Program outline

Mobility plan

First Year Syllabus in Torino

Second year Syllabus in Paris

EU 1st term (30 ECTS)

• Electrons and phonons in nanostructures
• Quantum theory of light
• Advanced Solid State Physics
• Photonic quantum devices
• Electronic quantum devices
• 2D Materials
• Nano-objects et atomic scale
• Experimental project (3 weeks)
• Visit of Laboratories

Electrons and phonons in nanostructures (3 ECTS) 

Professors
Prof. C. Voisin (Prof. UP, LPENS),
Prof. E. Deleporte (Prof. ENS Cachan, LPQM),
Ass. Prof. Francesca Carosella (MCF UP, LPENS)

Program :

-Fundamentals of solid state physics:

• Band structure and Bloch theorem 
• Density of states
• Effective mass
• Overview of phonons

-Envelope function approximation

-Electron – phonon interaction: weak coupling regime

• Fermi golden rule
• Rabi oscillations
• Importance of energy loss in opto-electronic devices

-Electron – phonon interaction: strong coupling regime

• Polarons in quantum dots
• Energy relaxation within polaron framework

-Optical absorption in a bulk material:

• Direct absorption, indirect absorption, selection rules
• Excitons

-Optical absorption in a quantum well:

• Interband and intraband transitions
• Type I and type II quantum wells,  superlattice 
• Excitonic effects

-Optical emission in bulk materials and quantum wells:

• Einstein coefficients
• Luminescence
• Different kinds of experience: electroluminescence, photoluminescence, excitation spectroscopy, time-resolved photoluminescence

-Effect of an external electric field on heterostructure electronic states and optical properties

-Effect of an external magnetic field on heterostructure electronic states and optical properties

Examples of problem class:

• Density of states and energy states calculation in various kind of heterostructures
• Determination of electrons lifetime in presence of phonons 
• Calculation of absorption coefficient in a bulk material
• Optical absorption in a quantum well
• Landau levels and magnetoabsorption

Advanced Solid State Physics (3 ECTS)

Professors
Prof. A. Sacuto (Prof. UP, MPQ)
Prof. F. Sottile (Prof, LSI, École Polytechnique)
Prof. F. Sirotti (DR CNRS, PMC, École Polytechnique)

Program :

-Reminder of Solid State Physics and Introduction to the course

• Electrons and nuclei
  
• Born-Oppenheimer approximation
  
• Bloch theorem
  
• spin and k-points
  
• magnetism (diamagnetic, paramagnetic, ferromagnetic, anti-ferromagnetic, etc.)

-Superconductivity

• An introduction to Superconductivity: Introduction to a short story of superconductivity and its fascinating properties, the quest of very low temperature, the discovery of superconductivity, the high-Tc superconductors, their properties with experiments performed during the lecture
• The Cooper’s model : bound electrons in a degenerate Fermi gaz, the superconducting gap
• A first approach to the microscopic theory of Bardeen Cooper Schrieffer (BCS): description of the ground state, the BCS Hamiltonian, the energy of the ground state and the superconducting gap
• Signatures of the superconductivity in some spectroscopy probes: tunnelling and ARPES, infrared and Raman, NMR

-Electronic structure: the ground-state

• ground-state quantities (lattice parameters, phonons, Bulk modulus, phase transitions)
  
• the many-body problem: independent particles
• Hartree and Hartree-Fock approaches
• Koopmans’s theorem and self-interaction concerns
• Density Functional Theory (theory, approximations and examples)
• Band-structure and Density of States
• Absorption in DFT 

-Photoemission spectroscopy

• Energy and momentum conservation
• ARPES
• XPS
• Spin-resolution
• Bulk surfaces and interfaces
• Cross sections
• Experimental issues: Ultra High Vacuum, X-rays sources, Electron energy analyzers, Examples

-Green’s Functions theory I

• The need for the Green’s function
• spectral representation
• the self-energy
• Hedin’s equations
• the GW approximations
• quasiparticle and satellites
• results and examples

-X-ray Absorption and Ellipsometry

• Valence spectroscopy and ellipsometry
• Core electrons: XAS, XANES, EXAFS
• Magnetic systems: Linear and circular Dichroism, Applications

– Green’s Functions theory II

• The need for the two-particle Green’s function
• the Bethe-Salpeter equation
• 4 points quantities, results and examples

– Scattering spectroscopies and TDDFT

• Scattering process and the inverse dielectric function
• electron energy loss, electron microscope
• inelastic x-ray scattering,
• experimental resolution: energy, momentum, space, time, Time Dependent Density Functional Theory, linear response and polarizability, approximations and applications

Electronic quantum devices (3 ECTS) 

Professors
Prof. P. Joyez (DR SPEC, CEA Saclay)
Prof. P. Lafarge (Prof. UP, MPQ)

Program :

• Basics of Solid State Physics : band structure, metals, semiconductors, phonons, balistic and diffusive electronic transport,…
• Second quantization
• Quantum transport : characteristic lenght scales, conductance quantum, Landauer formula, current noise in quantum conductors, localization, …
• Electrons in magnetic field : Landau levels, integer and fractionary quantum Hall effect, edge states, …
• Superconductivity : BCS theory, Josephson effect, mesoscopic superconductivity, Andreev reflexions.
• Electronic transport in carbon nanotubes.

