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 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 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 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

Bose-Einstein Distribution 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

Bose-Einstein Condensation 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!

BEC before it is forbiddened! 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

50nK 180nk 1600nk 200nK 400nK 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

Other type of BEC in Experiment 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