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,
- have an understanding of the basic concepts of light-matter interactions on the quantum level, 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,
- 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 optical technologies are likely to play in society, and have articulated an opinion on those effects.
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In this course we study the quantum properties of light and matter-light interaction, with some examples from modern quantum technologies, such as laser cooling and trapping, Bose-Einstein condensation and quantum sensing. After an introduction to the formalism of quantum optics, we dive into light-matter interaction. 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, and quantum memories.
Finally, we turn to laser cooling and trapping and Bose-Einstein condensation. Here, we encounter some of the groundbreaking experiments from the last 25 years, showing, e.g. quantum phase transitions and the condensation of gases (or light!) to a macroscopic quantum ground state.
Assessment
The course will be assessed by a combination of optional homework, obligatory 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 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).
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