Duration
25h Th
Number of credits
| Master in physics (120 ECTS) | 4 crédits | |||
| Master in physics (60 ECTS) (Registrations are closed) | 4 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
This course gives an introduction into the physical principles of Bose-Einstein condensation and their realization with ultracold atoms. We shall particularly discuss - quantum statistical physics - Bose-Einstein condensation with noninteracting particles - cold atoms in magnetic and optical traps - atom-atom interaction - mean-field theory of an interacting Bose-Einstein condensate - collective excitations within a condensate - superfluidity
Learning outcomes of the learning unit
The aim of this course is to understand the basics of Bose-Einstein condensation with ultracold atoms on the level that one is able to appreciate state-of-the-art experiments on the topic. This will also permit us to deepen the general knowledge of advanced quantum mechanics.
Prerequisite knowledge and skills
It is recommended to have followed the course "Advanced quantum mechanics", in order to better understand topics of advanced quantum theory that are needed to explain Bose-Einstein condensation with ultracold atoms (such as many-particle theory or scattering theory).
Planned learning activities and teaching methods
Mode of delivery (face to face, distance learning, hybrid learning)
The course will be given "ex cathedra" on the blackboard, in combination with the presentation of transparencies.
Recommended or required readings
Recommended literature: - K. Huang: "Statistical Mechanics" (John Wiley & Sons, 1963) - C.J. Pethick & H. Smith: "Bose-Einstein Condensation in Dilute Gases" (Cambridge University Press, 2002) - L. Pitaevskii & S. Stringari: "Bose-Einstein Condensation" (Oxford University Press, 2003) - L. D. Landau and L. M. Lifshitz: "Quantum Mechanics" (Pergamon Press, 1965)
Exam(s) in session
Any session
- In-person
oral exam
Additional information:
The evaluation will be done by an individual oral exam of 30 minutes on the contents of the course.
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Peter Schlagheck Département de Physique Université de Liège IPNAS, building B15, office 0/125 Sart Tilman 4000 Liège Phone: 04 366 9043 Email: Peter.Schlagheck@ulg.ac.be http://www.pqs.ulg.ac.be
Association of one or more MOOCs
Items online
Thomas-Fermi approximation
Thomas-Fermi approximation for a Bose-Einstein condensate in an isotropic trap, compared with a numerical solution of the Gross-Pitaevskii equation
Bosons and fermions
3 indistinguishable quantum particles in 3 states
calculation of the specific heat
calculation of the specific heat for a noninteracting Bose gas confined within a harmonic potential
Specific heat in free space
specific heat of a Bose gas in free space as a function of the temperature
Specific heat in a harmonic oscillator
specific heat of a Bose gas in a harmonic oscillator as a function of the temperature
Zeeman splitting for 87Rb
Zeeman splitting of the hyperfine states of 87Rb as a function of the magnetic field
variational energy of a Bose-Einstein condensate
ground-state energy of a Bose-Einstein condensate within an isotropic harmonic oscillator potential as a function of the variational parameter
wavefunctions of a Lennard-Jones potential
continuum eigenfunctions of a Lennard-Jones potential for different depths of the potential
Bose gas in 1, 2, and 3 dimensions
curves of constant N in the \mu-T diagram
Bose function
graphs of the Bose function g_p(z) for different p
s-wave scattering length in a Lennard-Jones potential
s-wave scattering length in a Lennard-Jones potential as a function of the depth of the potential
s-wave scattering length in a potential well
s-wave scattering length in a potential well as a function of the depth of the well
lecture notes
Lecture notes of the course "Ultracold Atoms and Bose-Einstein Condensates"
long-range order
This viewgraphh shows the behaviour of the spatial coherence of a gas of bosonic atoms as a function of the distance between two atoms. Above the condensation temperature, this coherence goes to zero if the distance goes to infinity, whereas it tends to a finite value below the condensation temperature.
Bogoliubov spectrum of a moving Bose-Einstein condensate
Bogoliubov spectrum of a moving Bose-Einstein condensate for different speeds v0
Bogoliubov spectrum of a free Bose-Einstein condensate
dispersion relation of the Bogoliubov modes of a Bose-Einstein condensate within free space