1. Efimov physics in ultracold gases Efimov physics in ultracold gases Rudolf Grimm “Center for Quantum Optics” in Innsbruck Austrian Academy of Sciences University of Innsbruck FB18, Santos, 26 Aug 06

2. Efimov physics in ultracold gases Efimov physics in ultracold gases Rudolf Grimm “Center for Quantum Optics” in Innsbruck Austrian Academy of Sciences University of Innsbruck

3. 1995: Bose-Einstein condensation 2003: molecular condensates 1999: degenerate Fermi gas 2004/05: fermionic condensates and superfluids milestones in the field 2002/03: ultracold dimers cold atoms in a nutshell atom trap: electromagnetic field (our case: focus of powerful infrared laser) cooling to nanokelvin: laser cooling & subsequent evaporative cooling atomic species: bosons and fermions nK 2006: Efimov states !!! BEC interaction tuning through Feshbach resonances !

4. molecular structure: scattering length r U(r) incident channel B a s­wave scattering length a determined by last bound level a bg last bound level many vib. levels

5. molecular structure: scattering length B a a bg r U(r) incident channel bound state coupling

6. Feshbach resonance r U(r) incident channel bound state magnetic moment of bound state differs from the magnetic moment of the incident channel B a s­wave scattering length a as a function of magnetic field B a bg B0B0 coupling

7. very large scattering lenghts r r0r0 U(r)  r  „quantum halo states“: deuteron, He 2, Feshbach molecules !!! weakly bound last level: scattering length a>>r 0 binding energy E b = - h 2 /(ma 2 ) a system with universal properties !!! weakly bound last level: scattering length a>>r 0 binding energy E b = - h 2 /(ma 2 ) a system with universal properties !!! open-channel dominated resonance: single-channel model

9. energy 1/a quantum states near two-body resonance a < 0 a > 0 E dimer =  h 2 /(ma 2 ) weakly bound dimer

10. energy 1/a quantum states near two-body resonance weakly bound trimer a < 0 a > 0 even more weakly bound trimer ×22.7 ×(22.7) 2 infinite series of weakly bound trimer states for resonant two-body interaction „Efimov states“ infinite series of weakly bound trimer states for resonant two-body interaction „Efimov states“

11. 36 years ago...

12. 35 years ago...

13. energy 1/a Efimov resonances a < 0 a > 0 three atoms couple to an Efimov trimer: „ triatomic Efimov resonance“ three atoms couple to an Efimov trimer: „ triatomic Efimov resonance“ one atom and a dimer couple to an Efimov trimer: „atom-dimer Efimov resonance“ one atom and a dimer couple to an Efimov trimer: „atom-dimer Efimov resonance“ resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979) resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

14. energy 1/a universality a < 0 a > 0 universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979) universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

15. energy 1/a universality a < 0 a > 0 universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979) universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

16. energy 1/a universality a < 0 a > 0 universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979) universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979) locations of Efimov states / resonance positions not universal !!! additional parameter needed locations of Efimov states / resonance positions not universal !!! additional parameter needed

17. experimental observations nuclear physics (Halo nuclei) molecular physics (He beams) ultracold atom physics none ! many new opportunities for Efimov-related few-body physics !

18. the probe three-body recombination atomic systems have deeply bound dimers states

19. three-body recombination

21. three-body recomb. theory basics L 3 : three-body loss coefficient [cm 6 /s] Fedichev et al., PRL 77, 2921 (1996) prediction of a 4 scaling, C = 3.9 Nielsen & Macek, PRL 83, 1566 (1999) Esry et al., PRL 83, 1751 (1999) Bedaque et al., PRL 85, 908 (2000) Braaten & Hammer, PRL 87, 160407 (2001) C(a) = C(22.7a) with upper limit ~70 for a>0 oscillatory behavior × e  ~ 22.7

22. Esry-Greene-Burke theory PRL 83, 1751 (1999) calculations for a sech 2 (r ij /r 0 ) model potential definition of a recombination length L3~a4L3~a4 L3~a4L3~a4 destructive interference effect destructive interference effect Efimov resonance !

