2. Physics and Astronomy Dept. Kevin Strecker, Andrew Truscott, Guthrie Partridge, and Randy Hulet Observation of Fermi Pressure in Trapped Atoms: The Atomic White Dwarf Star

3. Quantum Gases Quantum regime n7 3  1 Identical particles! Gas phase n  10 12 cm -3 Low temperature T  100 nK    1  m

4. Exchange Symmetry Bosons Symmetry with respect to particle exchange  12 (r 1,r 2 )  +  12 (r 2,r 1 ) S. Bose, 1924 A. Einstein, 1924-5 Multiple state occupation

5. Vortices Solitons Atom laser Atom wave guides Nonlinear atom optics Superfluidty Andrews et al., Science 275, 637, (1997) Atoms Occupy Lowest Energy State of Trap 7 Li Bose-Einstein Condensation

6. Bose-Einstein Condensation in an Almost Ideal Gas T c =   (N/1.2) 1/3

8. Exchange Symmetry Fermions Symmetry with respect to particle exchange  12 (r 1,r 2 )  -  12 (r 2,r 1 ) Obey Pauli Exclusion Principle Bosons  12 (r 1,r 2 )  +  12 (r 2,r 1 ) S. Bose, 1924 A. Einstein, 1924-5 Multiple state occupation E. Fermi, Feb. 1926 P.A.M. Dirac, Aug. 1926 EFEF

9. E. Fermi, Rendiconti Accademia Nazionale dei Lincei (2/2/26)

11. P.A.M. Dirac, Proc. Roy. Soc. (8/26/26)

13. and it comes in 2 nuclear spin states!

14. Lithium: Non-identical Twins 7 Li 3 e’s, 3 p’s, 4 n’s = 10 spin-½ particles  Boson 94% abundance 6 Li 3 e’s, 3 p’s, 3 n’s = 9 spin-½ particles  Fermion 6% abundance

15. Fermions - The Next Frontier Quantum Degenerate Fermi Gases 40 K: Demarco and Jin, Science 285, 1703 (1999) 6 Li: Truscott et al. (Rice), Science 291, 2570 (2001) 6 Li: Schreck et al. (Paris), Phys. Rev. Lett. 87, 080403 (2001). Current status: T  0.25 T F

16. Methods Laser cooling T  100  K Atom trapping n  10 12 cm -3 N  10 9  10 6 Evaporative cooling T  100  K  100 nK  -wave spin-flips Optical imaging

17. Laser Cooling Momentum is imparted to an atom when it scatters light from a laser Can slow or stop atoms in a beam Trapped and cooled to  K temperatures

18. Evaporative Cooling Spin flip ‘hot’ atoms at edge of trap Collisions re-thermalize distribution colder denser E f(E) RF Remove tail Re-thermalize

19. Sympathetic Cooling of 6 Li Pauli principle forbids s-wave interactions between identical fermions Use both 6 Li and 7 Li 6 Li 7 Li

20. Dual Source Apparatus 7 Li/ 6 Li Zeeman Slower Cloverleaf Trap Require vacuum pressure ~ 10 -11 Torr Oven

22. Imaging CCD Mirror Compound lens  -scope Zoom lens r A=e - 

23. 7 Li (Bosons) T = 240 nk T = 510 nk T = 810 nk 6 Li (Fermions) T/T F = 1.0 T/T F = 0.56 T/T F = 0.25 Truscott et al., Science 291, 2570 (2001) Sympathetic Cooling

24. Axial Profiles Truscott et al., Science 291, 2570 (2001)

25. Fermi Pressure in Trapped Atoms Truscott et al., Science 291, 2570 (2001)

26. Fermi Pressure Fermi pressure is result of Pauli Exclusion Principle Stabilizes white dwarf and neutron stars against gravitational collapse E F ~ n 1/3 (non-relativistic) E grav ~ n 1/3 Balance: Chandrasekar limit for white dwarf stars (1931)

27. Possible Experiments Boson/Fermion mixture –Phase separation –Superfluid probe Degenerate Fermi gas –BCS phase transition to a gaseous superfluid 6 Li has an enormous attractive interaction

28. BCS Transition in 6 Li? Cooper pairing –Superconductivity –Superfluidity 3 He –Dilute gas? – tunable interactions For s-wave pairing, T c  T F exp(-1/k F | a |) For 2 H, a = -4   T c = 1 fK @ 10 19 cm -3 –Leggett (1980) For 6 Li, a = -1100   T c = 30 nK @ 10 12 cm -3 –Stoof (1996) Induced interactions (fermi/fermi or bose/fermi) mod. T c –Heiselberg et al. (2000)

29. Cooper Pairing in 6 Li S-wave pairing symmetry forbidden between identical atoms  Create incoherent mixture of two states Stoof et al., PRL 76, 10 (1996)

33. Detecting Cooper Pairs Light scattering sensitive to –normal component, i.e. –pair correlation fcn. + –but r F ~ (E F / ½m  2 ) ½ ~ 50  m normal component r p ~ 1 / k F ~ 0.2  m pair correlation length Experiment: Zhang, Sackett, and Hulet, PRA 60, 504 (1999) Also, Ruostekoski, PRA 60, R1775 (1999) pairs normal  << E F  no significant change in density

34. Detecting Superfluidity Superfluids in anisotropic traps exhibit a “scissors” mode oscillation when displaced – Guery-Odelin and Stringari (theory) – Marago et al. (expt with BEC)