Theory of Ultracold Atoms
Lecturer: Prof. Dr. Tilman Enss
Link zum LSF
25 participants
The field of ultracold atomic gases has undergone a remarkable development over the past few years and is now a key area of manybody physics at the interface to condensed matter, atomic and nuclear physics. This course introduces the theoretical concepts and methods of ultracold quantum gases and covers many timely examples, as seen in current experiments also in Heidelberg. Many of the topics that we discuss for cold atoms (BoseEinstein condensation, superfluidity, fermion pairing, quantum phase transitions, thermalization) are at the same time more general paradigms of manybody physics and are used also in other areas of physics. The exercises also show how to compute experimental observables.
Dates and Location
Lecture Tuesday and Thursday 09.1511.00h, online starting April 13 [LSF].
Exercise Tuesday 14.1516.00h, online starting April 20.
You may unregister yourself before June 30.
Prerequisites
 Quantum Mechanics (PTP4)
 Theoretical Statistical Physics (MKTP1)

recommended: Advanced Quantum Theory (MVAMO2)
Literature
As an introduction, the lecture notes by Ketterle and Zwierlein are particularly recommended.
 Ketterle and Zwierlein, Making, probing and understanding ultracold Fermi gases, Varenna lecture notes (2008).
 Pitaevskii and Stringari, BoseEinstein Condensation, Clarendon Press 2003.
 Pethick and Smith, BoseEinstein Condensation in Dilute Gases, Cambridge University Press 2008.
 Zwerger (ed.), The BCSBEC Crossover and the Unitary Fermi Gas, Springer Lecture Notes in Physics 836 (PDF available from the university library).
 Diehl, ManyBody Physics with Cold Atoms, Innsbruck lecture notes (2013).
 Bloch, Dalibard, and Zwerger, Manybody physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).

Fetter and Walecka, Quantum Theory of ManyParticle Systems, Dover 2003.
Exam
The exam will be held on Thursday, 22 July 2021, from 09:0010:30h.
Curriculum / Timeline
The lectures and tutorials take place as a zoom video call (see link on lecture page); see the highlighted section in the time line below for the current lecture. You may discuss with your fellow students in the TUA chat channel.
Enjoy the course!

Strongly interacting fermions: the BCSBEC crossover

Lecture 01 (Tue 20210413): Trapped quantum gas
how do quantum particles behave in a potential landscape?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.1 on ideal Fermi and Bose gas in confining potential
no tutorial today: the tutorial starts next week (April 20)

Lecture 02 (Thu 20210415): Scattering theory
how do quantum particles scatter at low energy?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.2.1 on scattering theory, partial wave expansion, phase shifts, square well potential

Lecture 03 (Tue 20210420): Feshbach resonances and pseudopotential
how strongly can particles scatter and how can we tune it?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.2.4 on Feshbach resonances, pseudopotential and length scales
join the first tutorial at 14:15h (zoom link above)

Lecture 04 (Thu 20210422): Mean field theory and Cooper pairs
how can fermions form pairs already for weak attraction?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.3.1 on meanfield theory and Cooper pairs

Lecture 05 (Tue 20210427): BCS theory of superconductivity
how to construct a superconducting state
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.3.2 on reduced BCS model, Bogoliubov transformation, quasiparticles, gap and number equation
join the second tutorial at 14:15h (zoom link above)

Lecture 06 (Thu 20210429): BCS critical temperature and BoseEinstein condensation
how is the critical temperature related to the gap?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.4.1 on BCS gap and critical temperature, BoseEinstein condensation, offdiagonal long range order

Lecture 07 (Tue 20210504): Weakly interacting Bose gas and GrossPitaevskii equation
what is the effect of quantum and thermal fluctuations on a BEC?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.4.3 on Bogoliubov theory, quantum and thermal depletion, GrossPitaevskii equation, order parameter
join tutorial 3 at 14:15h (zoom link above)

Lecture 08 (Thu 20210506): Superfluidity
what is the difference between a condensate and a superfluid?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.4.4 on hydrostatics and hydrodynamics of BECs, vortices, superfluidity and Landau's twofluid model

Lecture 09 (Tue 20210511): BEC vs SF / Unitary Fermi gas
what is special about the Fermi gas at the scattering resonance?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.5.1 on quantum hydrodynamic Hamiltonian, BEC vs superfluid, unitary Fermi gas, scale transformations
join tutorial 4 at 14:15h (zoom link above)

Lecture 10 (Tue 20210518): Unitary Fermi gas
how can the universal equation of state be computed?
join the live lecture at 9:15h (zoom link above)
lecture notes sec. 1.5.2 (page TUA66) on scale transformations, virial theorem, Bertsch parameter, universal equation of state, theoretical manybody techniques
join tutorial 5 at 14:15h (zoom link above)
 Contact density and Tan relations
 Fermi polarons and spectroscopy

Lecture 01 (Tue 20210413): Trapped quantum gas

Bosons in optical lattices: the Mott Insulator—Superfluid transition
 Optical lattices and BoseHubbard model
 Mott Insulator—Superfluid transition
 Quantum Critical Point, excitations and Higgs mode
 FermiHubbard model
 Quantum Simulation

Realtime dynamics and transport
 Nonequilibrium dynamics and thermalization
 Collective modes and transport
Practice groups
 Group 1 (Enss)
25 participants
online, Tue 14:15  16:00