87951 - Quantum States of Matter and Radiation

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

This course provides an introduction to standard ideas in quantum information theory, covering applications to quantum optics and light-matter interactions, together with glimpses into quantum computation theory and quantum technologies.. The course is divided into two modules: Module 1 provides an introduction to quantum information concepts, ideas, and techniques, while Module 2 focuses on quantum optics and light-matter interactions.

Module 1: Entanglement, quantum information and quantum computation (L. Piroli - 32h)

• States and ensembles: Density matrices. Schmidt decomposition
• Quantum measurements: projective-valued measures (PVM) and positive operator-valued measures (POVM)
• Quantum evolution: Quantum channels and operations. CPT maps. Kraus and Stinesrping representations. Examples.
• Entanglement theory: EPR and Bell inequalities, entanglement measures
• Elements of Quantum Shannon Theory
• Entanglement as a resource. Local operations and classical communication. Dense coding, teleportation, quantum key distribution
• Elements of Quantum Computing

Module 2: Quantum states of atoms and light (C. Degli Esposti Boschi - 16h)

• 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; BEC with ultracold gases

Readings/Bibliography

Lecture notes will be available on-line in the university repository. In addition, the following references will be useful

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

Lecture notes will be available on-line in the university repository

Office hours

See the website of Lorenzo Piroli

See the website of Cristian Degli Esposti Boschi