Program

Quantum Theory of Materials

(3ECTS)

Teachers:
Christophe Voisin (PR UPC, LPENS)
Alain Sacuto (PR UPC, MPQ)
Francesca Carosella (MCF UPC, LPENS)
Francesco Sottile (DR CNRS, LSI Ecole Ploytechnique)

Part 1

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

Part 2

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

Quantum Theory of Light

(3ECTS)

Teachers :
Cristiano Ciuti (PR UPC, MPQ)
Loic Lanco (PR UPC, C2N)

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

Quantum Devices: Photonics

(3ECTS)

Teachers :
Angela Vasanelli (PR UPC, LPENS)
Carlo Sirtori (PR ENS, LPENS)

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

Quantum Devices: Electronics 

(3ECTS)

Teachers :
James O’Sullivan (DR CEA Saclay, Lab SPEC) 
Philippe Lafarge (PR UPC, MPQ)

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.

Experimental projects: from clean room fabrication to device physics

(6ECTS)

Teachers :
Maria Luisa Della Rocca (PR UPC, MPQ)
Anne Anthore (PR UPC, MPQ)
Roméo Bonnet (clean room engineer)
Rémy Braive (MCF UPC, C2N)

In this original course, students will get trained with experimental techniques used in nanosciences. During the first three weeks of the formation, students will realize in complete autonomy an experimental project in the field of nanosciences, on hot-topics such as electronic transport or optical properties of graphene and carbon nanotubes, molecular electronics, nanoplasmonics, photonic crystals, organic electronics, quantum transport in tunnel diodes,…
A specific nanoscience platform equipped with advanced facilities (AFM – atomic force microscopes and STM- tunneling effect microscopes, TEM – transmission electron microscope, SEM – scanning electron microscope, spectrometers, cryogenics, electronic transport measurements, etc.) will be available with free use of these instruments. All students will also be initiated to clean room techniques and activity by practicing the realization of their own device.

Quantum Computing: algorithms and hardware

(3ECTS)

Teachers :
Frédéric Magniez (DR CNRS, IRIF)
Luca Guidoni (CR CNRS, MPQ)
Florent Baboux (MCF UPC, MPQ)

The course is composed of two main parts, teached in parallel: a computer science part dedicated to quantum algorithms, and an experimental part describing the hardware implementations of quantum computing tasks.

The computer science part of the course introduces the principles of quantum information and computing, contrasting them with classical computing paradigms. It covers key quantum algorithms and their application (cryptography and optimization), error correction, and Hamiltonian simulation. The aim is to equip students with foundational knowledge and practical skills to explore quantum computational methods and their applications. Detailed content:

• Basics on quantum information, first uses of quantum transformation for computing tasks
• Quantum computing with circuits: basics on classical computing (decidability, complexity classes) universal set of gates, from classical to quantum circuits, first quantum algorithms (Deutsch-Josza, Bernstein-Vazirani, Simon), example of programmation of quantum circuits
• Quantum Fourier transform and application: Phase estimation, Shor algorithm and applications in cryptography
• Quantum Monte Carlo speedup using Grover algorithm
• Hamiltonian simulation and energy estimation
• Quantum error correction

The experimental part of the course starts by recalling the resources needed for the experimental implementation of a quantum computer, and describe the possible physical platforms available.

We first focus on atomic-based implementations. We quickly recall the Optical Bloch Equations (OBE) formalism that leads to the expressions of the optical forces used for cooling and trapping atoms with light. The OBE are also at the basis of single qubit operations in atomic systems that are then reviewed. In a second part we describe in particular the two-qubit gates based on Rydberg blockade that are at the core of neutral atom quantum computers as well as the architecture of processors based on optical tweezers arrays. In a third part we introduce the ion trap technology and the motional quantum gates at the heart of trapped-ion quantum computers.

We then switch to the description of superconducting qubits and photonic devices for quantum computing. We start by recalling the fundamentals of superconductivity and Josephson junctions, the various types of superconducting qubits (phase, flux, charge) are introduced, along with their experimental implementation and manipulation techniques. These concepts lead to the study of circuit quantum electrodynamics (CQED) in its resonant and dispersive regimes, describing the interactions between qubits and electromagnetic fields in microwave cavities. Photonic devices are then examined, highlighting the diversity of photonic degrees of freedom and the prospects offered by the on-chip integration for scalability. The main paradigms of optical quantum computing are then introduced, including the gate-based, measurement-based, and one-way quantum computing approaches. Finally, Boson Sampling is presented as an intermediate approach to demonstrate quantum advantage.

