300 likes | 1.22k Views
Bose-Einstein Condensation. Student: Miaoyin Wang Instructor: Elbio Dagotto Class: Solid State II, 2010, Spring Semester Institution: Department of Physics, University of Tennessee, Knoxville. 0. Structure of Presentaton. Bosons and Bose-Einstein Distribution
E N D
Bose-Einstein Condensation Student: Miaoyin Wang Instructor: Elbio Dagotto Class: Solid State II, 2010, Spring Semester Institution: Department of Physics, University of Tennessee, Knoxville
0. Structure of Presentaton • Bosons and Bose-Einstein Distribution • Bose-Einstein Condensation • Experiment Realization of BEC • Summary
1. Bosons & Bose-Einstein Distribution Bosons! Q: How to distinguish one object from another? - Think of daily life object -Think of microscopic particles
1. Bosons & Bose-Einstein Distribution Bosons vs Fermions Bosons – integer spin / no Pauli exclusion Fermions – half integer spin / Pauli exclusion Fermions - 1 way Bosons – 10 ways Classical?
1. Bosons & Bose-Einstein Distribution Bose-Einstein Distribution For N identical bosons with M available quantum states, there are ways that the particle can be distributed. For quantum states with different energies:
1. Bosons & Bose-Einstein Distribution Bose-Einstein Distribution Consider an ideal gas model for bosons, we have The entropy of the gas is S=kB ln W Thus we can apply Lagrange multipliers
1. Bosons & Bose-Einstein Distribution Bose-Einstein Distribution Finally, after some calculation, we get for each energy shell and thus Bose-Einstein Distribution
2. Bose-Einstein Condensation (BEC) Observe the equation: >= 0 >= 0 >= 1 (always!)
2. Bose-Einstein Condensation (BEC) Since f(E) is a distribution, it also fulfills Suppose there is a temperature that (we are not sure about it!) Have a try Temperature
2. Bose-Einstein Condensation (BEC) What will happen below Tc? Where do the particles go? : ( After Before keeps it constant There is no Total number decreased! Bose-Einstein Condensation
2. Bose-Einstein Condensation (BEC) Where do the particles go?
3. Experimental BEC How Tc changes upon n? To achieve BEC, one can either decrease the temperature or increase the particle density. A temperature-density phase diagram will help a lot!
3. Experimental BEC Difficulty to achieve BEC BEC before it is forbiddened! Make Time BEC << Time thermal equilibrium
3. Experimental BEC So: have to do it in a hurry - Pulsed laser beam as detector - Magneto-Optical Trap (MOT) Also: make thermal equilibrium time scale larger - Choice of atoms – Rubidium 87 Still: very very cold! - MOT cooling - Cool by expand
3. Experimental BEC Procedure Normal method Laser MOT Expand
3. Experimental BEC Result: velocity distribution data 50nK 180nk 1600nk 200nK 400nK
3. Experimental BEC Anisotropy of the data Due to Heisenberg Uncertainty Principle (h~x*p) + Anisotropy of the space distribution
3. Experimental BEC Other type of BEC in Experiment • Superfluid ~Helium-4 @ 2.17K ~only about 8% of the atoms accumulate in ground state - not a “pure” BEC. • Fermions ~extremely low temperature ~must “pair up” to form compound particles (like molecules or Cooper pairs) that are bosons. • Magnons ~ a BEC transmission temperature at room temperature ~achieved by pumping the magnons into the system and form a high density n
4. Summary • BEC is predicted early and achieved tens of years later, inspiring a lot of related technologies. • BEC in lab is very fragile. Extremely low temperature and density is required. • BEC can be useful in very basic physics. • It can also be used in ultra-sensitive measurements. (Think of laser)
5. References [1] Superconductivity, Superfluids and Condensates, J.F.Annett, ISBN 7-03-023624-1 [2] Thermodynamics and Statistical Mechanics, Zhicheng Wang, ISBN 7-04-011574-3 [3] Levi, Barbara Goss (2001). "Cornell, Ketterle, and Wieman Share Nobel Prize for Bose–Einstein Condensates". Search & Discovery. Physics Today online. http://www.physicstoday.org/pt/vol-54/iss-12/p14.html. [4] Bose-Einstein Condensation, Wikipedia, http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate#cite_note-nobel-4 [5] M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell (1995). "Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor". Science 269 (5221): 198–201. [6 ] S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm (2003). "Bose–Einstein Condensation of Molecules". Science 302 (5653): 2101–2103 [7] Demokritov, S.O.; Demidov, VE; Dzyapko, O; Melkov, GA; Serga, AA; Hillebrands, B; Slavin, AN (2006). "Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping". Nature 443 (7110): 430–433
Thank you! Student: Miaoyin Wang Instructor: Elbio Dagotto Class: Solid State II, 2010, Spring Semester Institution: Department of Physics, University of Tennessee, Knoxville