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Oct. 20, 2009, Rome

Oct. 20, 2009, Rome. Historical remark. Size of Efimov molecules?. Exploring Efimov states of ultracold atoms. Michigan lake. Cheng Chin . James Franck institute and Department of Physics, University of Chicago. Observation of Efimov resonance (Innsbruck 2006).

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Oct. 20, 2009, Rome

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  1. Oct. 20, 2009, Rome • Historical remark. • Size of Efimov molecules? Exploring Efimov states of ultracold atoms Michigan lake Cheng Chin James Franck institute and Department of Physics, University of Chicago

  2. Observation of Efimov resonance (Innsbruck 2006) Nature 2006, Physics Today 06

  3. 7.4G a= -850 a0 Innsbruck 2005 a=400 aB a=0 a=-2500 aB

  4. David Rychtarik (Ph.D. Thesis, Innsbruck, 2004) Abteilungsleiter R&D bei Q-Cells SE

  5. Tino Weber (Wall in the Cs lab, Innsbruck, 2002)

  6. Chu group, Stanford (1999) No two-body resonances in the range of 0~45G. (NIST, year 2000)

  7. Feshbach spectroscopy of cesium (2001~03) 62 Feshbach resonances: C. Chin et al., PRL 01, 03, PRA 04 Two-body theory: P. Julienne, NIST

  8. In 3/2003, I had my postdoc interview with Rudi in Innsbruck… Rudi asked, “What do you want to work on here?” “Efimov states”, I answered. Rudi was like ….Hmm…. “We start with creating Feshbach molecules.” Rudi said, “ Sounds good.”

  9. One last mystery… How did Steve Chu know about Efimov resonances?

  10. Amazing progress since 2006 • Efimov resonances in Cs, Li6, Li7 and K39 • Universal scaling • Bosonic, fermionic and mixture systems • Atom-atom-atom, atom-dimer collisions • Four-body universal states Our motivation… No Efimov effect in 2D T.K. Lim and P.A. Maurone, Phys. Rev. B 22, 1467 (1980) Two trimer states in 2D E. Nielsen et al., Phys. Rev. A 56, 3287 (1997) (one is Efimov-like) Our idea: measuring the size of Efimovtrimer in a 2D trap?

  11. Experiment procedure gravity & B field 1064 nm Cs gas X Y Z 20 m 1064 nm dipole trap: 25 m 20 m 20 m

  12. Experiment procedure (step 1: light sheet) light sheet (1mm x 60m) gravity & B field 1064 nm Cs gas X Y Z 20 m 1064 nm dipole trap: 1064 nm light sheeet: 25 m 20 m 20 m 2 m 2 m

  13. Experiment procedure (step 2: vertical lattice) 2 Yb-laser beams gravity & B field 1064 nm Cs gas X Y Z 20 m 1064 nm dipole trap: 1064 nm light sheet: 1064 nm z-lattice: 25 m 25 m 20 m 2 m 45 m 40m 0.2 m 2 m 0.2 m

  14. In situ imaging of a 2D gas (in the lattices) Resolution: 1.3 µm Pixel size: 0.6 µm Lattice const.: 0.53 µm

  15. Quantum Phase Transition and Quantum Criticality correlation   Tc 0 0  (gap) S. Sachdev, Nature Physics (2008) Temperature U/t (nor. interaction) Exploring quantum criticality: Mott plateaus (Nature 460 995, 2009). Cooling & dynamics across QPT (arXiv:0910.1382) Postdoc positions available!!

  16. What does 2D regime mean? Oscillator lengths x y z a rvdw n-1/3

  17. What does 2D regime mean? x y a rvdw z n-1/3 3D regime 2D regime 2m =40,000 aB 100 aB 1,000 aB

  18. From 3D to 2D Scattering length a (aB) y/2 y 0 -2500 50 -890 20 40000 7000 2000 9000 1700 15000 1200 aB Hz

  19. From 3D to 2D Scattering length a (aB) y/2 y 0 50 -890 -2500 4-body Efimov 20 40000 7000 2000 9000 1700 15000 1200 aB Hz

  20. Efimov resonance position shift (preliminary) 20 Bohr/kHz

  21. Efimov resonance position shift (preliminary) -700 Scattering length (aB) -800 Trap frequency z/2 (Hz)

  22. Efimov resonance position shift (preliminary)

  23. From 3D to 2D Scattering length a (aB) y/2 y 0 50 -890 -2500 4-body Efimov 20 40000 2D 7000 2000 2D 9000 1700 2D 15000 1200 aB Hz

  24. We are not deep in the 2D regime: z > size of the trimer • We can treat the 2D confinemen perturbatively. • Estimated trimer energy shift E3= 10kHz. Energy B field

  25. We are not deep in the 2D regime: z > size of the trimer • We can treat the 2D confinemen perturbatively. • Estimated trimer energy shift E3= 10kHz. Energy 3E0atom-E0trimer B field

  26. Conclusion • Efimov resonance shifts in a 2D trap. • Finite 3-body states in 2D • 2D resonance shift could be a finite energy effect? • Can we derive the Efimov molecular size from the shift? • Strong confinement ~ finite kinetic energy? • Future: Preparation of LiCs in optical lattices • Finally, a question to all Efimov experts.

  27. Question Recombination rate constant Two-body scattering length a=f[2 (B)]=f(B) is field dependent. Why is a*=g(3 ) field independent? This is equivalent to ask… Where are the regular 3-body Feshbach resonances?

  28. Efimov resonance position shift -600 aB 20 Bohr/kHz -750 aB -900 aB

  29. Finite temperature shifts 20 Bohr/100nK H.-C. Naegerl, et al., Proceedings of ICAP 2006, cond-mat/0611629

  30. Is 2D shift a simple finite energy effect? Ek = (3/2)kT = 150nK Ek=kT+(1/4) hbarz= 20 nK • Temperature shift: 20 Bohr/100nK • Confinement shift: 20 Bohr/kHz Confinement shifts seems stronger!

  31. From 3D to 2D y/2 y Scattering length a (aB) -2500 0 -900 20 40000 7000 2000 9000 1700 15000 1200 aB Hz

  32. T.K. Lim and P.A. Maurone, Phys. Rev. B 22, 1467 - 1469 (1980)

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