Detailed content:

1)    Introduction on experimental implementations of quantum computing
–       Requirements for a universal quantum computer
–       Review of available platforms, from atomic to solid-state systems

2)    Neutral Atoms
–       Reminders on light-atom interaction
o   Optical Bloch Equations
o   Optical forces
o   Laser cooling and trapping
–       Single qubit operations (optical or microwave driven)
–       Rydberg coupling between qubits, quantum logic
–       Experimental implementations, state-of-the-art, bottlenecks

3)    Trapped ions
–       principles of trapping
–      laser cooling
–      Coulomb crystals
–      quantum logic implementation
–      sideband cooling and coherent manipulation
–      scalability strategies
–       Experimental implementations, state-of-the-art, bottlenecks

4)     Superconducting qubits
–       Reminders on Superconductivity
o   Superconducting wavefunction
o   Flux quantization
–       The Quantum LC circuit
–       Josephson junction as a fundamental building block
–       Phase qubit
–       Flux qubit
–       Charge qubit
–       Coupling between qubits (capacitive, inductive)
–       Circuit quantum electrodynamics:
o   resonant regime of CQED
o   dispersive regime of CQED
–       Experimental implementations and state-of-the-art

5)    Photonic devices
–       Diversity of photonic degrees of freedom for quantum information
–       Integrated photonics for scalability
–       Gate-based optical quantum computing
o   Single-qubit gates: examples in polarization & path
o   Two-qubit gates: the challenge of the CNOT gate
–       Measurement-based optical quantum computing
o   Quantum teleportation
o   Gottesman–Chuang teleportation trick
–       One-way quantum computing
–       Boson Sampling as an intermediate step to prove quantum advantage
o   Two-photon interference: Hong-Ou-Mandel effect
o   Standard Boson Sampling
o   Scattershot Boson Sampling
o   Gaussian Boson Sampling

Quantum Communication: ressources and protocols

(3ECTS)

Teachers :
Eleni Diamanti (DR CNRS, LIP6)
Sara Ducci (PR UPC, 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.

Theoretical concept and protocol implementation

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

Photonics devices for quantum communication

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

Nanomagnetism and spintronic devices

(3ECTS)

Teachers :
Hanri Jaffres (PR École Polytechnique, UMR CNRS -Thales)
Pierre Seneor (PR Paris Saclay, UMR CNRS -Thales)

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.

Low dimensional materials: Nano-objets at the atomic scale

(3ECTS)

Teachers :
Damien Alloyeau (DR CNRS, MPQ)
Amandine Bellec (DR CNRS, MPQ)
Hakim Amara (DR ONERA)

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)

QuanTech Projects (3ECTS)

Project: Quantum optimization for graph problems
Responsible: Elie Bermot

Combinatorial optimization seeks to find optimal solutions to a wide range of NP-hard problems. One such problem is the Maximum Independent Set (MIS), which involves identifying the largest set of non-adjacent nodes in a graph. This problem can be naturally mapped to the ground state of a neutral atom Hamiltonian. In this project, students will demonstrate how to solve instances of the MIS problem using Pasqal’s quantum hardware, by mapping the problem to the device and preparing its corresponding ground state. To validate their approach, students will use a quantum emulator to assess how their strategy would perform on actual hardware.

Project: Exploring Quantum Materials at the Atomic Scale
Responsibles: Nathaly Ortiz & Hakim Amara

Quantum technologies are advancing rapidly and their success depends on mastering materials with complex and often unpredictable structures. This is especially true for low-dimensional materials (such as nanoparticles, carbon nanotubes, and 2D materials), which exhibit unique properties and are central to global research efforts in quantum science.

During this project, students will explore the relationship between the atomic structure of low-dimensional materials and their electronic behavior, key to unlocking next-generation quantum devices.

Through this project we will:

• Characterize nanostructures using cutting-edge transmission electron microscopy (TEM) techniques enhanced by AI-based image processing.
• Model electronic properties with numerical simulations based on tight-binding Hamiltonians, a powerful approach to understanding quantum behavior in materials.

Key research directions include:

• Carbon Nanotubes & Quantum Computing: Carbon nanotubes offer a promising platform for quantum bits (qubits), thanks to their ability to confine charge in solid environments—enhancing electron protection and increasing coherence times. You’ll explore their role in addressing the limitations of current computing architectures.
• Twisted 2D Materials & Quantum Light Sources: Slightly rotating two stacked 2D layers can radically change their electronic properties—flattening energy bands and creating new electronic states. These “twisted” materials are promising candidates for stable, miniaturized quantum light sources, such as single-photon emitters.

Project: Single and entangled photon sources
Responsibles: Sara Ducci

High-quality sources of single photons and entanglement are key resources for a wide variety of applications in quantum technologies.

This project will allow the investigation of the quantum properties of light generated through spontaneous parametric downconversion in nonlinear crystals using state-of-the-art components (lasers, optics, single photon detectors).

Students will be trained to:

• • Build a Heralded Single-Photon Source
  • Use Coincidence Counting Techniques to Distinguish Classical from Non-Classical Light Sources
  • Analyze the Polarization State of Single Photons
  • Build an entangled photon source and perform a Bell Test

Project: NV centers as “solid state atoms” for quantum technologies
Responsibles: Luca Guidoni

Atomic qubits play a prominent role in the international efforts to build a quantum computer. NV centers (defects in the diamond structure that can trap an electron) are considered a very promising solid-state implementation at room temperature of atomic qubits.

This project will allow the investigation of the quantum properties of such a system through the combined techniques of optical and microwave manipulation of the electronic states of NV centers.

Students will be trained to:

• Build a setup to optically excite and detect an ensemble of NV centers
• Study the optical pumping technique to prepare pure electronic states
• Use the system as a “quantum magnetometer”
• Implement a pulsed-optical + pulsed-microwave excitation of the NV center to study Rabi oscillation phenomenon, the key of coherent manipulation