EU 1st term (30 ECTS) | EU 2nd term (30 ECTS) |

Electrons and phonons in nanostructures | Quantum optoelectronics |

Quantum theory of light | Devices and quantum information |

Advanced Solid State Physics | Nanomagnetism ans spintronics |

Introduction to photonic quantum devices | Functional Materials |

Introduction to electronic quantum devices | Internship |

Nanomaterials for Nanomedecine | |

Imaging nano-objects | |

Experimental project (3 weeks) | |

Visit to Laboratories |

The first term (September-January) includes lectures on the fundamental concepts and tools of quantum photonics and electronics in condensed matter, high-tech analysis tools (electronic microscopy, STM, AFM…), a large panorama of quantum devices and functionalized materials and proposes a series of seminars on hot research topics.

The second term (January-June) details the different fields of research (Electronic transport, Spintronics, Quantum Photonics) and includes a research project.

The course is given by lecturers from several laboratories specializing in quantum devices and nanosystems.The training is based on a permanent interaction between students and research teams, and includes: experimental projects, guided tours of laboratories and a research project.

**First term**

**Electrons and phonons in semiconductor heterostructures (3ECTS**

Professors :

- Christophe Voisin (Prof. UPD, LPA),
- Emmanuelle Deleporte (Prof. ENS Cachan, LPQM),
- Francesca Carosella (MCF P7, LPA)

### 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 framewor

**Quantum theory of light (3ECTS)**

Professors :

- Edouard Boulat (MCF UP7,MPQ),
- Perola Milman (CR CNRS, MPQ)

### Program:

SEMI-CLASSICAL THEORY OF LIGHT MATTER INTERACTION

- 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

**Advanced Solid State Physics (3ECTS)**

Professors :

- Alain Sacuto (Prof. UPD, MPQ)
- Francesco Sottile (DR CNRS, LSI, Ecole Polytechnique)
- Fausto Sirotti (DR CNRS, PMC, Ecole Polytechnique)

### Program:

REMINDER OF SOLID STATE PHYSICS AND INTRODUCTION (F. Sottile)

Scope of this first introductory session is to give the outline of the course, remind few concepts of basic solid-state theory, and assess the knowledge of the students on the different topics.

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

SUPERCONDUCTIVITY (A. Sacuto)

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 (F. Sottile)

The electronic problem is introduced. In particular the state-of-the-art approach for the ground-state, Density Functional theory is presented. The needs for certain spectroscopy, introduced here, stimulates the need for the next experimental sessions.

- 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 (F. Sirotti)

- 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 FUNCTION THEORY I (F. Sottile)

The green’s function approach is presented, wih particular emphasis on the one-particle Green’s function, that contains the removal and addiction energies of the electrons, for a direct comparison with photoemission spectroscopy.

- 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 ELLIPSOMERY (F. Sirotti)

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

GREEN’S FUNCTION THEORY II (F. Sottile)

Absorption spectroscopy require the two-particle Green’s function, which is presented briefly here.

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

SCATTERING SPESTROSCOPIES AND TDDFT (F. Sottile and F. Sirotti)

Scattering spectroscopies are presented in the first half of the session, namely Electron Energy Loss Spectroscopy and Inelastic X-ray Scattering. This gives the occasion to introduced the concept of screening and the theoretical approach Time Dependent Density Functional Theory.

- 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 (theory, linear response and polarizability, approximations and applications)

**Introduction to photonic quantum devices (3ECTS)**

Professors :

- François Ozanam (DR, LPMC)
- Bruno Gerard (Thales and Ecole Polytechnique)

### Program:

FIRST PART: BASICS OF OPTOELECTRONICS AND SEMICONDUCTOR PHOTONIC DEVICES

1 – 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

2 – 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

3 – 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

4 – 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

5 – 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

SECOND PART: FABRICATION OF PHOTONIC DEVICES

6 – Introduction to semiconductor device processing

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

7 – Heteroepitaxy : the example of Germanium on Silicon

8 – Nanowires and nanostructures : growth and characterization

9 – Visit at Thales (Palaiseau)

**Introduction to electronic quantum devices (3ECTS)**

Professors :

- Philippe Joyez (Ch SPEC, CEA Saclay)
- Philippe Lafarge (Prof. UPD, MPQ)

Program:

- Rappels de physique des solides : structures de bandes, métaux, semiconducteurs, phonons, transport diffusif…
- Seconde quantification
- Transport quantique : longueurs caractéristiques, quantification de la conductance, formule de Landauer, bruit de courant dans les conducteurs quantiques, localisation…
- Electrons en champ magnétique : niveaux de Landau, effet Hall quantique entier, fractionnaire, états de bord.
- Supraconductivité : Théorie BCS, effet Josephson, supraconductivité mésoscopique, réflexion d’Andreev.
- Transport dans les nanotubes de carbone.

