5 - The Fermi Liquid

Summary

1. Introduce density distribution and momentum distribution of non-interacting Fermi gas.

2. Discuss the transport property of a Fermi gas through a quantum point contact.

3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid.

4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid.

5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy.

6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example.

7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails.

8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue.

9. Summarize different spectroscopy measurements in ultracold atomic systems.