Theory of Ultracold Atoms

summer term 2021
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 many-body 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 (Bose-Einstein condensation, superfluidity, fermion pairing, quantum phase transitions, thermalization) are at the same time more general paradigms of many-body 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 09.15-11.00h, online starting April 13 [LSF].
Exercise Tuesday 14.15-16.00h, 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, Bose-Einstein Condensation, Clarendon Press 2003.
  • Pethick and Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press 2008.
  • Zwerger (ed.), The BCS-BEC Crossover and the Unitary Fermi Gas, Springer Lecture Notes in Physics 836 (PDF available from the university library).
  • Diehl, Many-Body Physics with Cold Atoms, Innsbruck lecture notes (2013).
  • Bloch, Dalibard, and Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  • Fetter and Walecka, Quantum Theory of Many-Particle Systems, Dover 2003.
     

Exam

The exam will be held on Thursday, 22 July 2021, from 09:00-10:30h.

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!

  1. Strongly interacting fermions: the BCS-BEC crossover
     
    • Lecture 01 (Tue 2021-04-13): 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 2021-04-15): 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 2021-04-20): 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 2021-04-22): 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 mean-field theory and Cooper pairs
       
    • Lecture 05 (Tue 2021-04-27): 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 2021-04-29): BCS critical temperature and Bose-Einstein 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, Bose-Einstein condensation, off-diagonal long range order
       
    • Lecture 07 (Tue 2021-05-04): Weakly interacting Bose gas and Gross-Pitaevskii 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, Gross-Pitaevskii equation, order parameter
      join tutorial 3 at 14:15h (zoom link above)
       
    • Lecture 08 (Thu 2021-05-06): 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 two-fluid model
       
    • Lecture 09 (Tue 2021-05-11): 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 2021-05-18): 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 TUA-6-6) on scale transformations, virial theorem, Bertsch parameter, universal equation of state, theoretical many-body techniques
      join tutorial 5 at 14:15h (zoom link above)
       
    • Contact density and Tan relations
    • Fermi polarons and spectroscopy
  2. Bosons in optical lattices: the Mott Insulator—Superfluid transition
    • Optical lattices and Bose-Hubbard model
    • Mott Insulator—Superfluid transition
    • Quantum Critical Point, excitations and Higgs mode
    • Fermi-Hubbard model
    • Quantum Simulation
  3. Real-time dynamics and transport
    • Nonequilibrium dynamics and thermalization
    • Collective modes and transport

Exercise sheets

Practice groups

 
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Theory of Ultracold Atoms
summer term 2021
T. Enss
Link zum LSF
25 participants
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