Observation of universality in 7 Li three-body recombination across a Feshbach resonance

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

2. Observation of universality in 7Li 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 minimum This resonance

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| >> r0

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

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

8. Experimental realization with 7Li 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) Ytterbium Fiber Laser P = 100 W N=2x106 T=300 mK w0 = 31 mm U = 2 mK main trap Q = 19.50 * The helping beam is effective only when the main beam is attenuated helping beam w0 = 40 mm

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on F=1 state Atoms are optically pumped to F=1 state Theoretical predictions for Feshbach resonances S. Kokkelmans, unpublished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, mF=0>

13. Feshbach resonances on mF=0 state Compared to Cs or 6Li the background scattering length is small: abg ~ 20 a0 Straightforward approach is: Do we have a broad resonance? What is the extension of the region of universality ?

14. Feshbach resonances on mF=0 state Resonance effective range is extracted from the effective range expansion: |Re| =2r0 40 G A broad resonance – Re crosses zero. A narrow resonance – Re is very large Far from the resonance – Re > r0

15. Experimental results Low temperature scan for Feshbach resonances (T = 3 mK), 50 ms waiting time. Positions of Feshbach resonances from atom loss measurements: Narrow resonance: 845.8(7) G Wide 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. S. Kokkelmans, unpublished 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.

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

18. Tree-body recombination rate Experiment: This simplified model neglects the following effects: - saturation of K3 to Kmax 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 K3 as far as a factor of 10 below Kmax 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 K3 by ~23%.

19. Tree-body recombination rate a > 0: T= 2 – 3 mK; K3 is expected to saturate @ a = 2800 a0 a < 0: T= 1 – 2 mK; K3 is expected to saturate @ a = -1500 a0 N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

20. Summary of the results Both features are deep into the universal region: Minimum is found @ a= 1150 a0= 37 x r0 Efimov resonance is found @ |a|= 264 a0= 8.5 x r0 Fitting parameters to the universal theory: a+ = 244(34) a0 Experiment: a+/|a-| = 0.92(0.14) a- = -264(10) a0 a+/|a-| = 0.96(0.3) UT prediction: h+ = 0.232(0.036) h- = 0.223(0.036) Randy Hulet’s talk: minima are found @ a= 119 a0 and a= 2700 a0 (BEC – 0 temperature limit!) Efimov resonance is found @ |a|= 298 a0 (similar temperatures)

21. Summary of the results Both features are deep into the universal region: Minimum is found @ a= 1150 a0= 37 x r0 Efimov resonance is found @ |a|= 264 a0= 8.5 x r0 Fitting parameters to the universal theory: a+ = 244(34) a0 Experiment: a+/|a-| = 0.92(0.14) a- = -264(10) a0 a+/|a-| = 0.96(0.3) UT prediction: h+ = 0.232(0.036) h- = 0.223(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 (6Li 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 B0 = 894.65 (11) a < 0 B0 = 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 B0 = 894.65 (11) a < 0 B0 = 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 K3were to increase by 25% (overestimation of atom number by ~12%), the position of the Feshbach resonance from the fit would perfectly agree: a > 0 B0 = 894.54 (11) a < 0 B0 = 894.57 (25) Minimum would be @ a= 1235 a0 a+/|a-| = 0.938 Efimov resonance would be @ |a|= 276.4 a0

25. Feshbach resonance on the absolute ground state |Re| =2r0 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, mF=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? Eindhoven University of Technology, The Netherlands Bar-Ilan University, Israel Noam Gross Zav Shotan L. Kh. Servaas Kokkelmans