冷原子實驗之基本原理 (I)

1. 冷原子實驗之基本原理(I) 韓殿君 國立中正大學物理系 2003年 8月5日 於理論中心

2. Outline • Introduction • Works on the Degenerate Bose Gas • Cooling, Trapping, and Manipulating Tools • BEC Behavior • Remarks on the Current BEC Experiments and Future Directions

3. Introduction • Brief History of Bose-Einstein condensation (BEC) • Special Features of Dilute Bose condensates (Why dilute is important?)

6. nphase≧1 !! Phase Space!! spatial density Goal to achieve? Momentum space p: Cooling: lower T → larger d Coordinate(Position) space r: Trapping: increase n → smaller d

8. Superfluidity Vortices Excitation Mott Insulator Quantum Entanglement Feshbach Resonance ( a knob tuning the interactions!!) Coherence Interference Atom Laser Weakly Interacting Bose Gas Strongly Correlated Boson Systems Low Dimension Cold Molecules Multi- Species Phase fluctuations Nonlinearity Tonks Gas Works on the Degenerate Bose Gas

9. Cooling, Trapping, and Manipulating Tools Tools: Electric and magnetic fields (DC and AC ) EM waves – photons (visible, IR, microwave …) Systems: Atomic ensembles (atom number: 103 – 109) Macroscopic size: 5 – 500 m Ultrahigh vacuum environment (very little impurities) Ultralow temperatures ( 1 K) • No physical wall • Quiet and almost no defect potentials (as in the texbooks) are possible

10. Magnetic Trapsnot all the states are Trappable!! Please see the other file!

11. near resonance light! “scattering force” far-detuned light light! “dipole force” x |E0(x)|2 F(x) x |E0(x)|2 x x F(x) z z Optical Dipole Trap

12. BEC Behavior Starting from the Gross-Pitaevskii equation!!

13. “internal energy” or “mean field energy”

14. Time-Evolution of a Wavefunction in Free Space

15. neglected! Kanstanz, 1998 Thomas-Fermi Regime • NBEC > 105 atoms  Thomas-Fermi regime kinetic energy << internal energy • Cloud shape  inverted paraboloid

16. Phase transition (Lambda Point) energy per particle (Bose gas) condensate fraction JILA, 1996

17. Remarks on the Current BEC Experiments and Future Directions

18. Collective Mode Excitations JILA, 1996

19. Sound Propagation MIT, 1997

20. Superfluidity and Vortices laser beam condensate Votex lattice (a line-like excitation) MIT, 2002 critical velocity in a superfluid MIT, 2000

21. Skyrmions in a Multicomponent BEC- point-like excitation Utrecht, 2001 NOT YET realized experimentally!!

22. Two-Component Condensates JILA, 1997

23. Spinor Condensates MIT, 1999

24. Coherence and Correlation interference between two condensates three-body recombination rate 1st order correlation MIT, 1996 3rd order correlation JILA, 1997

25. Superradiant Rayleigh Scattering MIT, 1999

26. Matter Wave Amplification NIST, 1999

27. Nonlinear Atom Optics- Four Wave Mixing NIST, 1999

28. Bright Solitons Dark solitons were also observed! (NIST, 1999) Rice, 2002

29. Fechbach Resonaces- a tuning tool for atom-atom interaction MIT, 1998

30. Optical Lattices

31. Quantum Phase Transition 超流態轉變為非超流態(Mott 絕緣態)之量子相變 Max-Planck Institute, 2002

32. (a) x01 x02 (b) xb1(t) xa2(t) xa1(t) xb2(t) Quantum Entanglement (proposed idea) 凝聚體原子於光晶格中進行 量子糾纏(quantum entanglement) 簡易之二位元量子邏輯閘 (two-qubit logic gate) Innsbruck, 1999

33. Low Dimension Atom Traps 1D traps: large aspect ratio in one direction with the other two optical dipole trap and magnetic Ioffe traps are available 2D (surface) Traps: optical dipole trap and magnetic traps are available too

34. Phase Fluctuations (1D trap) Bragg spectroscopy in momentum space stripes on1D traps (different aspect ratios) Orsay, 2003 Hannover, 2001

35. Unexpected New Physics!!