Fermi Quantum Gases

Course manual 2017/2018

Course content

Part I: Theory

1. Ultracold Fermi gases. Elastic and inelastic collisions between atomic fermions.
2. Ideal Fermi gas. Ground state and excitations. Ideal Fermi gas in an external harmonic potential.
3. Weakly interacting Fermi gases. Fermi gas with repulsive interaction between particles.
4. Landau Fermi liquid theory. Zero sound.
5. Weakly interacting Fermi gas with attractive interaction between particles. Cooper instability. BCS approach and single-particle excitations.
6. Gap equation. Collective modes. Andreev reflection.
7. Superfluidity in Fermi systems. Critical velocity. Superfluid and normal components.
8. Thermodynamics. Ginzburg-Landau equations. Vortices in Fermi gases.
9. Unconventional superfluid pairing. Pairing in a harmonic potential.
10. Strongly interacting Fermi gases. Universal thermodynamics in the unitarity regime. BCS-BEC crossover.
11. Two-dimensional Fermi gases. Interaction between particles and superfluid phase transition.
12. One-dimensional Fermi gases. Spin-charge separation. Diagram of states.

Part II: Experiment

See also lecture notes on www.strontiumbec.com/Teaching/Teaching.html.

Introduction: Quantum simulation

Part 1: Simulation of crystalline solids: Lattices: dispersion relation, Brillouin zone, Bloch states, Wannier states, Bloch oscillations, experimental realization; Derivation of Hubbard Hamiltonian, discussion of approximations; Superfluid to Mott-Insulator phase transition: phase diagram obtained by Gutzwiller Ansatz; Experimental observation: momentum distributions, measurement of gap, precise comparison with numerical solution; Observation of Mott shells by absorption imaging; Quantum gas microscopy: observation of superfluid to Mott-insulator phase transition.

Part 2: Artificial gauge fields: Artificial gauge fields by rotation, detection of vortices; The quantum Hall effect; Artificial gauge fields and Berry phase; BEC in a uniform light-induced vector potential; Synthetic magnetic fields for ultracold neutral atoms; Optical lattice with magnetic flux; The Harper-Hofstadter Hamiltonian and the Hofstadter butterfly; Realizing the Harper-Hofstadter Hamiltonian; Spin-orbit coupling

Part 3: Fermi gases: Creation and detection; Interaction tuning: Feshbach resonances; BEC-BCS crossover: what is it? Measuring the pairing gap; The unitary Fermi gas: equation of state, second sound; Polarons.

Part 4: Quantum simulation with ions and atom ion mixtures: trapped ions; trap technology; laser cooling; internal state control; gates; readout; examples; atom ion mixtures; reaching the quantum regime

Study materials

Literature

• R.P. Feynman, 'Statistical Mechanics'.
• K. Huang, 'Statistical Mechanics'.
• Ph. Nozieres and D. Pines, 'Theory of quantum liquids', Vol II.
• S. Stringari and L. Pitaevskii, 'Bose-Einstein condensation'.
• C.J. Pethick and H. Smith, 'Bose-Einstein condensation in dilute gases'
• J.F. Annet, 'Superconductivity, Superfluids and Condensates'.
• E. Demler, Strongly correlated systems in atomic and condensed matter physics, Lecture notes for Physics 284, Harvard University (2011)
• J.I. Cirac and P. Zoller, Goals and opportunities in quantum simulation, Nature Physics, 8, 264 (2012)
• I. Bloch, J. Dalibard, S. Nascimbéne, 'Quantum simulations with ultracold quantum gases', Nature Physics, 8, 264 (2012)

Other

• lecture notes available on blackboard.

Objectives

This course will bring students close to current research topics in ultracold quantum gases. The theory part gives a treatment for the phenomenon of superfluidity in Fermi systems. Starting from the properties of a normal Fermi gas, we give a detailed analysis of BCS pairing instability and reveal its many-body nature. Various possible mechanisms of pairing together with the properties of superfluid fermionic systems will be discussed. We will then address the issues of superfluid pairing in two-dimensional Fermi systems and the phenomenon of spin-charge separation in one dimension. The lectures emphasize advances in theory and the description of the remarkable experimental progress with ultracold quantum gases over the last two decades.

The second part explains how to study quantum physics using ultracold quantum gases and trapped ions in the spirit of quantum simulation. The most important building blocks of quantum simulators are introduced, both their theoretical description and their experimental implementation.

After following this course, the student is ready to take on a master thesis in the field of ultracold quantum gases.

Teaching methods

• Lecture
• Self-study
• Supervision/feedback meeting

Lectures and seminars.

Learning activities

Attendance

Requirements concerning attendance (OER-B).

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Additional information

Recommended prior knowledge: course 'Bose-Einstein condensates'.

Contact information

Coordinator

• prof. dr. Florian Schreck