Nano-objects at the atomic scale (3 ECTS)

Professors
Prof. D. Alloyeau (CR CNRS, MPQ)
Prof. V. Repain (Prof. UP, MPQ)
Prof. H. Amara (Chercheur, Onera)

Program :

Electronic, magnetic and optical properties down to the molecular scale:

• Microscopes history and state-of-the-art optical microscopes: Diffraction principle, optical resolution, Beyond diffraction
• Near field microscopy: A brief history, General principle of working, Scanning Tunneling Microscope and Atomic Force Microscope, signal to noise and resolution
• Electronic properties : Local Density of States, Quantized levels and wavefunctions mapping, Superconductivity at the nanoscale
• Magnetic properties: Local Tunnel Magneto-Resistance, Single atom magnetism, superparamagnetism and non-collinear magnetism
• Optical properties: Optical Luminescence from a nanometer scale junction, Tip Enhanced Raman Scattering

Structure-related properties of nanomaterials:

• The atomic structure of nanomaterials: a key to understand and optimize their properties
• Revealing the atomic structure and the electronic properties of nanomaterials with a transmission electron microscope: Image and diffraction , Phase-contrast microscopy at the atomic scale (high-resolution TEM), Electron and X-ray spectroscopies, Plasmon mapping at the nanoscale
•  Studying the dynamics of nanomaterials in realistic environments: In situ electron microscopy and X-ray scattering methods, Nucleation and growth phenomena, Life cycle of nanomaterials in biological media 

Modlisation of structural and electronic properties of nanomaterials:

• Different approaches at atomic scale: DFT calculations, Tight-binding formalism (diagonalization scheme, order N method, Green function, second moment approximation …), Empirical potentials (Lennard Jones, EAM, MEAM, Brenner, Tersoff, …), Different types of atomic calculations (static, Molecular Dynamics, Monte Carlo, energy landscape exploration methods, …)
• Electronic properties of nano-objects: Carbon nanomaterials (nanotube, graphene), Green functions formalism, Carbon nanotubes (imaging molecular orbitals), Doped Graphene (DFT vs Tight-binding)

-Structural properties of nano-objects: Thermodynamic of nanoalloys (driving forces : size, surface energy, ordering tendency, …) empirical and semi-empirical approaches, Growth mechanisms (nanorod, carbon nanotube, graphene)

Visit of laboratories

Visits of different laboratories in Paris and Parisian region are organized on a weekly basis. This give the opportunity to students to be aware of the hot-topics in research activities in the domain of quantum devices, to have scientific exchange with internationally recognized researchers and research teams and finally to get informed on internship proposals. 

Quantum Communication (3 ECTS) 

Professors
Prof. E. Diamanti (DR CNRS, LIP6)
Prof. S. Ducci (Prof. UP, MPQ)

Quantum Communication constitutes one of the pillars of the field of quantum information and encapsulates a vast array of technologies that range from laboratory experiments, to real-world implementations and to commercial reality. Its applications can have a profound impact in cybersecurity and in communication practices in next-generation network infrastructures. Photonics plays a central role in this field, as it is based on techniques from classical, nonlinear and quantum optics, and light-matter interactions.

This course covers the different aspects of this rapidly evolving field: from theoretical concepts, to the development of integrated sources and detectors of quantum states of light, circuits for their manipulation, and then to major protocols such teleportation and quantum key distribution, and to their implementation within fiber and satellite-based quantum networks.

The lectures are highly interactive, with students presenting recent scientific papers during the sessions, and include a ‘live’ experimental demonstration on the generation of Bell states and their analysis.

