Many Particle Physics with Ultracold Atoms

The module will give an introduction to basic concepts in many-body physics in the context of ultracold gases. Emphasis is laid on an understanding of the underlying physics, with a minimum of formalism. It is assumed that students are familiar with quantum mechanics (including some scattering theory) and statistical physics. Detailed lecture notes and references to the relevant literature will be provided. The lecture is structured as follows:

I. Bose-Einstein Condensation, Optical Lattices

1. Bose-Einstein Condensation and Superfluidity
2. Bose-Hubbard model, Superfluid-to-Mott Insulator Transition
3. Ultracold Gases in one dimension, Bosonization and Luttinger liquids
4. Higgs-mode in lattice Superfluids

II. Ultracold Fermions

1. Feshbach Resonance
2. Zero-range interactions and Tan Relations
3. Unitary Fermions, Scale Invariance
4. RF-Spectroscopy, Spectral Functions
5. Quantum Limits for Viscosity and Spin-Diffusion

After successful completion of the module the students are able to:

• describe and apply the physical foundations related to many-body physics in the context of ultracold gases
• list and explain the basic properties of Bose-Einstein condensates as well as discuss their experimental observation
• explain the Bose-Hubbard model and apply it to superfluid-to-Mott quantum phase transitions
• understand the concept of bosonization of fermions
• discuss one-dimensional conduction in ultracold gases and Luttinger liquids (as opposed to Fermi liquids)
• understand optical lattice superfluids
• describe the concept of a Higgs Mode in lattice superfluids
• explain Feshbach resonances in many-body systems
• understand and discuss the physical foundations of unitary Fermi gases, Tan relations, zero-range interactions and scale invariance
• illustrate and discuss radio-frequency spectroscopy, interpret spectral functions in its context
• explain the quantum limits for viscosity and spin-diffusion

No preconditions in addition to the requirements for the Master’s program in Physics.

In the thematically structured lecture the learning content is presented. With cross references between different topics, the relevant physical concepts are shown. In scientific discussions the students are involved to stimulate their analytic intellectual strength. The lecture notes contain references to textbooks, review papers and publications, which intoduce the students to their independent literature research. The students are led to independently deepen the knowledge acquired in the lecture through their own research.

In the exercise the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

• blackboard
• lecture notes

• I. Bloch, J. Dalibard, W. Zwerger: Many-body physics with ultracold gases, Rev. Mod. Phys 80, 885, (2008)
• L. Pitaevskii, S. Stringari: Bose-Einstein Condensation and Superfluidity, Oxford University Press, (2016)
• C.J. Pethick, H. Smith: Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, (2008)

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Name the fundamental properties of Bose-Einstein condensation
• Explain the foundations of the Bose-Hubbard model
• Discuss how the Superfluid-to-Mott-Insulator transition can be described by the Bose-Hubbard model
• Explain the concept of Feshbach resonance
• How is a unitary gas defined and what special properties does it have?
• Discuss the quantum mechanical limits for viscosity and spin-diffusion

In the exam no learning aids are permitted.