Quantum Gases: Past, Present, and Future

1. Quantum Gases: Past, Present, and Future Jason Ho The Ohio State University Hong Kong Forum in Condensed Matter Physics: Past, Present, and Future HKU and HKUST, Dec 18-20

2. Where we stand What’s new Fundamental Issues Challenges

3. A decade since discovery of BEC : Still expanding rapidly Discoveries of new systems, new phenomena, and new technique keep being reported in quick succession. Highly interdisciplinary -- (CM, AMO, QOP, QI, NP) New Centers and New Programs formed all over the world. England, Japan, Australia, CIAR, US (MURI&DARPA) Puzzling phenomena being to emerge in fermion expts Worldwide experimental effort to simulate strongly correlated CM systems using cold atoms

4. J=1/2 alkali atoms J Bosons and Fermions with large spins e I Spin F=1, F=2 bosons: F=I+J Hyperfine spin Spin F=1/2, 3/2, 5/2, 7/2, 9/2 fermions

5. Magnetic trap B Atoms “lose” their spins! Spinless bosons and fermions

6. Magnetic trap B Mixture of quantum gases: Ho and Shenoy, PRL 96 Pseudo-spin 1/2 bosons: D.S. Hall, M.R. Matthews, J. R. Ensher, C.E. Wieman, and E.A. Cornell PRL 81, 1539 (1998)

7. Focused laser Optical trapping: BEC or cold fermions All spin states are trapped, Spin F=1, F=2 bosons: T.L.Ho, PRL 1998 Spin F=1/2, 3/2, 5/2, 7/2, 9/2 fermions

8. Condensed Matter Physics Atomic Physics BEC Quantum Optics Nuclear Physics Quantum Gases Quantum Information High Energy Physics

9. Quantum Gases system symmetry environments interaction 3D 2D 1D 0D B BB BF FF F U(1) Magnetic trap, spins frozen S0(3)Optical trap, spins released stationary fast rotating single trap lattice

10. 1996 Discovery of BEC! 1997 Mixture of BEC and pseudo spin-1/2 Condensate interference collective modes solitons Spin-1 Bose gas (Super-radiance) Bosanova Bragg difffration, super-radience, Superfluid-Mott oscillation 1999 Low dimensional Bose gas (Vortices in 2-component BEC) 2000 (Vortices in BEC,Slow light in BEC) 2001 Fast Rotating BEC, Optical lattice, BEC on Chips 2002 Quantum degenerate fermions (Spin dynamics of S=1/2 BEC, Coreless vortex in S=1 BEC, evidence of universality near resonance) 2003 Molecular BEC, (Spin dynamics of S=1 BEC, noise measurements) Fermion pair condensation! (pairing gap, collective mode) BEC-BCS crossover, Vortices in fermion superfluids, discovery of S=3 Cr Bose condensate, observation of skymerion in S=1 Bose gas. Effect of spin asymmetry and rotation on strongly interacting Fermi gas. Boson-Fermion mixture in optical lattices.

11. New Bose systems: “spin”-1/2, spin-1, spin-2 Bose gas, Molecular Bose gas. (BEC at T=0) Un-condensed Bose gas: Low dimensional Bose gas, Mott phase in optical lattice Strongly Interacting quantum gases: Atom-molecule mixtures of Bosons near Feshbach resonance Fermion superfluid in strongly interacting region Strongly interacting Fermions in optical lattices Possible novel states: Bosonic quantum Hall states, Singlet state of spin-S Bose gas, Dimerized state of spin-1 Bose gas on a lattice. Fermion superfluids with non-zero angular momentum

12. Often described as experimental driven, but in fact theoretical ideas are crucial. Bose and Einstein, Laser cooling, Evaporative cooling

13. What is new ? A partial list: Bosons and Fermions with large spins Fast Rotating Bose gases Superfluid Insulator Transition in optical lattices Strongly Interacting Fermi Gases

14. Question: How do Bosons find their ground state?

15. Question: How do Bosons find their ground state? Conventional Bose condensate : all Bosons condenses into a single state.

