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| PHYS2027-2 | Ultracold atoms and Bose-Enstein condensates
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| Duration : | 25h Th |
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| Number of credits : |
| Master in Physical Sciences, in-depth approach, 1st year | | 4 |
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| Master in Physical Sciences, in-depth approach, 2nd year | | 4 |
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| Master in Physical Sciences, didactic approach, 1st year | | 4 |
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| Master in Physical Sciences, didactic approach, 2nd year | | 4 |
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| Master in Physical Sciences, specialized approach, 1st year | | 4 |
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| Master in Physical Sciences, specialized approach, 2nd year | | 4 |
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| Master in Physical Sciences | | 4 |
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| Lecturer : | Peter Schlagheck |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| 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 |
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Learning outcomes of the course :
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| 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. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| A necessary prerequisite for this course is to have basic knowledge of quantum mechanics.
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). |
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Planned learning activities and teaching methods :
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Mode of delivery (face-to-face ; distance-learning) :
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| The course will be given "ex cathedra" on the blackboard, in combination with the presentation of transparencies. |
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Recommended or required readings :
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| 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) |
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Assessment methods and criteria :
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| The evaluation will be done by an individual oral exam of 30 minutes on the contents of the course. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| 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 |
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| Items online : |
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| Bosons and fermions |
| 3 indistinguishable quantum particles in 3 states |
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| calculation of the specific heat |
| calculation of the specific heat for a noninteracting Bose gas confined within a harmonic potential |
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| Specific heat in free space |
| specific heat of a Bose gas in free space as a function of the temperature |
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| Specific heat in a harmonic oscillator |
| specific heat of a Bose gas in a harmonic oscillator as a function of the temperature |
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| Zeeman splitting for 87Rb |
| Zeeman splitting of the hyperfine states of 87Rb as a function of the magnetic field |
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| 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 |
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| wavefunctions of a Lennard-Jones potential |
| continuum eigenfunctions of a Lennard-Jones potential for different depths of the potential |
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| Bose gas in 1, 2, and 3 dimensions |
| curves of constant N in the \mu-T diagram |
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| Introduction |
| schedule and main topics of the course |
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| Bose function |
| graphs of the Bose function g_p(z) for different p |
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| 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 |
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| 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 |
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| Bogoliubov spectrum of a moving Bose-Einstein condensate |
| Bogoliubov spectrum of a moving Bose-Einstein condensate for different speeds v0 |
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| Bogoliubov spectrum of a free Bose-Einstein condensate |
| dispersion relation of the Bogoliubov modes of a Bose-Einstein condensate within free space |
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