**Nanomaterials for nanomedicine (3ECTS)**

Professors :

- Sébastian Bidault (DR CNRS, Inst. Langevin)
- Corinne Chanéac (Prof. UPMC, INSP)

### Program:

Nanomedicine is defined as the application of nanotechnology to medicine. Thanks to a scale convergence, nano-objects can interact with the body at the subcellular scale with a high degree of specificity. By this way, the unique physical properties of nanodevices can be imported into living cells and organisms, paving the way of many biomedical applications. This lecture will introduce how nanoparticles can be potent effectors for sensing, diagnostic and therapy owing to their specific responses to external stimuli. We will focus particularly on nanomagnets and optical nanoparticles, which combine multiple functionalities that are useful for medical imaging, targeted treatments and therapeutic hyperthermia. The general issue of nanotoxicity and fate of nanoparticles in the organism will be also discussed.

The outline of the lecture is given below:

PHOTONIC NANOPARTICLES FOR NANOMEDICINE

### Plasmonic nanoparticles

- Localized plasmon
- Engineering optical properties
- Scattering, absorption and luminescent nanoprobes
- Nanosensor, Plasmon Rulers and Molecular beacon
- Nanosources for localized hyperthermia
- Contrast agents for in vivo imaging

### Quantum Dots and other fluorescent probes

- Principle and properties
- Synthesis and biofunctionalization
- In vivo imaging
- Biosensing and Barcode
- Switchable fluorophore and Ultramicroscopy

NANOMAGNETS FOR NANOMEDICINE

- Interaction of nano-objets with cells / with living organisms
- Nanotoxicity / Nanoparticles fate in the organism
- Examples of bionanomagnetism: a magnetic sense ?
- Nano-robots inside the cell
- Nano-sensors for diagnostic
- Nano-tracors for medical imaging
- Nano-vectors for targeted therapies
- Nano-tools for regenerative medicine

**‘Imaging’ nano-objects**

Professors :

- Damien Alloyeau (CR CNRS, MPQ)
- Jérôme Lagoute (CR CNRS, MPQ)

### Program:

### SINGLE NANO-OBJECTS IMAGING: FROM NANOMETER TO SUB-ANGSTROM SCALE (8h)

Microscopes history and state-of-the-art optical microscopes

Electron microscopy

- Microscope and Image formation
- Transmission mode : high resolution imaging
- Aberrations corrector : principle and unprecedented performances
- Tridimensional imaging
- Future challenges in electron optic

Near field microscopy

- A brief history
- General principle of working
- Scanning Tunneling Microscope, Atomic Force Microscope, Scanning Near-field Optical Microscope : signal to noise and resolution
- State-of-the-art examples : from single atoms to biological proteins

### STRUCTURAL AND CHEMICAL ANALYSIS OF NANO-OBJECTS (8 h)

Structural analysis

- Structure of surfaces with near field microscopes
- X-ray diffraction and synchrotron radiation
- Electron diffraction : quantitative analysis of single nano-objects

Chemical analysis

- Probing atomic-scale chemistry by electron spectroscopy (Electron Energy Loss Spectroscopy) and photo-electron spectroscopy (Energy Dispersive X-ray analysis, X-ray Photoelectron Spectroscopy, Angle Resolved PhotoEmission Spectroscopy…)
- Indirect ‘chemical’ mapping with near field microscopes (Inelastic Electron Tunneling Spectroscopy, Chemical Force Microscopy…)

### MEASURING PHYSICAL PROPERTIES OF NANO-OBJECTS (8 h)

Electronic mapping of nano-objects

- Wavefunctions in quantum dots and complex systems with Scanning Tunneling Spectroscopy
- Plasmon imaging using EELS

Magnetic properties of nano-objects

- Holography and magnetic circular dichroism
- Magnetic Force Microscope and Spin Polarized-STM

**Experimental projects in nanosciences (6ECTS)**

Professors :

- Maria Luisa Della Rocca (MCF UPD, MPQ)
- Fabrice Raineri (MdC UPD, C2N)
- R. Braive (MdC UPD, 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.

