OVERVIEW

This course will present a theoretical overview of quantum properties in electronic and photonic  systems.

AIMS AND CONTENT

LEARNING OUTCOMES

The principal task of the present course is to provide a clear background and a panorama on quantum systems both electronic and photonic.

AIMS AND LEARNING OUTCOMES

At the end of this course, the student will be able to:

• describe the physics of electronic and photonic quantum systems, highlighting fundamental aspects of quantum mechanics even out of equilibrium;
• use mathematical tools such as Green's functions and master equations to manipulate and obtain results on the physical properties of quantum systems;
• apply tools of the linear response theory to out-of-equilibrium quantum systems;
• calculate transport properties in the quantum regime for different electronic systems such as one-dimensional wires, quantum dots and Hall liquids;
• calculate photonic correlations and single and double photon interference properties.

TEACHING METHODS

The lessons will be frontal on the blackboard. The physical properties treated will be obtained, calculated and explained. Presentations with slides will be used as regards the aspects of experimental measurements associated with the physical phenomena treated.

SYLLABUS/CONTENT

The first part of the course describes general aspects of the out of equilibrium phenomena in quantum systems with the explanation of the linear response theory. In the second part several examples are presented which are directly connected with electronic and photonic quantum systems. An introduction to quantum optics will be presented and a focus on  transport properties of electronic systems will be given. Below the detailed  program.

Linear response theory and Green functions

• Time evolution of out of equilibrium density matrix. Applications to the electrical conductivity and to the tunneling between metals. Fluctuation-Dissipation theorem and thermal noise in quantum conductors.

Introduction to photonic systems and quantum optics

• Quantum states of radiation: Fock states, coherent states and squeezed states.
• Glauber's coherence function, photodetection and coincidences.
• Single photon interferometers: Mach-Zehnder and Fabry-Pérot. Intensity interferometers: Hanbury-Brown-Twiss and Hong-Ou-Mandel.

Quantum electronic systems

• Heterostructures, bidimensional gas. Scattering processes in solids, length scales in the mesoscopic regime, ballistic transport.
• Quantum wires, quantum point contact: conductance quantization, two and four terminal measurements. Landauer Formula.
• Quantum dots: theoretical decription, single electron transistor and Coulomb blockade oscillations.
• Aharonov-Bohm effects. Introduction to paths integrals and phase of the wave function. Applications and experiments  to solid state systems. Berry phase and its connection with the AB phase.
• Integer Quantum Hall effect: Landau level, disorder and edge states. Phenomenological description of fractional quantum Hall effect. Introduction to topological systems in two dimensions.

RECOMMENDED READING/BIBLIOGRAPHY

RECOMMENDED BIBLIOGRAPHY

• H. Bruus, K. Flensberg, "Many-body Quantum Theory in Condensed Matter Physics" Oxford University Press (2004).
• G.F. Giuliani, G. Vignale. "Quantum theory of the electron liquid". Cambridge Univ. Press (2005)
• Y.V. Nazarov, Y.M. Blanter. "Quantum Transport. Introduction to Nanoscience". Cambridge Univ. Press (2009). 
• T. Ihn. "Semiconductor Nanostructures" Oxford University Press (2010).
•  Mark Fox “Quantum Optics. An introduction”.
• Rodney Loudon “The Quantum Theory of Light”.
• S. Haroche, J.-M. Raimond “Exploring the quantum. Atoms, Cavities, and Photons.”

TEACHERS AND EXAM BOARD

Exam Board

MAURA SASSETTI (President)

DARIO FERRARO

FABIO CAVALIERE (President Substitute)

LESSONS

LESSONS START

Consult the calendar at the link:

https://corsi.unige.it/corsi/9012/studenti-orario

EXAMS

EXAM DESCRIPTION

The exam consists in an oral part.

ASSESSMENT METHODS

The oral exam is done by the teacher responsible of the course and another expert in the field, usually a teacher of the staff. The duration of the oral exam is about 40 minutes.

The oral exam is always conducted by the teacher in charge and by another expert in the subject (usually the co-teacher) and lasts about 40 minutes. It is articulated in a part developed by the student and by further questions concerning the entire exam programme.

This allows the commission to judge, in addition to the preparation, the degree of achievement of the objectives of communication, autonomy and logical clarity in the exposition.

With these methods, and given the many years of experience of exams in the discipline by the teachers of the examination commission, it is possible to verify with high accuracy the achievement of the educational objectives of the teaching. When these are not achieved, the student is invited to deepen the study and to make use of further explanations from the  professor in charge of the course.

Exam schedule