Program :

Part 1

Theoretical concepts and protocol implementations

• Introduction to quantum information theory concepts. Entanglement and Bell inequalities
• Applications of entanglement: quantum teleportation and entanglement swapping
• Theory and implementation of quantum key distribution
• Quantum networks with fiber-optic and satellite links

Part 2

Photonic devices for quantum communications

• Photon statistics; photon antibunching (Handbury-Brown and Twiss setup).
• Established technologies for single photon detection; implementation of integrated single photon sources (requirements, design and experimental evaluation of their performances)
• Physical processes generating two-photon entangled states and experimental evaluation of entanglement level
• Implementation of integrated sources of entangled states and quantum photonic circuits

Experiment:

Bell’s inequality violations and density matrix reconstruction with a Quantum Entanglement Demonstrator

EU 2nd term (30 ECTS)

• Quantum Computing
• Quantum Communication
• Nanomagnetism ans spintronics
• Functional Materials
• Internship

Quantum theory of light (3 ECTS)

Professors
Ass. Prof. E. Boulat (MCF UP,MPQ)
Ass. Prof. L. Lanco (MCF UP, C2N)

Program :

Free particle of Spin 1/2
Jauge invariance of Schroedinger equation ; Pauli Hamiltonian
Semiclassical theory of light – matter interaction
Electron-field interaction and Fermi golden rule ; transition rate

QUANTUM NATURE OF LIGHT : PHOTONS

• Fock space
  
• Operators : electric field, momentum, photon number
  
• The Casimir effect
  
• Special states of the electromagnetic field : coherent states, squeezed states

PHOTON EMISSION AND ABSORPTION

• Hamiltonian electron-photon; revisiting the Fermi golden rule
  
• Spontaneous and stimulated emission
  
• Natural linewidth
  
• Dipolar electric emission
  
• Diffusion of a photon from an atom

Photonic quantum devices (3 ECTS)

Professors
Prof. C. Sirtori (Prof. ENS, LPENS)
Prof. A. Vasanelli (Prof. UP, LPENS)

Program :

BASICS OF OPTOELECTRONICS AND SEMICONDUCTOR PHOTONIC DEVICES

– Basics of semiconductor physics

• Electrons in solids: wavefunctions, band structures, effective mass
• Statistics of semiconductors: Fermi-Dirac, semi-classical approximation, free-carrier density
• Semiconductor doping: donors and acceptors, temperature regimes
• Optical absorption: matrix element and absorption coefficient in direct-bandgap semiconductors, joint density of states, phonons and absorption in indirect-bandgap semiconductors
• Non-radiative recombination

– Basics of semiconductor devices

• Transport in semiconductors: diffusion and conductivity, Drude and Boltzmann
• Quasi-neutral approximation: rate equations in doped semiconductors, minority-carrier evolution, application to photocarrier injection and surface recombination
• p-n junctions: space charge and band profile, I-V characteristics and Shockley approximation, quasi Fermi levels
• Photovoltaic detectors

– When electric fields come into play

• Perturbation of electronic states: enveloppe function approximation, Franz-Keldysh effect
• Application to heterostructures: quantum wells, intersubband transitions, QWIPs
• Modulators: Quantum Confined Stark effect, QCSE vs. FK, designs
• Introduction to non-linear optics: coupled-wave equations, slowly-varying-amplitude approximation, second-order processes and wave-vector mismatch
• Second-order non-linear optics in semiconductors: susceptibility enhancement, phase-matching schemes

– Light emission in semiconductors

• Radiative recombination and photoluminescence spectrum
• Light-Emitting Diodes: carrier lifetime, internal quantum yield, light extraction
• Stimulated emission: absorption, optical gain and Bernard-Duraffourg inversion condition
• Double-heterostructure laser: electron and photon confinement, threshold, processing
• Quantum-well laser: separate confinement, interband absorption and gain in quantum wells, threshold, comparison with DH, structures
• Introduction to quantum-cascade laser: unipolar scheme, active part, superlattices and injector design

– From optoelectronics to photonic devices

• Distributed-feedback lasers: principle, mode coupling, DFB operation
• Vertical-cavity surface-emitting lasers: principle, Bragg mirrors, cavity design, electrical injection
• Introduction to photonic crystals: DBR as 1D photonic crystals, modes and band structures, 2D and 3D generalisation, application to integrated optics, analogy with electron states and limits
• Application to light extraction: emission from a cavity, light extraction and refractive-index engineering

FABRICATION OF PHOTONIC DEVICES

– Introduction to semiconductor device processing

• Growth : molecular beam epitaxy, MOCVD
• Photolithography
• Processing of devices : etching, metallisations, …

– Heteroepitaxy : the example of Germanium on Silicon

– Nanowires and nanostructures : growth and characterization

2D Materials (3 ECTS)

Professors
Prof. J. Lagoute (CR CNRS, MPQ)
Prof. Y. Gallais (Prof. UP, MPQ)

Program :

Since the discovery of graphene with its remarkable transport and optical properties, the field of two-dimensional crystals has flourished, and many materials can now be studied down to the single atomic layers. Compared to bulk materials two dimensional materials provide highly tunable platforms for novel functionalities and exotic opto-electronic phenomena. The goal of this course is to give an overview of this vibrant field by providing some basic concepts of two-dimensional materials (device fabrication, electronic and optical properties) and then focus on a selection of recent developments in the field (van der Waals heterostructures, defect engineering, di-chalcogenides, topological insulators…).

