury Brown Twiss effect
- Discuss effects that cannot be explained with a classical field: spontaneous emission, behavior of single photon states, anti-bunching, the Hong Ou Mandel effect, measurements below the standard quantum limit
On completion of the course students should be able to:
- have a strategy to determine whether a light field is non-classical
- understand a paper discussing modification of spontaneous emission rates and Purcell factors
- understand a paper discussing photon bunching or antibunching
- understand a paper about beating the standard quantum limit in a measurement.

1. Classical electrodynamics, especially use of the Coulomb gauge and dipole radiation 2. Elementary quantum mechanics: Dirac notation, the harmonic oscillator, the hydrogen atom, notions of spin and angular momentum, a little perturbation theory.

- C. Gerry, P.L. Knight, "Introductory quantum optics" Cambridge, 2005. - G. Grynberg, A. Aspect, C. Fabre, "Introduction aux lasers et à l'Optique Quantique", Ellipses 1997. - L. Loudon, "The quantum theory of light", 3rd Ed. Oxford, 2003. - M. Scully, S.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU

The Master’s thesis consists of a research project and thesis, beginning in March and lasting a minimum of 4 months. Visits of laboratories will be arranged to allow students to choose their project. Details about the project must be submitted to the course programme coordinators before the end of January. Please note that administrative procedures including authorisations and clearance from the Ministry of Defense in some laboratories may take up to one month before the student is allowed to start the project. Students should submit their final report to the course programme coordinators before the end of August. The length of the report should be approximately 40 pages; references must be included. The evaluation of the Master’s thesis will take into account the written report (25%), an oral presentation of 30 minutes to be held in the beginning of September (25%) and the overall assessment by the project supervisor (50%).

Mars - Avril - Mai - Juin - Juillet.

Kenza CHERKAOUI Alexia DE GROULARD Renata LEBBE.

This sequence is called IDEAS WELCOME, because your participation and imagination are welcome!
You will be joining the Institut d’Optique students- starting in September, in one of three modules:

IW 1 The intercultural work place
IW 2 American independent films
IW 3 Professional polish

All subjects are handled by experienced teachers, all include advanced language work and real life examples.

Septembre - Octobre - Novembre - Décembre.

PALAISEAU