On completing the course, the students will;
- understand the quantum mechanical description of the electromagnetic field and the associated concepts such as field correlation functions, basic quantum states of light and Wigner functions,
- be able to perform basic calculations within quantum optics,
- have an understanding of the basic concepts of quantum information theory, including entanglement and the density matrix formalism, and to be able to perform calculations in this formalism,
- have knowledge of the present state of the art in experimental quantum optics, including the engineering challenges involved,
- understand the basic operations of a quantum computer,
- have a sufficient grounding in the field to be able to understand the broad outlines of research work when presented with such (in the form of research papers),
- have a deeper understanding of the role quantum technologies are likely to play in society, and have articulated an opinion on those effects.
In this course we study the quantum properties of light, with a particular emphasis on the role of light in modern quantum technologies, such as quantum computation, communication, and sensing. The course consists of three parts: an introduction to the formalism of quantum optics, and two applications of that formalism, namely light-matter interaction and quantum information processing.|
We start with the quantization of the electromagnetic field, which leads to the introduction of the photon as the quantum of light. Then, we look at various interesting quantum states of the light field and their statistical properties, including the seminal Hanbury-Brown Twiss and Hong-Ou-Mandel experiments. Next, we introduce the machinery of multi-particle quantum optics, which will be needed in the rest of the course.
In the second part, we take a look at light-matter interaction, treating the Bloch sphere, Cavity QED and the Jaynes Cummings model, with applications to atom clocks, quantum memories and Bose-Einstein condensates.
Finally, we turn to quantum information processing. Here, we encounter some of the unusual effects for which quantum mechanics is famous, such as quantum teleportation and Bell’s Theorem. We will briefly take a look at some computational aspects of quantum information including Shor’s Trilemma, error correction and the notion of a quantum advantage. We will discuss experimental results on the demonstration of “quantum supremacy” and its implications. This part of the course ends with a programming assignment on a real online quantum computer such as that from IBM.
The course will be assessed by a combination of homework, two programming assignments and an exam. The exam will test the content of the course in general, with a combination of calculation assignments centred on the formalism, technical questions about the engineering aspects, and questions about a recent research paper (which will be provided with the exam).
The first programming assignment will focus on the formalism of the quantum optics of a single optical mode. The second assignment will focus on programming a quantum computer. The homework will consist of exercises. The assignments and exam are obligatory. The homework is optional, but students are strongly encouraged to work on it by the rule that the result only counts towards their final grade if it doesn’t lower that grade.
The grade is determined as follows: a preliminary grade is determined by taking the weighted average of the assignments and the exam, where the assignments count for 10% each, and the exam counts for the remaining 80% of the grade. Then, this grade is revised upwards if there are homework sets whose grade is higher than the preliminary grade. The final grade is determined by taking the weighted average of such homework sets (each counting for 5%) and the preliminary grade (accounting for the remainder).
|191411291 Applied Quantum Mechanics||Verplicht materiaal-Aanbevolen materiaal|
|Quantum Optics - an introduction" by Mark Fox, Oxford University Press, ISBN 978-0-19-856673-1|
|Assignments and handouts are handed out at the lectures.|