1. Three-body recombination at vanishing scattering lengths in 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 Ultrahigh vacuum environment Dissipative trap N ~ 5x10 8 atoms n ~ 10 10 atoms/cm 3 T ~ 300  K Close to the resonance (orbital electronic states) visible (laser) light – 671 nm (~2 eV) Magnetic fields Magneto-optical trap of Li atoms Dilute gas of atoms:

3. Experimental setup: ultracold 7 Li atoms Zeeman slower MOT ~10 9 atoms CMOT ~5x10 8 atoms (300  K) ~2x10 4 atoms ~1.5  K Crossed-beam optical trap Trapping: conservative atom trap (our case: focus of a powerful infrared laser) Temperature :  K Typical numbers: Relative velocities : few cm/sec Collision energies : few peV N. Gross and L. Khaykovich, PRA 77, 023604 (2008) Evaporation: Cooling:

4. Study of Efimov scenario with ultracold atoms

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

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

7. Three-body recombination E b /3 2E b /3 Release of the binding energy causes loss of atoms from a finite depth trap which probes 3-body physics. Three body inelastic collisions result in a weakly (or deeply) bound molecule. K 3 – 3-body loss rate coefficient [cm 6 /sec] Loss rate from a trap: U0U0

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

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

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

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

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

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

14. Experimental results - 7 Li a > 0: T= 2 – 3  K a < 0: T= 1 – 2  K 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 7 Li lower hyperfine level. Feshbach resonance m F =0 state. 850 G 575 G 412 G

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

20. Early observations Universal region.

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

22. Two-Body Physics

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

24. Feshbach resonances and zero-crossings Scattering length and 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). K. O’Hara et. al., Phys. Rev. A 66 041401(R) (2002). Zero-crossing of 6 Li resonance.

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

27. Three-body physics near zero-crossing Universal limit: Recombination length: We measure K 3 and represent the results as L m. B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999). Formal definition: The universal limit maximal value(*): (*) 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 Waals length:

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  K Red: T = 10  K Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113, 053202 (2014). Three-body recombination shows no energy dependence. Rules out other possibilities to construct L e such as (in analogy to two-body collisions)

31. Three-body physics near zero-crossings Low field zero-crossing. Prediction for the recombination length in the resonances’ region. B [G] Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113, 053202 (2014). Experimental resolution limit is 100 a 0.

32. Optimization of evaporative cooling Scattering length compensation of 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 length is?

35. People Eindhoven University of Technology, The Netherlands Servaas Kokkelmans Bar-Ilan University, Israel Zav Shotan, Olga Machtey