1. Bose-Einstein Condensate Fundaments, Excitation and Turbulence Vanderlei Salvador Bagnato Instituto de Física de São Carlos – Universidade de São Paulo USHUAIA -2012

2. Lectures: 1)Basic concepts for BEC 2)Excitations – collective modes Thermodynamics – Global variables 3)Vortices and Quantum turbulence Future directions

3. BEC OPTICS CONDENSED MATTER FLUIDS FIELD THEORY STAT. PHYS. MAGNETISM. LASERS ATOMIC PHYS. SUPERFLUID QUANT. VORTICES TURBULENCE

4. Quantum turbulence has recently become one of the most important branches in low temperature physics. Quantum turbulence has been studied thoroughly in superfluid 4He and 3He, but never addressed in atomic Bose-Einstein condensates. BECs may be a nice system for QT

5. Vortex latticeVortex tangle Superfluid He Atomic BEC There are two main cooperative phenomena of quantized vortices; Vortex lattice under rotation and Vortex tangle (Quantum turbulence). Non e 3. 1. QT in a trapped BEC M. Tsubota

6. How to form the vortices?

7. Main aspect of vortex in the superfluid  quantized (1) Circulation (2)core size is very small. Stability => n = 1 r Healing length = ( 8π ρ a ) - 1/2 MIT

8. BEC is a superfluid

9. Idea of turbulent regime in superfluids 1955: Feynman proposed that “superfluid turbulence” consists of a tangle of quantized vortices.

10. Liquid Helium 1955 – 1957: Vinen observed “superfluid turbulence”. Mutual friction between the vortex tangle and the normal fluid causes dissipation of the flow. Hard to see individual components in the turbulent fluid Observations are indirectly done

11. T > T c T < T c T << T c TurbulenceThermodynamicsMagnetismFinite Temperature Mixture of BECs: K,Na

12. ΩxΩx ΩzΩz Vortex lattice Vortex tangle ? 0 ωx×ωzωx×ωz From M. Tsubota Original motivation: Vortex lines are subject to many effects: oscillations, reconnections, etc…

13. GENERATION OF VORTICES FORMATIONS OF VORTICES CLUSTERS EMERGENCE OF TURBULENCE SELF-SIMILAR EXPANSION DIAGRAM OF EXCITATIONS FINITE SIZE EFFECT GRANULATION GENERALIZED THERMODYNAMICS MODEL FOR SELF-SIMILAR EXPANSION SECOND SOUND EXCITATION (COUNTER FLOW ) KINETIC ENERGY SPECTRUM 200 9 2012 Sequence of works

14. BEC

15. Displacement, Rotation and Deformation of the potential ADDITION OF “SHAKING” COILS EXCITATION BY OSCILLATION OF THE POTENTIAL Atomic washing machine

16. E. A. L. Henn et al., J. Low Temp. Phys. 158, 435 (2010) Total potential

17. PRODUCING BEC ( 1 MIN ) EXCITATION ( 0 TO 70 ms ) Time and amplitude Rest ( 20 ms) TOF FOLLOWED BY ABSORPTION IMAGE

18. VARYING AMPLITUDE AND TIME OF EXCITATION WE OBSERVE Oscillatory bending vortic es Phys. Rev. A 79, 043618 (2009)

19. Vortices and anti-vortices are together) Three-vortex configurations in trapped Bose-Einstein Phys. Rev. A 82,033616(2010)

20. Looking at stable three-vortex configurations we know that our excitation is able to create vortices and anti-vortices at the same time. J.A. Seman, et al. Phys. Rev. A 82, 033616 (2010) BEC-I: results

21. PROLIFERATION

22. Vortices to tangle vortices “TURBULENCE” J Low Temp Phys (2010) 158: 435–442 Phys. Rev. Lett. 103, 045301 (2009) Increasing amplitude or time of excitation: Explosion and proliferation of many vortices but no regular pattern and hard to count NON REGULAR – MANY POSITIONS ORIENTATIONS AND LENGTH

23. Tangle vortices region

24. KELVIN MODES Vortex breaking and reconnecting

25. Thermal BEC Turbulent Cloud expansion ( hydrodynamics) J. Phys. Conf.Ser.264,012004(2011)

27. A FEW VORTICES DOES NOT CAUSE SELF SIMILAR EXPANSION

28. JLTP 166, 49-58 (2012

30. Las. Phys. Lett. 8,691(2011)

31. Vortices ( TURBULENCE) Vortices ( NO TURBULENCE) CRITICAL LINE ------ Fitting: A+Ao = C/t Finite size effects on the QT Laser Phys. Lett. 8,393(2011)

32. EXCITATION RATE DEPENDS ON AMPLITUDE OVERPOPULATION OF VORTICES IN THE CLOUD TURBULE NCE

33. SIMPLE MODEL BASED ON ENERGY BALANCE Rate of energy transferred to the cloud ( Energy Coupled to the cloud )

34. ( Number of vortices formed) Turbulence takes place when vortices densely fill the trap:

35. There is a “kind “ of critical number of vortices introduced in the cloud before it gets to be turbulent  Determination of the board between non-turbulent and turbulent  For our conditions we calculated around 20 vortices

36. Simulation by Tsubota, Kasamatsu and Kobayashi - Japan

37. Needs dissipation

38. Vortex arrayVortex tangle Superfluid He Atomic BEC Conclusions: 2. 3. Intrinsic difficulties Hope The wider significance of QT rises interesting questions. I believe that many aspects of it are applicable in other fields. Grigory Volovick ( Finland ) suggests, for example that QT might have been important in the evolution of cosmic strings in the early universe. Certainly QT may throw light on many unsolved problems. The contribution of BEC for all that is in the very beginning……..