Solitons in atomic Bose-Einstein Condensates (BEC)

1. Solitons in atomicBose-Einstein Condensates(BEC) Gediminas Juzeliūnas Institute of Theoretical Physics and Astronomy of Vilnius University, Vilnius, Lithuania

2. Collaboration • P. Öhberg, Heriot-Watt University, Edinburgh, Scotland • J. Ruseckas, Institute of Theoretical Physics and Astronomy of Vilnius University • M. Fleischhauer, Technische Universität Kaiserslautern, Germany

3. OUTLINE • Ultra-cold atomic gases • Atomic Bose-Einstein condensates (BEC) • Solitons & solitons in atomic BEC • Creation of solitons in atomic BEC • A new method of creating solitons in BEC • Conclusions

4. Atomic

5. Applications

7. Heidelberg Experiment (Applied Physics Letters, 27 June 2006)

8. Bose-Einstein Condensation (Velocity distribution)

9. BEC – A giant (non-linear) matter wave

10. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of a condensate For simplicity V=0 (no trapping potential):

11. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of the condensate • Interaction strength • between the atoms

12. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of the condensate Linear wave equation Wave-packet is spreading out

13. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of the condensate Non-linear wave equation Non-spreading wave-packets (solitons) are possible

14. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of the condensate Bright soliton Dark soliton

15. Non-linear Schrödinger equation(Gross-Pitaevskii) • Wavefunction of the condensate Bright soliton Dark soliton What is a bright and a dark soliton?

16. Intensity and phase of the condensate

17. Intensity and phase of the condensate Dark soliton:

18. Difference between dark and bright solitons

19. Bright soliton Dark soliton

20. Intensity and phase of the condensate

21. First observation of (bright) solitons (1844, J. Scott Russell ) Observed a solitary water wave in a water canal near Edinburgh John Scott Russell (1808 – 1882)

22. Recreating Russell’s soliton in 1995

23. Currently • Optical solitons (bright, dark) since the 60’s (Depends on the sign of non-linearity) • Solitons in BEC (dark, bright), since 1999 • Rb, Na – dark solitons (κ>0) • Li – bright solitons (κ<0)

24. Usual way to create a (dark) soliton in BEC • To imprint the phase (by illuminating a half of the BEC)

25. Drawbacks • Not very sharp phase slip • No hole in the density • Sensitive to the duration of illumination • Not robust method

26. A very sharp phase slip & a hole in the density are needed:

27. Our method:Adiabatic passage in a tripod configuration • Robust • Both solitons and soliton molecules can be produced

28. How does the adiabatic passage work?

29. Adiabatic passage Λ configuration:

30. Two beams of light:Probe beam:Control beam:

31. Dark state:Destructive interferenceCancelation of absorption:- no losses- EIT

32. Dark state:

33. Dark state:Atom remains in the dark state: Adiabatic passage(STIRAP) - a smooth transition 1→2by changing the ratio

34. Dark state:Atom remains in the dark state: Adiabatic passage1→2 →1Double STIRAP (two STIRAPs)

35. Dark state:Adiabatic passage1→2 →1πphase slip

36. Dark state:Atom remains in the dark state: Adiabatic passage1→2 →1πphase slip A problem

37. Dark state:Atom remains in the dark state: Adiabatic transition 1→2 →1πphase slip The problem by-passed

38. Tripod configuration • Two degenerate dark states: e.g., J. Ruseckas, G. Juzeliūnas and P.Öhberg, and M. Fleischhauer, Phys. Rev. Letters 95, 010404 (2005).

39. Tripod configuration

40. A suggested setup to create solitons in BEC (Double STIRAP with a support beam 3) BEC initially in the state 1: π phase imprinting on the BEC in the state 1:

41. After the sweeping • Phase imprinting → (dark) soliton formation • πphase slip; • a hole in the density

42. After the sweeping • Phase imprinting → (dark) soliton formation • More specifically - dark-bright soliton pair • πphase slip; • a hole in the density

43. A soliton molecule - two component dark soliton (dark-dark soliton pair) • Both components 1 and 2 are populated after the sweeping (with a π phase slip) Subsequently the solitons oscillate:

44. Oscillation of solitons forming the molecule

45. Conclusions • A new method of creating solitons • Robust • Creation of soliton molecules is possible

46. Thank you!