# Lecture: Advanced Ultracold Quantum Gases

## What is the goal of this course?

The two goals of this course are firstly, to teach some fundamental concepts and techniques used in ultracold atoms research, and secondly to give an overview over the different aspects and flavours of this still very new, but quite diverse field.

By the end of the course, you should have the ability to read current scientific literature on most subjects within the field, you should have an idea of what kind of research is being conducted, and should be able to understand many talks, or discuss current work of researchers from this field.

In addition, because of the many connections of cold atom science with other fields, you will also learn about other fields such as condensed matter physics and general quantum physics (quantum information, quantum sensing etc.).

## Who should take this lecture?

Anybody with an interest in the cold atom field, of course. This is especially true if you are considering doing thesis research in the field. More generally, if you would like to learn more about atomic physics and about quantum mechanics. One specific aspect about this field is that in many cases, the basic theory is simple enough that it is possible to cover the important parts of the theory together with experimental aspects and actually make meaningful calculations. So if you like fields where theory and experiments are still relatively close together, this course is for you.

## Prerequisites (what do I need to know?)

Good working knowledge in quantum mechanics is required, as well as some basic knowledge in atomic physics. A few very important topics of these fields will be shortly re-introduced in this lecture, but without prior knowledge this will not be enough. Knowledge in statistical physics and condensed matter is helpful (but not required).

## Does it make sense to take this class if I have not taken the Ultracold Quantum Gases class?

Yes, it is not a requirement to have taken the "Ultracold Quantum Gases" introduction class in the winter semester. The course is explicitly designed to make it possible to join without a prior introduction class. A very small fraction (two to three lectures) of the content from the earlier course will come up again because of this, although in a different context.

Other classes from the winter semester which are useful for this lecture are "Quantum Optics I" and "T_M1/TV Advanced Quantum Mechanics". The mathematical methods and notations used in the ultracold atoms classes are very similar to those used in the Quantum optics class, and also are taught in the Quantum Mechanics II class.

## Topics of the class

This course will cover a relatively wide area of the field, and will discuss both important experiments and methods as well as introduce the related theoretical aspects.

We will start by reviewing shortly a few important concepts about how to describe an ensemble of particles quantum mechanically, and by discussing the connection of the quantum mechanical description to a classical field description.

Topics which we plan to discuss are:

- Discrete quantum systems
- Degenerate Fermi gases
- BEC/BCS crossover: Superconductivity and condensation of Fermions
- Fermi gases in periodic potentials, Hubbard models
- Quantum magnetism
- Quantum gases in reduced dimensions
- "Real" and "artificial" gauge fields
- Haldane / Hofstadter model
- Fractional hall effect, quantum states with topological properties
- Lattices with non-trivial unit cells: SSH model, Graphene ...
- Quantum gas microscopes
- Quantum gases with long-range interactions