We will first review the basics of the physical properties of graphene with an emphasis on the properties of graphene-based devices and the means to characterize them. We will then introduce the physics of other two-dimensional materials like di-chalcogenides and black phosphorus which have been discovered more recently and whose optical and electrical properties differs from graphene. The course will end by an introduction to the unusual two-dimensional electronic states that forms at the surface of topological insulators.

-The Physics of graphene and its devices:

• Introduction: graphene and its band-structure 
• Transport properties of graphene devices 
• Optical properties and application to opto-electronic devices 
• Local spectroscopies and defect engineering 
• Graphene based heterostructures and van der Waals engineering: concept and fabrication 

-Beyond graphene: dichalcogenides, black phosphorus and topological insulators :

• Introduction to dichalcogenides and their band structure in the 2D limit: the case of semiconducting MoS2 
• Spin and valley degrees of freedom in semiconducting dichalcogenide + proximity effect 
• Correlated states in metallic dichalcogenides: density wave and superconductivity 
• Black-phosphorus 
• Introduction to topological insulators 

Experimental projects in nanosciences (6 ECTS) 

Professors
Ass. Prof. M. L. Della Rocca (MCF UP, MPQ)
Ass. Prof. F. Raineri (MCF UP, C2N)
Ass. Prof. R. Braive (MCF UP, C2N)

In this original course, students will get trained with experimental techniques used in nanosciences. During the first three weeks of the Master, students will have to make an experimental project in the nanosciences field like the elaboration and characterization of metallic nanoparticles, the optic of semiconducting laser, the electronic conduction in atomic contacts or organic materials, nanotubes physics, quantum optics…

A specific nanoscience area dedicated to teaching will be available with free of use instruments like an atomic force microscope, a scanning tunnelling microscope, a transmission electron microscope or an optic microscope. All students will also be initiated to clean room techniques during three days of practise. 

Quantum Computing (3 ECTS) 

Professors
Prof. P. Milman (DR CNRS, MPQ)
Prof. H. Perrin (DR CNRS, LPL)

Program :

• Introduction to quantum computing: complexity classes, communication, universal gates, discrete and continuous variables, coding a qubit …
• Trapped ions for quantum computation: methods of trapping, cooling, interrogation, realization of elementary single qubit gates
  
• Detailed presentation of two algorithms: Shor algorithms and Grover algorithms, presentation of the project on IBM qbits
  
• Coupling ions : two qubit gates; example of the realization of an algorithm with ions ; quantum SIS Josephson junctions, superconducting qubits
• Error correcting codes
• Quantum computing with superconducting qubits (experimental realization) ; qubits based on spin quantum dots ; other platforms for quantum computing (NMR, photons …)
• Another approach: quantum simulation (discrete and continuous)
• Quantum simulation platforms: quantum gases (bulk or lattices), cold Rydberg atoms in optical tweezers, polaritons …
  

Nanomagnetism and spintronics (3 ECTS)

Professors
Prof. H. Jaffres (Prof. École Plytechnique, UMR CNRS -Thales)
Prof. P. Seneor (Prof. UPSaclay, UMR CNRS -Thales)

Program :

The ‘NanoMagnetism and Spintronics’ course targets the physics of Magnetism, of Magnetism at the nanometer scale (NanoMagnetism) and the spin-dependant transport in magnetic Nanostructures, scientific discipline designated today as Spin Electronics. 

– Fundamentals of orbital and spin localized magnetism in ionic systems

– Paramagnetic, ferromagnetic and antiferromagnetic orders

– Band-ferromagnetism of 3d transition metals, atomic exchange interactions. 

– Spin-dependent transport in magnetic nanostructures (magnetic multilayers, nanowires, magnetic tunnel junctions) – Spin-dependent conduction in the diffusive regime, spin diffusion length and spin accumulation 

– Giant MagnetoResistance (GMR) and Tunnel Magnetoresistance (TMR) 

– Magneto-Coulomb effects with nanoparticules dispersed between ferromagnetic reservoirs 

– Spin transfer effects in metallic nanopillars and magnetic tunnel junctions

Master thesis project (march to june) (18 ECTS)

The final four-month Master thesis project can be conducted in one of the academic or industrial laboratory supporting the formation or in another Lab in France or abroad. 

The evaluation is based on a project report and an oral presentation.

Functional Materials (3 ECTS)

Professor
Prof. S. Biermann (Prof. École Polytechnique, CPHT)

This course consists mainly of invited seminars given by international researchers on topics at the interface between fundamental and applied physics/materials science (i. e. Meta-Materials, 2d Materials for Valleytronics, 2d oxide heterostructures, Nanoparticles, battery materials, ….). The lectures are held at Ecole Polytechnique.