Experimental and Theoretical Aspects of Quantum Gases

General remarks on the exercise class

Problem sets will be handed out on Tuesdays during the lecture (not during the first week), and are to be handed in before the next Monday at 12:00. Your solutions may be handed in via the mailboxes next to the secretaries on the K-floor of the HIT building. Please put them in the mailbox of Sina Zeytinoglu.

Note: Please clearly indicate on your solution sheets which exercises you want to have explicitly checked, if you find that the exercise class and solution sheet are not enough. Handing in your solutions will be noticed irrespective of whether you want them to be checked or not.

Lecture notes

1. DownloadChapter 1 (PDF, 1.6 MB)vertical_align_bottom
2. DownloadChapter 2 (PDF, 1.4 MB)vertical_align_bottom
3. DownloadChapter 3 (PDF, 1.7 MB)vertical_align_bottom
4. DownloadChapter 4 (PDF, 1.4 MB)vertical_align_bottom
5. DownloadChapters 5 & 6 (PDF, 2.9 MB)vertical_align_bottom
6. DownloadChapter 7 (PDF, 2.2 MB)vertical_align_bottom
7. DownloadChapter 8 (PDF, 3.5 MB)vertical_align_bottom
8. DownloadChapter 9 (PDF, 2 MB)vertical_align_bottom
9. DownloadChapter 10 (PDF, 1.6 MB)vertical_align_bottom

Paper references for the paper discussions

1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science 269, 198 (1995).
2. Inouye, et al. Observation of Feshbach resonances in a Bose–Einstein condensate, Nature 392, 151 (1998)
3. Buggle, et al., Interferometric Determination of the s and d-Wave Scattering Amplitudes in Rb87, Phys. Rev. Lett. 93, 173202 (2004).
4. Buggle, et al., Interferometric Determination of the s and d-Wave Scattering Amplitudes in Rb87, Phys. Rev. Lett. 93, 173202 (2004).
5. Madison, et al., Vortex Formation in a Stirred Bose-Einstein Condensate, Phys. Rev. Lett. 84, 806 (2000)
6. Steinhauer, et al., Excitation Spectrum of a Bose-Einstein Condensate, Phys. Rev. Lett. 88, 120407 (2002)
7. Raman, et al., Evidence for a Critical Velocity in a Bose-Einstein Condensed Gas, Phys. Rev. Lett. 83, 2502 (199)
8. Bloch, et al., Measurement of the spatial coherence of a trapped Bose gas at the phase transition, Nature 403, 166 (2000)
9. Greiner, et al., Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature 415, 39 (2002)
10. Endres, et al., The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature 487, 454 (2012)
11. Kinoshita, et al., Observation of a One-Dimensional Tonks-Girardeau Gas, Science 305, 1125 (2004)

Exercises

1. Problem Set 1
2. Problem Set 2
3. Problem Set 3
4. Problem Set 4
5. Problem Set 5
6. Problem Set 6
7. Problem Set 7
8. Problem Set 8
9. Problem Set 9
10. Problem Set 10

Journal Club

1. Z. Hadzibabic et al., Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas, Nature, 441, 1118 (2008)
2. T. Jeltes et al., Comparison of the Hanburry-Brown-Twiss effect for bosons and fermions, Nature 445, 402 (2007)
3. S. Foelling et al., Spatial quantum noise interferometery in expanding ultracold atom clouds, Nature 434, 481 (2005)
4. M. Greiner et al., Collaps and revival of the matter wave field for a Bose-Einstein condensate, Nature, 419, 51 (2003)
5. T. Donner et al.: Critical Behavior of a Trapped Interacting Bose Gas, Science 315, 1556 (2007)
6. W.S. Bakr et al., A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature, 462, 74 (2009)
7. J. Billy et al., Direct observation of Anderson localization of matter waves in a controlled disorder, Nature 453, 891, (2008)
8. X. Zhang, et al., Observation of Quantum Criticality with Ultracold Atoms in Optical Lattices, Science, 335, 1070 (2012)
9. T. Kinoshita et al., A quantum Newton’s cradle, Nature 440, 900 (2006)
10. M. Vengalattore et al., Spontaneously Modulated Spin Textures in a Dipolar Spinor Bose-Einstein Condensate, Phys. Rev. Lett., 100, 170403 (2008)
11. P. Schauss et al., Observation of spatially ordered structures in a two-dimensional Rydberg gas, Nature 491, 87 (2012)

Literature

You will find a list of useful literature below. The list might be updated during the course of the lecture.

1. C. J. Pethick and H. Smith, Bose-Einstein condensation in dilute gases, Cambridge University Press, 2008.
2. L. P. Pitaevskii, S. Stringari, Bose-Einstein condensation, Oxford University Press, 2003.
3. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, external pageTheory of Bose-Einstein condensation in trapped gasescall_made, Rev. Mod. Phys. 71, 463 (1999).
4. S. Giorgini, L. P. Pitaevskii, and S. Stringari, external pageTheory of ultracold atomic Fermi gasescall_made, Rev. Mod. Phys. 80, 1215 (2008).
5. W. Ketterle, D. S. Durfee, and D. M. Stamper-Kurn, external pageMaking, probing and understanding Bose-Einstein condensatescall_made, Proceedings of the Enrico Fermi International School of Physics, Course CXL (ed. M. Inguscio, S. Stringari, and C.E. Wieman), p. 67, IOS Press, Amsterdam, 1999.
6. W. Ketterle and M. W. Zwierlein, external pageMaking, probing and understanding ultracold Fermi Gasescall_made, Proceedings of the International School of Physics Enrico Fermi, Course CLXIV (ed. M. Inguscio, W. Ketterle, and C. Salomon), p. 95, IOS Press, Amsterdam, 2007.
7. J. Dalibard, external pageCollisional dynamics of ultra-cold atomic gasescall_made, Proceedings of the International School of Physics Enrico Fermi, Course CXL (ed. M. Inguscio, S. Stringari, and C. E. Wieman), p.321, IOS Press, Amsterdam, 1999.