1. Critical fluctuations of an attractive Bose gas in a double well potential (no molecules here) Marek Trippenbach, with B. Malomed, P. Ziń, J. Chwedeńczuk, B. Oleś, K. Sacha, Ngien Viet Hung, M. Matuszewski, J. Gocałek EUROQUAM SATELLITE MEETING ON COLD AND ULTRACOLD MOLECULES

2. Plan Introducing CIGMA and BEC collisions BEC in double well Effects of higher dimensions Instability during collisions

4. Elastic collisions

6. BEC collision – the experiment A. Perrin et al. PRL 99, 150405 (2007) 2-nd order corelation

7. Theoretical model for collision Hamiltonian Bogoliubov approximation Condensate wave-function

8. Spontaneous versus Stimulated P. Ziń et al., Phys. Rev Lett. 94, 200401 (2005) J. Chwedeńczuk et al., Phys. Rev. Lett. 97, 170404 (2006) P. Ziń, J. Chwedeńczuk and M. Trippenbach, Phys. Rev. A 73, 033602 (2006)

9. Equations of motion the condensate: Gross-Pitaevskii Equation field of scattered atoms: time-dependent Bogoliubov approximation small 1st order perturbation theory

10. Theory versus experiment Close momenta opposite momenta

11. BEC in 1D double well by Markus Oberhaler

12. Experiment: Double well structure Markus Oberthaler, 2005

13. Oberthaler data

14. Why are we surprized: linear case

15. Linear case: tunneling only

16. Mean Field Approach

18. Energy diagram

19. Phase Space Dynamics

20. Dynamics

22. Two body interactions: Hamiltonian Introducing interactions Noninteracting particles … Localized states

23. Schrodinger Equation … and approximation

24. Continuum approximation Effective one dimensional equation

25. Effective potential

26. Fluctuations … can be done even in the repulsive case, if multicomponent

29. Wigner Function

36. BEC in double well effects of higher dimensions

37. Two channel potential

39. Hysteresis

40. Two channel solitons

41. Gap solitons

42. Two channel potential + lattice

43. Two channel potentail + lattice

44. Experimental Proposal: Hysteresis Wieslaw Krolikowski Pawel Zin Jan Chwedenczuk

49. Experimental Proposal: Collisions Nguen Viet Hung Pawel Zin Czesław Radzewicz