Three-body recombination at vanishing scattering lengths in ultracold atoms

1. Three-body recombination at vanishing scattering lengthsin ultracold atoms Lev Khaykovich Physics Department, Bar-Ilan University, 52900 Ramat Gan, Israel Critical Stability workshop, Santos Brasil 10/14/2014

2. System: dilute gas of ultracold atoms Magneto-optical trap of Li atoms Close to the resonance (orbital electronic states) visible (laser) light – 671 nm (~2 eV) Magnetic fields Ultrahigh vacuum environment Dissipative trap N ~ 5x108 atoms n ~ 1010 atoms/cm3 T ~ 300 mK Dilute gas of atoms:

3. Experimental setup: ultracold7Li atoms Cooling: Trapping: conservative atom trap (our case: focus of a powerful infrared laser) Zeeman slower Crossed-beam optical trap Evaporation: ~2x104atoms ~1.5 mK MOT ~109 atoms Typical numbers: Temperature: ~ mK CMOT ~5x108 atoms (300 mK) Relative velocities: few cm/sec Collision energies: few peV N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

4. Study of Efimov scenario with ultracold atoms

5. Efimov scenario – universality window k first excited level lowest level Borromean region: trimers without pairwise binding

6. Efimov scenario and real molecules a < 0 a > 0 No 2-body bound states One 2-body bound state Real molecules: many deeply bound states

7. Three-body recombination Three body inelastic collisions result in a weakly (or deeply) bound molecule. 2Eb/3 Eb/3 U0 Release of the binding energy causes loss of atoms from a finite depth trap which probes 3-body physics. Loss rate from a trap: K3 – 3-body loss rate coefficient [cm6/sec]

8. Experimental observables k One atom and a dimer couple to an Efimovtrimer Three atoms couple to an Efimovtrimer Experimental observable - enhanced three-body recombination.

9. Experimental observables k Two paths for the 3- body recombination towards weakly bound state interfere destructively. Three atoms couple to an Efimovtrimer Experimental observable – recombination minimum.

10. Experimental observables Recombination length: Recombination minimum Efimov resonance B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999).

11. Efimov scenario: a short overview • Efimov physics (and beyond) with ultracold atoms: • 2006 - … 133Cs Innsbruck • 2008 – 2010 6Li 3-component Fermi gas in Heidelberg, Penn State and Tokyo Universities • 2009; 2013 39K in Florence, Italy • 2009 41K - 87Rb in Florence, Italy • 2009; 2013 7Li in Rice University, Huston, TX • 2009 - … 7Li in BIU, Israel • 2012 - … 85Rb and 40K - 87Rb JILA, Boulder, CO • 2014 - 133Cs - 6Li in Chicago and Heidelberg* Universities *Eva Kuhnle’s talk on Friday.

12. Experimental playground - 7Li 3 identical bosons on a single nuclear-spin state. Absolute ground state Next to the lowest Zeeman state

13. Experimental playground - 7Li Absolute ground state The one but lowest Zeeman state Feshbach resonance Feshbach resonance N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011).

14. Experimental results - 7Li a > 0: T= 2 – 3 mK a < 0: T= 1 – 2 mK mf = 1; Feshbach resonance ~738G. mf = 0; Feshbach resonance ~894G. N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

15. Three body recombination at vanishing scattering lengths

16. Motivation • Purely academic.

17. Motivation • Purely academic. • Application: optimization of evaporative cooling in an optical trap. Evaporative cooling in a nutshell: - high energy atoms are evaporated due to final potential depth; - elastic collisions re-establish the thermal equilibrium; - Good collisions: elastic; - Bad collisions: three-body recombination (heating); - optical trap weakens during evaporation; which can be compensated by increasing a. But:

18. Zero-crossings 7Li lower hyperfine level. Feshbach resonance mF =0 state. 850 G 412 G 575 G

19. Early observations Same scattering length – different three-body recombination rates.

20. Early observations Universal region.

21. Early observations Saturation of the three-body recombination rate. N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

22. Two-Body Physics

23. Scattering phase shift at zero-crossing Effective range expansion of the scattering phase shift: Inconvenient when Inverted expression: Well defined when Effective volume: See also: C. L. Blackley, P. S. Julienne and J. M. Hutson, PRA 89, 042701 (2014).

24. Feshbach resonances and zero-crossings Scattering lengthand effective range: N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

25. Two-body physics near zero-crossing Energy dependent two-body collisional cross-section: Condition for vanishing collisional cross-section: The zero-crossing position is well defined now by precise characterization of Feshbach resonances: N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011). P. S. Julienne and J. M. Hutson, Phys. Rev. A 89 052715 (2014) (Data from Heidelberg, ENS, Rice and Bar Ilan). Experimental approach to test the temperature dependence of the cross-section – evaporative cooling around zero-crossing. S. Jochim et. al. , Phys. Rev. Lett. 89 273202 (2002). Zero-crossing of 6Li resonance. K. O’Hara et. al. , Phys. Rev. A 66 041401(R) (2002).

26. Evaporative cooling near zero-crossing Evaporation during 500 ms Initial temperature: 31 mK Zero-crossing is at 849.9G Maximum is at 850.5G Two-body collisions show energy dependence. Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

27. Three-body physics near zero-crossing Universal limit: Formal definition: The universal limit maximal value(*): Recombination length: B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999). We measure K3 and represent the results as Lm. (*) N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

28. Three-body physics near zero-crossing Three-body recombination length: Van der Waalslength:

29. Effective recombination length Measured recombination length: From the effective range expansion the leading term is proportional to the effective volume. Effective recombination length: Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

30. Three-body physics near zero-crossing Black: T=2.5 mK Red: T=10 mK Three-body recombination shows no energy dependence. Rules out other possibilities to construct Le such as (in analogy to two-body collisions) Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

31. Three-body physics near zero-crossings Prediction for the recombination length in the resonances’ region. Low field zero-crossing. B [G] Experimental resolution limit is 100 a0. Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

32. Optimization of evaporative cooling Scattering length compensationof the density decrease. Bad/Good collisions ratio:

33. Phase space density

34. Conclusions • Zero-crossing does not correspond to the minimum in 3-body recombination rates. • Three-body recombination rate is different at different zero-crossings. • We suggest a new lengthscale to describe the 3-body recombination rates. • Energy independent 3-body recombination rate. • We predict a minimum in 3-body recombination in the non-universal regime. • The question is how general the effective lengthis?

35. People Bar-Ilan University, Israel Eindhoven University of Technology, The Netherlands ServaasKokkelmans ZavShotan, Olga Machtey