**Second semester**

**Quantum optoelectronics (3ECTS)**

Professors :

- C. Sirtori (Prof. UPD, MPQ)
- A. Vasanelli (Prof. UPD, MPQ)

Program:

The role of quantum devices in current technologies

- Introduction to quantum optoelectronic devices
- p-n diodes
- Tunnel diodes
- Transfer matrix and tunnelling current
- Mobility and modulation doping
- Two-dimensional electron gas
- Field effect transistors
- Bipolar transistors
- Transistor HEMT

Charge oscillations of quantized states

- Superlattices
- Bloch oscillations and Wannier Stark quantization
- Intersubband transitions and electron dispersion
- Oscillator strength
- Dipole charge oscillations

Quantum cascade lasers

- Introduction: Laser diodes vs quantum cascade lasers
- Reminder of guided optics
- Plasmon waveguides
- Rate equations
- Gain
- From near infrared to THz optoelectronics

Quantum detectors

- Quantum well infrared photodetectors
- Quantum cascade detectors

Magnetic field applied to 2D structures

- Landau quantization
- Magneto-transport
- Shubnikov-de Haas effect
- Aharonov-Bohm effect

Light-matter coupling in microcavities

- Two level atom in an ideal cavity: Jaynes-Cummings Hamiltonian
- Spontaneous emission in a cavity
- Strong coupling / Weak coupling regime
- Strong coupling regime in semiconductor systems: polaritons
- Microcavity polaritons: exciton – polaritons, intersubband polaritons

**Devices and quantum information (3ECTS)**

Professors :

- E. Diamanti (CNRS, LIP6)
- S. Ducci (Prof. UPD,MPQ)

### Program:

### THEORETICAL QUANTUM INFORMATION

The qubit and its states

- quick review of the basic quantum formalism (kets, bras and density matrices)
- No cloning theorem and Wiesner’s unforgeable banknotes
- Quantum Key Distribution and BB84 protocol

Quantum Entanglement 1: Definition and some Properties

- Formal definition (as non separable state)
- Apparent Heisenberg inequality violation
- Link with partial trace
- Entanglement detection for pure and mixed states
- Entanglement monogamy and application to QKD
- Partial transpose and its physical meaning

Quantum Entanglement 2: Bell inequalities and Application

- Entanglement is not a limitation of quantum formalism
- Bell inequalities (mainly CHSH)
- GHZ Paradox
- Some Entanglement application
- The 4 Bell States
- Quantum Dense Coding
- Quantum Teleportation

Introduction to Quantum Computation

- Grover’s Algorithm
- Quantum Error Correcting Codes

### DEVICES FOR QUANTUM INFORMATION

Introduction: Experimental implementation of quantum information : challenges and some famous experiments.

Photon sources: Single photon sources and their characterization : Hanbury Brown and Twiss interferometry, colloidal and grown quantum dots, colored centers in diamonds,..

Entangled photon sources and their characterization : Bell inequality test, density matrix reconstruction, nonlinear dielectric crystals and fibers, quantum dots, semiconductor waveguides,…

Single photon detectors: Photomultipliers, single photons avanlanche photodiodes, supraconducting detectors

Quantum metrology: absolute detector calibration, absolute radiance measurement, polarization mode dispersion, quantum ellipsometry …

Physical implementations of quantum computation: General overview, exemple of trapped ions.

**Nanomagnetism and spintronics (3ECTS)**

Professors :

- H. Jaffres (CNRS, UMR CNRS -Thales)
- 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. After having introduced the fundamentals of orbital and spin localized magnetism in ionic systems, the course will tackle the important notions of paramagnetic, ferromagnetic and antiferromagnetic order. An important effort will be brought on the understanding of the establishment of band-ferromagnetism of 3d transition metals taking into account atomic exchange interactions. The second part of this course will be devoted some more actual problems of spin-dependent transport in Magnetic nanostructures (magnetic multilayers, nanowires, Magnetic tunnel junctions). The concepts of spin-dependent conduction in the diffusive regime, spin diffusion length and spin accumulation will be clearly emphasized to explain Giant MagnetoResistance (GMR) and Tunnel Magnetoresistance (TMR) effects. An opening will be done on the Magneto-Coulomb effects obtained with nanoparticules dispersed between ferromagnetic reservoirs and on spin transfer effects observed on metallic nanopillars and magnetic tunnel junctions.

**Functional materials (3ECTS)**

Professors :

- S. Bierman (PR, LPMC)

**Master thesis project (mars to june):**

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.