Course Unit Page

Academic Year 2019/2020

Learning outcomes

At the end of the course, the student will become confident with the intrinsic and specific properties of states of a quantum system, acquiring knowledge about: the notion of entanglement and its manifestation through correlations existing in quantum matter; the quantum nature of light and its interaction with atoms. The student will be able to interpret some notable quantum phenomena involved in the manipulation of atoms and electromagnetic radiation, in order to study modern quantum information and computation theory.

Course contents

Despite being more than a century old, many aspects of quantum mechanics still leave students puzzled because of their counter-intuitive predictions with respect to our classical experience.

Such “unusual” behaviour is due to the properties and the kind of information that “quantum states” can hold.

In the first part of the course, we will study in detail the property of a generic quantum system, by revising the founding postulates of quantum mechanics in the light of modern applications. In particular the concept of entanglement and how it can be used to devise protocols that are not allowed in classical physics will be described.

In the second part of the course, we will see how these fundamental concepts exhibit in the collective behaviour of atoms (matter) and photons (light), showing how quantum effects can manifest also at a macroscopic scale.

In both parts, some lectures will be devoted to the description of the principal experiments that are driving the research for testing quantum mechanics and/or developing state-of-the-art applications.

  • Quantum states & entanglement as a resource (about 24h)
  • Density matrices (pure and mixed); Complements on the theory of measurements: PVM, POVM
  • Separable and entanglement states; Schmidt decomposition, entanglement entropy, other criteria and witnesses
  • Entanglement-based Protocols: EPR and Bell inequalities; teleportation
  • Some notions of quantum information (distinguishability, accessible info, noise,..) and computation (q-bits, q-gates, parallelism)
  • The problem of decoherence
  • Experimental realizations: some physical realizations of q-bits; Aspect’s and recent experiments on Bell’s inequality; teleporting particles

  • Quantum states of atoms and light(24h) (about 24h)
  • Quantum theory of light; electromagnetic oscillator, Fock states
  • Coherent states: theory and properties (quasi-classicality, quasi-probabilities, …); squeezed states
  • Atoms in e.m. field; dipole approximation; the Rabi and Jaynes-Cummings models; notions of atoms in cavities
  • Some notions on cold atoms and macroscopic quantum mechanics: BEC & macroscopic coherence.
  • Some recent example of experimental realizations of: quantum states of light, atoms in optical lattices and cavities, quantum simulators


Notes available on-line in the university repository.

More specific references might be suggested during lectures.

Teaching methods

Lectures in class at the blackboard and/or slides

Assessment methods

Oral exam.

It consists of (at least) two questions, one for each part of the program.

Students should demonstrate to be familiar and have a good understanding of the different subjects.

They will be asked to both present an introduction to the main general topics and to prove more specific results, making connections among the different parts of the syllabus.

The organization of the presentation and a rigorous scientific language will be also considered for the formulation of the final grade.

The “cum laude” honor will be granted to students who demonstrate a personal and critical rethinking of the subject.

According to the general rules of the University, students will be allowed to reject the grade only once, but they can withdraw at any time during the exam.

Teaching tools

Most of the material is available on-line in the university repository.

Office hours

See the website of Elisa Ercolessi

See the website of Cristian Degli Esposti Boschi

See the website of Francesco Minardi