Molecules and Cooper pairs in Ultracold Gases Krynica 2005

1. Molecules and Cooper pairs in Ultracold GasesKrynica 2005 Krzysztof Góral Marzena Szymanska Thorsten Köhler Joshua Milstein Keith Burnett

2. Outline 1. History 2. Feshbach Resonances 3. Atom-Molecule Coherences 4. BEC Molecules to BCS Pairs 5. Molecular Projection 6. Future work

3. Condensate

4. You've got the cutest little condensate

5. Nobel Committee's sure to take the bait

6. Condensate

7. You sure started something THE WASHINGTON POST FRIDAY, JULY 14, 1995

8. now this field is jumping 31 new BECs reported

9. condensate

10. I'm up in Stockholm when I'm in the trap ground state

11. Molecule Of the Year The Bose-Einstein Condensate No matter what the phase, I'm sure that atoms lase

12. In your pretty condensate

13. Bosons Fermions Hulet et al. (2003) Bose-Einstein Condensation Quantum Degenerate

14. Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

17. Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

18. Tuneable Interactions as>0 as<0 s-wave as<0, attractive as>0, repulsive 2-body bound states

19. Feshbach resonances Single resonance state approximation

20. Formal Feshbach Result

21. Entrance channel dominated resonance

22. Feshbach molecules can be huge!

23. Molecular binding energies 85Rb * N.R. Claussen et al., Phys. Rev. A 67, 060701 (2003); S. Kokkelmans, private communication.

24. Ramsey interferometry

25. Ramsey Interferometer

26. Ramsey fringes

27. The NLSE Gross-Pitaevskii Equation Collective modes Superfluidity Vortex formation Non-linear Atomic Optics

28. Microscopic quantum dynamics method Non-Markovian non-linear Schrödinger equation Zero momentum plane wave of the relative motion of two atoms in the entrance channel

29. Simulation Results For molecular Condensate

30. DecayingOscillations

31. Oscillation frequency

32. Molecular Condensation & Fermionic Superfluidity Jin et al. (2004) Jin et al. (2004) Repulsive Interactions Molecular bound states Attractive Interactions Many-body paired states

33. Momentum Spatial -k -k k k k+q -k’+q’ k’+q’ -k+q q q’ q’’ “BCS-Superfluid” Overlapping Pairs Edge of Fermi Surface “Crossover Regime” Clusters Smeared Fermi Surface “BEC-Superfluid” Distinct Pairs No Fermi Surface

34. BCS-BEC in K

36. Gap Equations for BCS-BEC 1) Single channel system works fine close to resonance. Two channel works over wider range. 2) Mean-Field Theory Solution

37. BCS-BEC in K

38. BCS-BEC in K

39. BCS-BEC in K

40. BCS-BEC in K

41. BCS-BEC in K

42. Condensate BCS-BEC in K Overlap zero at around half a Gauss above resonance

43. BCS-BEC in K

44. Momentum Spatial -k -k k k k+q -k’+q’ k’+q’ -k+q q q’ q’’ “BCS-Superfluid” Overlapping Pairs Edge of Fermi Surface “Crossover Regime” Clusters Smeared Fermi Surface “BEC-Superfluid” Distinct Pairs No Fermi Surface

45. Fee-Fi-Fo-Fum Cluster Model Variational Approach: Gaussian Wavepackets Dynamics/Thermodynamics of Small Clusters

46. Non-interacting Four independent particles BEC Limit Discrete, bound pairs

47. BCS-Limit Intermediate Limit Spatially overlap Bound pairs Distinctly fermions

48. Acknowledgments The Royal Society and Wolfson Foundation EPSRC EU Cold Quantum Gases Network EC Marie Curie Fellowships

49. Summary • New era of strong correlation studies • Dynamical aspects are crucial • Much theory to be done.