87951 - Quantum States of Matter and Radiation

Academic Year 2021/2022

  • Moduli: Pierbiagio Pieri (Modulo 1) Davide Vodola (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics (cod. 9245)

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.

  • Entanglement, quantum information and quantum computation  (D. Vodola - 24h)
  • States and ensembles: Density matrices. Schmidt decomposition

  • Quantum measurements: PVM and POVM

  • Quantum evolution: Quantum instruments. CPT maps. Kraus representation. Examples: amplitude damping, dephasing, depolarizing channels

  • Entanglement theory: EPR and Bell inequalities, entanglement measures

  • Entanglement as a resource: Dense coding, teleportation, quantum key distribution 

  • Quantum states of atoms and light (P. Pieri - 24h)
  • Quantum theory of light; electromagnetic oscillator, Fock states
  • Coherent states: theory and properties, squeezed states
  • Atoms in e.m. field; dipole approximation; the Rabi and Jaynes-Cummings models
  • Some notions on macroscopic quantum-coherent phenomena: introduction to superfluidity and superconductivity; explanation of basic phenomenology in terms of macroscopic wave function; Landau criterion for superfluidity
  • BEC with ultracold gases


Entanglement, quantum information and quantum computation

1) Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information, ‎Cambridge University Press

2) Mark M. Wilde, Quantum Information Theory, Cambridge University Press

Quantum states of atoms and light

1) Lecture notes available on the repository virtuale.unibo.it

2) Christopher C. Gerry, Peter L. Knight, Introductory Quantum Optics, Cambridge University Press, Cambridge (2005)

3) Ulf Leonhardt, Measuring the Quantum State of Light, Cambridge University Press, Cambridge (1997)


Teaching methods

Lecture-based teaching

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 Pierbiagio Pieri

See the website of Davide Vodola


Quality education

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.