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Bose-Einstein Condensate Fundaments, Excitation and Turbulence

Bose-Einstein Condensate Fundaments, Excitation and Turbulence. Vanderlei Salvador Bagnato. Instituto de Física de São Carlos – Universidade de São Paulo USHUAIA -2012. Lectures: Basic concepts for BEC Excitations – collective modes Thermodynamics – Global variables

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Bose-Einstein Condensate Fundaments, Excitation and Turbulence

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

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

  3. SUPERFLUID OPTICS CONDENSED MATTER ATOMIC PHYS. BEC FLUIDS LASERS MAGNETISM. FIELD THEORY QUANT. VORTICES STAT. PHYS. 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. 1. QT in a trapped BEC There are two main cooperative phenomena of quantized vortices; Vortex lattice under rotation and Vortex tangle (Quantum turbulence). None M. Tsubota 3.

  6. How to form the vortices?

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

  8. BEC is a superfluid

  9. Idea of turbulent regimein 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 > Tc T < Tc T << Tc Turbulence Thermodynamics Magnetism Finite Temperature Mixture of BECs: K,Na

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

  13. Sequence of works 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 2009 2012

  14. BEC

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

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

  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 Phys. Rev. A 79, 043618 (2009) vortices

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

  20. BEC-I: results 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)

  21. PROLIFERATION

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

  23. Tangle vortices region

  24. KELVIN MODESVortex breaking and reconnecting

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

  26. A FEW VORTICES DOES NOT CAUSE SELF SIMILAR EXPANSION

  27. JLTP 166, 49-58 (2012

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

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

  30. EXCITATION RATE DEPENDS ON AMPLITUDE OVERPOPULATION OF VORTICES IN THE CLOUD TURBULENCE

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

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

  33. 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

  34. Simulation by Tsubota, Kasamatsu and Kobayashi - Japan

  35. Needs dissipation

  36. Conclusions: Intrinsic difficulties 2. 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…….. 3.

  37. THANKS

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