Physique quantique

The aim of this lecture is to provide a description of quantum transport in disordered systems, with an emphasis on important phenomena like weak localization, Anderson localization and the Anderson metal-insulator transition. During the lecture, a number of important theoretical tools needed to describe quantum particle scattering in the presence of spatial disorder will be introduced in a pedagogical fashion, such as the Green's function technique, diagrammatic approaches to weak localization and transfer matrices. The lectures will be also illustrated by experimental examples and tutorials, especially taken from the physics of quantum gases and  condensed matter.

The goal of this course is to introduce the main concepts and challenges of quantum computing, a new set of technologies and techniques that promise to solve hard computational problems.

Recent years have seen enormous experimental progress in preparing, controlling and probing quantum systems in various regimes far from thermal equilibrium. Examples include systems as ultra-cold atomic quantum gases under time-dependent perturbations, driven non-linear cavity QED systems or strongly correlated electrons in solid-state materials under ultra-fast optical excitations.

Since the 80’s, laser cooling has enabled the production of sub-milliKelvin dilute atomic gases - which can be further cooled to the nanoKelvin regime.

The lectures are in English, the TDs are in French. See below for the course description in English.

Ce cours donne une introduction aux principes de base de la mécanique quantique. 

Nous commençons par une étude détaillée des systèmes à deux états (spin 1/2, qbit,...). Cela permet de bien comprendre les principes de la mécanique quantique sans formalisme mathématique compliqué, et de voir des applications importantes comme le maser ou la résonance magnétique. Nous étudions en quelques détails le lien entre le groupe des rotations de l'espace et les spins 1/2.

Ensuite, un long chapitre traite des systèmes composés de plusieurs de ces systèmes à deux états (N spins 1/2, N qbits, ...). On verra la notion importante d'états intriqués, les inégalités de Bell, le théorème de non-clonage et le protocol de télé-portation quantique, ainsi que le calcul ZX pour la simplification des circuits quantiques. 

Dans la deuxième moitié du cours nous abordons la description d'une particule évoluant dans l'espace et dans un potentiel. Après l'introduction des notions mathématiques (espace de Hilbert de dimension infinie, opérateurs auto-adjoints et théorème spectral, transformée de Fourier, et l'explication détaillée des bases impropres x et p) on étudie quelques systèmes simples à une dimension comme les marches de potentiel et l'omniprésent oscillateur harmonique. Nous terminons par la théorie des perturbations.

L'étude des systèmes à 3 dimensions, du moment cinétique et des problèmes à potentiel central sera réservé au deuxième cours au printemps.

Ce cours sera accompagné par des notes écrites détaillées (en anglais).

Le cours est complété par des travaux dirigés (en français) où sont traités de nombreux exemples, le plus souvent inspirés par des données expérimentales.

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English version :

These lectures are an introduction to the fundamental concepts and applications of quantum mechanics.

We begin with a detailed study of two-state systems (spin 1/2, qbit, etc). This will allow us to understand  the principles of quantum mechanics without having to deal with any complicated mathematical formalism. It will also allow us to discuss some important applications such as the maser or magnetic resonance. We study in some detail the relation between the group of spatial rotations and the spin 1/2.

Then a long chapter deals with systems composed of several  2-state systems (N spin 1/2, N qbits, etc). We will see the important notion of entangled states, Bell's inequalities, the no-cloning theorem and the quantum teleportation protocol, as well as the ZX calculus that plays an important role in quantum circuit simplification.

The second half of these lectures is devoted to the quantum mechanical treatment of a particle that evolves in space in some potential. A long chapter will introduce the necessary mathematical concepts (Hilbert space of infinite dimension, self-adjoint operators and spectral theorem, Fourier transform, as well as a detailed discussion of the generalised basis' of position or momentum eigenstates). Then we discuss a few simple systems of a particle in one spatial dimension, like the potential well, the tunnel effect and, of course, the ubiquitous harmonic oscillator. This part ends with stationary and time-dependent perturbation theory.

The study of systems in 3 spatial dimensions, the angular moment, and central potential problems will be dealt with (among others) in the second course in the spring.

There are detailed lecture notes in English for this course.

In addition to the lectures, there are exercise sessions (in French) during which numerous applications and examples are treated, often inspired by experiment and real experimental data.