Master 2 courses in Physics - Quantum processes, Optics and Matter track

2nd year Master - 1st Semester - 6 ECTS - English Level: B2 (no test required)

Brief Description

This course presents the basics of matter-radiation interaction and introduces the optical gain processes that enable the laser effect. The operating principles of lasers are explained and illustrated by examples of high-performance lasers used in spectroscopy and metrology. In a second part, an introduction to molecular physics and molecular spectroscopy and to X-ray and Auger spectroscopy and Moseley's Law is proposed.

Prerequisites

Basics in optics (wave optics, electromagnetism), quantum mechanics, molecular and atomic physics

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course provides an introduction to the basic concepts and main tools of quantum optics. It then describes a number of applications, such as the generation of non-classical states of light (single-photon states, squeezed states, entangled states) and the field-atom interaction inside an optical cavity (cavity quantum electrodynamics).

Prerequisites

Quantum mechanics: Symmetries in quantum physics, composition of kinetic momentum. tensorial product.  Central potential. Hydrogen atom (fine and hyperfine structure). Perturbation theory. Time-dependent problems. Dynamics of a particle in a periodic potential. Light-matter interaction.

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course deals with the notion of polarization of waves propagating in an anisotropic medium. It will focus on the effects of non-linear propagation: generation of new frequencies, parametric oscillators, nonlinear index. A few examples will be chosen from a wide range of applications: spectroscopy, multiphoton absorption, spatial solitons.

Prerequisites

Wave optics, electromagnetism in material media, polarization of light, birefringent materials

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 6 ECTS - English Level: B2 (no test required)

Brief Description

The first part of this course masters the physical and statistical analysis of signals and noises. The objectives are to know the main fundamental noises and methods for improving the signal-to-noise ratio and to be able to analyze, interpret and present measurement results. The second part is about ultrastable lasers used in metrology (Notion of phase noise/frequency noise,  phase noise and linewidth). The last part of this course focuses on the interaction of light with condensed matter with two topics: electromagnetism in matter and properties of electrons and photons in condensed matter.

Prerequisites

Basics in statistical analysis, electrostatics (Gauss theorem), electromagnetism in material media, basis in solid state physics

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

Ultrafast phenomena represent an important part of atomic and molecular physics and deal with small systems interacting with strong and ultrashort electromagnetic fields. The latter could be obtained either with laser or through collisions with very highly charged ions. The main objectives of this course are to introduce a number of fundamental aspects that are used to predict, describe and analyze the highly non-linear response of these systems. Experimental and theoretical (analytical and numerical) methods to study the processes involved will be extensively presented. Differences and similarities will be exemplified throughout the course.

Prerequisites

Basics in atomic and molecular physics and the physics of collisions

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The aim of this course is to show how laboratory studies of the interaction between radiation and molecular matter (in gaseous or solid form) are essential for observing and understanding the universe. Using on-board telescopes or on the ground, light analysis enables us to determine the physico-chemical conditions in interstellar environments light-years away from our solar system. Although some of the properties of molecular matter can be determined directly by observation, laboratory experiments are needed to shed light on molecular mechanisms at work in the interstellar medium, which have important consequences for the evolution of interstellar matter.

Prerequisites

Diatomic molecules: Molecular Hamiltonian, the molecular frame; Born-Oppenheimer approximation ; Vibration and rotation: rigid rotor harmonic approximations; Improvements to these approximations, vibration-rotation interactions; Hund’s coupling cases. Spectra of Diatomic Molecules: Transition Matrix Elements and selection rules (electric dipolar transitions); Rotational transitions ; Vibrational-Rotational transitions ; Electronic transitions, Franck-Condon principle

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course is dedicated to the field of physics where atoms, cooled to temperatures close to absolute zero, must be considered as atomic waves that can interfere, like electromagnetic waves, and reveal a set of fascinating quantum properties. Applications of atom interferometers range from ultra-precise clocks for testing general relativity, improving the GPS system or its European competitor GALILEO, to oil prospecting by detecting variations in the gravitational field. Applications of quantum gases include the development of a new class of simulators - quantum simulators - for studying superfluidity, magnetism or superconductivity on a model system. This course also includes a practical laboratory session on a laser atom cooling experiment.

Prerequisites

Electromagnetism, quantum mechanics, interferometry in optics

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

The aim of this course is to provide students with the knowledge they need to understand and use today's optical microscopy concepts and methods. Both theoretical and experimental aspects are covered. After an introduction to the physical principles of imaging, this course explains the operation and practical use of an optical microscope, and looks at the most recent advances.

Prerequisites

Geometric optics and wave optics, nonlinear optics (second and third orders nonlinear optics)

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course deals with various aspects of quantum optics and opens the door to problems in quantum information. The electromagnetic field, an ideal tool for the study of quantum physics, is at the heart of this course. Over the past twenty years, research in quantum optics has focused on the realization of non-classical states of radiation (single photons, entangled states) and their application to quantum information protocols (cryptography, teleportation, quantum computation).

Prerequisites

Knowledge in quantum optics. Density operator formalism: Pure states, statistical superposition, non-isolated systems, purity, entanglement. Field quantization: decomposition into modes, conjugate variables, quantization,  Hamiltonian operators, momentum, mode basis and state basis. Non-classical states of light.

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 1st Semester - 3 ECTS - English Level: B2 (no test required)

Brief Description

This course is designed to provide students with a solid grounding in selected areas of nanophotonics, which has been expanding rapidly over the past fifteen years: plasmonics (localized modes, propagative modes), metamaterials, photonic crystals and their developments. This knowledge is reinforced by its experimental application, enabling students to acquire operational skills in this field.

Prerequisites

Electromagnetism in material media, properties of electron and photon in condensed matter (Bloch theorem)

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)

2nd year Master - 2nd Semester - 6 ECTS - English Level: B2 (no test required)

Brief Description

Different activities are included in this course: pratical sessions on optics and lasers, a bibliographic project on a active field of research about light-matter interaction under the supervision of a researcher specialist of the topic and an IT project with Python.

Prerequisites

Knowledges in laser physics, wave optics, optics in anisotropic media, basics of Python.

Contact

Catherine Schwob (schwob@insp.jussieu.fr)
Hugues Fillion (hugues.fillion@sorbonne-universite.fr)