1. Molecules and Cooper pairs in Ultracold Gases Krynica 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

7. T HE W ASHINGTON P OST F RIDAY, J ULY 14, 1995

8. 31 new BECs reported

11. Molecule Of the Year The Bose-Einstein Condensate

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

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

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

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

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 85 Rb * 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. Decaying Oscillations

31. Oscillation frequency

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

33. “BCS-Superfluid” Overlapping Pairs Edge of Fermi Surface Spatial k+q -k+q -k’+q’ k’+q’ k -k k q q’ q’’ Momentum “Crossover Regime” Clusters Smeared 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

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

43. BCS-BEC in K

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

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

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

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

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

49. Summary 1.New era of strong correlation studies 2.Dynamical aspects are crucial 3.Much theory to be done.

55. T HE W ASHINGTON P OST F RIDAY, J ULY 14, 1995

56. 31 new BECs reported

59. Molecule Of the Year The Bose-Einstein Condensate