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  • This lecture aims at the description of the interaction between quantum matter in its simplest form, an atom, and an electromagnetic field. A semi-classical approach, where the field is classical, is first considered, including relaxation of the atom. We then study the quantization of the electromagnetic field and its relaxation, before its interaction with an atom is described in a full quantum model.

The goal of this course is to introduce somewhat "advanced" topics in quantum matter, tackle truly quantum-entangled, strongly interacting, phases of matter and materials, and present how quantum matter is a particularly rich field, with many open theoretical problems.

This course is about how to describe complex systems using ideas of the renormalization group (‘coarse-graining’) and statistical field theory.

Master Quantum Engineering

PSL’s quantum engineering programme is a 2-year program that provides cutting-edge training. It is spread over two years and 120 ECTS, requesting full-time studies. 

Quantum technologies are a strategic global topic for academia and industry. These disruptive technologies have the potential to revolutionise the design and implementation of information and communication sciences and technologies. France is investing nearly €2 billion in this field over the next four years.

A new interdisciplinary training programme in quantum technologies has been launched by PSL University in September 2022. It results from an unprecedented synergy between some of its founding schools, namely: Ecole normale supérieure, ESPCI Paris, Mines Paris, École nationale supérieure de Chimie de Paris - PSL and the Observatoire de Paris, and it is part of PSL’s graduate programme in physics.


The academic year is divided into two semesters.

  • Semester 1: Courses and Practicums (30 ECTS).
  • Semester 2 : Internship : France or abroad (30 ECTS).
Master ICFP

The ICFP  Master is a top-level program designed specifically for the best French and international students.

By choosing the École normale supérieure (ENS), students are assured of benefiting from the prestigious teaching that has made the ENS's reputation since its creation in 1794.