23. Three-body loss coefficient loss into deeply bound molecules loss into shallow dimer effective field theory (Braaten & Hammer) Efimov resonances Phys. Rep. 428, 259 (2006)

24. ultracold.at oms Innsbruck two teams working on Efimov physics with ultracold cesium atoms T. Kraemer, M. Mark, J. Danzl, S. Knoop, F. Ferlaino B. Engeser, K. Pilch, A. Lange two teams working on Efimov physics with ultracold cesium atoms T. Kraemer, M. Mark, J. Danzl, S. Knoop, F. Ferlaino B. Engeser, K. Pilch, A. Lange H.-C. Nägerl, R. Grimm

25. magnetic tunability of Cs 150 G 50 G100 G -1000 1000 2000 -2000 3000 0 magnetic field (G) scattering length (a 0 ) F=3, m F =3 0 there should be an Efimov resonance !

26. Cs BEC

27. exp. results ! T = 10nK 200nKtriatomic Efimov resonance Braaten-Hammer theory  *=1/210a 0,  *=0.06

28. exp. results ! Braaten- Hammer theory Esry, Greene, Burke theory 1999 ! !triatomic Efimov resonance T = 10nK 200nK

29. exp. results (again) T = 10nK 200nK higher temperature (200nK) recombination rate is unitarity limited & shift of loss maximum higher temperature (200nK) recombination rate is unitarity limited & shift of loss maximum

30. triatomic continuum resonance 1/a Efimov-trimer 200 nK 100 nK 50 nK Efimov-resonance (a<0) E=0 Bringas, Yamashita, Frederico, PRA 69, 040702(R) (2004)

31. resonance shift B. Engeser et al., to be published linear fit theoretical calculations of T-dependent shift by three groups: Yamashita et al., Esry et al., S. Jonsell (work in progress)

32. energy 1/a Efimov resonances a < 0 a > 0 resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979) resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979) triatomic atom-dimer

33. energy structure of cesium atoms dimers

34. energy structure of cesium dimers atoms we can measure inelastic atom-dimer collisions at various magnetic fields ! we can measure inelastic atom-dimer collisions at various magnetic fields !

35. inelastic atom-dimer collisions atom-dimer resonance new ! Aug. 06

36. inelastic atom-dimer collisions a  400a 0 atom-dimer resonance +r 0 -r 0 universal ???

37. outlook

38. outlook I taking full advantage of Cs tunability our expts so far the ideal Feshbach resonance for Efimov physics ?! can we see the full Efimov period (x22.7) ?

39. outlook II spectroscopy on Efimov states (rf-spectroscopy or modulation method) energy 1/a a < 0 a > 0 h

40. outlook III Few-body physics & Efimov states in an optical lattice  optical lattice: a 3D array of nanotraps Stoll & Köhler, PRA 71, 022714 (2005) making Efimov trimers in an optical lattice 85 Rb

41. outlook IV other three-body systems 1 2 3 a 12 a 23 a 13 three non-identical particles equal masses 6 Li lowest three spin states mixed-species systems different masses M m M many combinations available Bose-Bose, Bose-Fermi, Fermi-Fermi e.g., mass ratio 6 Li- 174 Yb 1:29

42. outlook V four-body physics energy 1/a a < 0 a > 0 D+A A+A+A Tri Tri

43. outlook V four-body physics energy 1/a a < 0 a > 0 D+A+A D+D A+A+A+A Tri+A Tri+A Tetramer states ? dimer-dimer scattering resonances?

44. Conclusion ultracold atoms nanokelvin Feshbach resonances FB ultracold atoms with tunable interactions a new era of few-body physics is just beginning! ultracold atoms with tunable interactions a new era of few-body physics is just beginning!

45. loss minimum three-body loss after 200ms storage in recompressed trap minimum at 210a 0 half Efimov period (22.7 1/2 ): min.-max. loss ! expt. optimization of evaporative cooling towards BEC ! → 210a 0 ! Kraemer et al., Appl. Phys. B 79, 1013 (2004) but r 0  100a 0 (vdW range): applicability of universal theory questionable ! but r 0  100a 0 (vdW range): applicability of universal theory questionable !