16. What happens when there are several degenerate state for the Bosons to condensed in? G: Number of degenerate states N: Number of Bosons

17. What happens when there are several degenerate state for the Bosons to condense in? G: Number of degenerate states N: Number of Bosons Pseudo-spin 1/2 Bose gas: G =2

18. G: Number of degenerate states N: Number of Bosons Spin-1 Bose gas : G=3, G<<N

19. G: Number of degenerate states N: Number of Bosons Spin-1 Bose gas : G=3, G<<N Bose gas in optical lattice: G ~N

20. G: Number of degenerate states N: Number of Bosons Spin-1 Bose gas : G=3, G<<N Bose gas in optical lattice: G ~N Fast Rotating Bose gas: G>>N

21. Effect of spin degeneracy on BEC Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap Only the lowest harmonic state is occupied => a zero dimensional problem

22. Spin dynamics of spin-1 Bose gas Spin-1 Bose Gas A deep harmonic trap Hilbert space

23. Effect of spin degeneracy on BEC Effect of spin degeneracy on BEC Spin-1 Bose Gas A deep harmonic trap Under spin rotation, rotates like a 3D Cartesean vector . : 3D rotation

24. C>0 Conventional condensate :

25. C>0 = Exact ground state : Ho and Yip, PRL, 2004

26. Relation between singlet state and coherent state z Average the coherrent state over all directions Because y The system is easily damaged x

27. Transformation of singlet into coherent states as a function of External field and field gradient: If the total spin is non-zero Bosonic enhancement

28. Transformation of singlet into coherent states as a function of External field and field gradient: If the total spin is non-zero Bosonic enhancement

29. Transformation of singlet into coherent states as a function of External field and field gradient: If the total spin is non-zero

30. Transformation of singlet into coherent states as a function of External field and field gradient: If the total spin is non-zero With field gradient

31. S=2 Cyclic state S=3 Spin biaxial Nematics

32. A geometric representation : Generalization of Barnett et.al. PRL 06 & T.L.Ho, to be published

33. Cycle Tetrahedron S=2 Octegonal S=3 Cubic S=4 Icosahedral S=6 T.L. Ho, to be published

34. Rotating the Bose condensate condensate Generating a rotating quadrupolar field using a pair of rotating off-centered lasers K. W. Madison, F. Chevy, W. Wohlleben, J. DalibardPRL. 84, 806 (2000)

36. The fate of a fast rotating quautum gas : Superfluidity ----> Strong Correlation Boson Quantum Hall Vortex lattice Overlap => Melting Normal Quantum Hall Fermion In superconductors

37. A remarkable equivalence Rotating quantum gases in harmonic traps Electrons in Magnetic field external rotation trap as

38. No Rotation : Two dimensional harmonic oscillator , n>0, m>0. E m

39. , n>0, m>0. E As , Angular momentum states organize into Landau levels ! m

40. E m

41. Mean field quantum Hall regime: in Lowest Landau level E condensate m

42. E Strongly correlated case: interaction dominated m

43. E. Mueller and T.L. Ho, Physical Rev. Lett. 88, 180403 (2002)

44. Simulate EM field by rotation: Eric Cornell’s latest experiment cond-mat/0607697 TL Ho, PRL 87, 060403(2001) V. Schweikhard, et.al. PRL 92, 040404 (2004) (JILA group, reaching LLL)

45. Fermion quantum Hall Boson + Fermion

46. Strongly interacting Fermi gases

47. Cooling of fermions Pioneered by Debbie Jin Motivation: To reach the superfluid phase Depends only on density For weakly interacting Fermi gas To increase Tc, use Feshbach resonance, since Holland et.al. (2001)

48. Weak coupling Dilute Fermi Gas : S-wave scattering length Normal Fermi liquid Weak coupling BCS superfluid

49. What Happens? Dilute Fermi Gas : S-wave scattering length Normal Fermi liquid Weak coupling BCS superfluid

50. Key Properties: Universality (Duke, ENS) Evidence for superfluid phase: Projection expt: Fermion pair condensataion -- JILA, MIT Specific heat -- Duke Evidence for a gap -- Innsbruck Evidence for phase coherence -- MIT BEC -- BCS crossover is the correct description Largest Origin of universality now understood