1. Observation of universality in 7 Li three-body recombination across a Feshbach resonance Lev Khaykovich Physics Department, Bar Ilan University, 52900 Ramat Gan, Israel ITAMP workshop, Rome, October2009 If it is not an accidental coincidence

2. Observation of universality in 7 Li three-body recombination across a Feshbach resonance Lev Khaykovich Physics Department, Bar Ilan University, 52900 Ramat Gan, Israel ITAMP workshop, Rome, October2009

3. Efimov scenario This resonance This minimum

4. Experimental system: bosonic lithium Why lithium? Compared to other atomic species available for laser cooling, lithium has the smallest range of van der Waals potential: Thus it is easier to fulfill the requirement: |a| >> r 0

5. Experimental system: bosonic lithium Bulk metal – light and soft MOT setup Magneto-optically trapped atoms What’s lithium?

6. Experimental system: bosonic lithium Hyperfine energy levels of 7 Li atoms in a magnetic field The primary task: study of 3-body physics in a system of identical bosons

7. Experimental system: bosonic lithium Hyperfine energy levels of 7 Li atoms in a magnetic field Absolute ground state The one but lowest Zeeman state

8. Experimental realization with 7 Li atoms: all-optical way to a Bose-Einstein condensate

9. Optical dipole trap N. Gross and L. Khaykovich, PRA 77, 023604 (2008) Direct loading of an optical dipole trap from a MOT 0 order(helping beam) +1 order(main trap) main trap helping beam * The helping beam is effective only when the main beam is attenuated Ytterbium Fiber Laser P = 100 W w 0 = 31  m U = 2 mK  = 19.5 0 w 0 = 40  m N=2x10 6 T=300  K

10. Feshbach resonances on F=1 state Atoms are optically pumped to F=1 state Theoretical predictions for Feshbach resonances S. Kokkelmans, unpublished

11. Search for Feshbach resonances High temperature scan: the magnetic field is raised to different values + 1 s of waiting time. The usual signatures of Feshbach resonances (enhanced inelastic loss). Enhanced elastic scattering: spontaneous evaporation. From the whole bunch of possible resonances only two were detected.

12. Spontaneous spin purification Spin selective measurements to identify where the atoms are. Spin-flip collisions: |F=1, m F =0>

13. Feshbach resonances on m F =0 state Compared to Cs or 6 Li the background scattering length is small: a bg ~ 20 a 0 Do we have a broad resonance? What is the extension of the region of universality ? Straightforward approach is:

14. Feshbach resonances on m F =0 state A narrow resonance – R e is very large A broad resonance – R e crosses zero. Resonance effective range is extracted from the effective range expansion: Far from the resonance – R e > r 0 |R e | =2r 0 40 G

15. Experimental results Low temperature scan for Feshbach resonances (T = 3  K), 50 ms waiting time. Positions of Feshbach resonances from atom loss measurements: Narrow resonance: 845.8(7) GWide resonance: 894.2(7) G

16. Two-body loss What type of loss do we see (we are not on the absolute ground state)? Coupled-channels calculations of magnetic dipolar relaxation rate. This rate is ~3 orders of magnitude smaller than the corresponding measured rate. Unique property of light atoms! For heavier atoms the situation can be more complicated: second order spin-orbit interaction in Cs causes large dipolar relaxation rates. S. Kokkelmans, unpublished

17. Tree-body recombination rate Analytical results from the effective field theory: Theory:

18. Tree-body recombination rate Experiment: This simplified model neglects the following effects: - saturation of K 3 to K max due to finite temperature - recombination heating (collisional products remain in the trap) - “anti-evaporation” (recombination removes cold atoms) The first two are neglected by measuring K 3 as far as a factor of 10 below K max For the latter, we treat the evolution of the data to no more than ~30% decrease in atom number for which “anti-evaporation” causes to underestimate K 3 by ~23%.

19. Tree-body recombination rate a > 0: T= 2 – 3  K; K 3 is expected to saturate @ a = 2800 a 0 a < 0: T= 1 – 2  K; K 3 is expected to saturate @ a = -1500 a 0 N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

20. Summary of the results Fitting parameters to the universal theory: a + = 244(34) a 0 a - = -264(10) a 0 a + /|a - | = 0.92(0.14) Experiment: UT prediction: a + /|a - | = 0.96(0.3) Minimum is found @ a = 1150 a 0 = 37 x r 0 Both features are deep into the universal region: Efimov resonance is found @ | a| = 264 a 0 = 8.5 x r 0  - = 0.223(0.036)  + = 0.232(0.036) Randy Hulet’s talk: minima are found @ a = 119 a 0 and a = 2700 a 0 (BEC – 0 temperature limit!) Efimov resonance is found @ | a| = 298 a 0 (similar temperatures)

21. Summary of the results Fitting parameters to the universal theory: a + = 244(34) a 0 a - = -264(10) a 0 a + /|a - | = 0.92(0.14) Experiment: UT prediction: a + /|a - | = 0.96(0.3) Minimum is found @ a = 1150 a 0 = 37 x r 0 Both features are deep into the universal region: Efimov resonance is found @ | a| = 264 a 0 = 8.5 x r 0  - = 0.223(0.036)  + = 0.232(0.036) The position of features may shift for lower temperature. How much do they shift?

22. Summary of the results H.-C. Nagerl et.al, At. Phys. 20 AIP Conf. Proc. 869, 269-277 (2006). K. O’Hara ( 6 Li excited Efimov state): 180 nK -> 30 nK the resonance position is shifted by ~10% (and coincides with the universal theory) J. D’Incao, C.H. Greene, B.D. Esry J. Phys. B, 42 044016 (2009).

23. Summary of the results Fitting of the Feshbach resonance position: a > 0 B 0 = 894.65 (11) a < 0 B 0 = 893.85 (37) The resonance position according to the atom loss measurement: 894.2(7) G Detection of the Feshbach resonance position by molecule association The resonance position according to The molecule association: 894.63(24) G

24. Summary of the results Fitting of the Feshbach resonance position: a > 0 B 0 = 894.65 (11) a < 0 B 0 = 893.85 (37) The resonance position according to the atom loss measurement: 894.2(7) G The resonance position according to the molecule association: 894.63(24) G If K 3 were to increase by 25% (overestimation of atom number by ~12%), the position of the Feshbach resonance from the fit would perfectly agree: a > 0 B 0 = 894.54 (11) a < 0 B 0 = 894.57 (25) Minimum would be @ a = 1235 a 0 Efimov resonance would be @ | a| = 276.4 a 0 a + /|a - | = 0.938

25. Feshbach resonance on the absolute ground state |R e | =2r 0 40 G

26. Preliminary results for the absolute ground state

27. Conclusions We show that the 3-body parameter is the same across the Feshbach resonance on |F=1, m F =0> spin state. The absolute ground state possesses a similar Feshbach resonance – possibility to test Efimov physics in different channels (spin states) of the same atomic system. Mixture of atoms in different spin states – a system of bosons with large but unequal scattering length.

28. Who was in the lab and beyond? Bar-Ilan University, Israel Eindhoven University of Technology, The Netherlands Servaas Kokkelmans Noam Gross Zav Shotan L. Kh.