1. Experimental study of Efimov scenario in ultracold bosonic lithium
Lev Khaykovich
Physics Department, Bar-Ilan University,
52900 Ramat Gan, Israel
FRISNO-11, Aussois, 28/3/2011

2. Outline Experimental approach - all optical BEC of lithium
Exploring Feshbach resonances on F=1 state.
Spontaneous spin purification.
Universal quantum states in three body domain (scattering length a is the largest length scale in the system)
Weakly bound Efimov trimers.
Log periodic behavior of three-body recombination.
Evidence of spin independent short range 3-body physics.
Mapping between the scattering length and the applied magnetic field – direct association of Feshbach molecules.
Conclusions – is the nonuniversal part of the theory nonuniversal?

3. 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 universal physics requirement: |a| >> r0

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

5. All optical BEC: optical dipole trap
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
N. Gross and L. Khaykovich, PRA 77, (2008)

6. Tuning the s-wave scattering length
Feshbach resonance
A weakly bound state is formed for positive a – Feshbach molecule

7. Feshbach resonances on F=1 state
Theoretical prediction for Feshbach resonances
S. Kokkelmans, unpublished

8. Search for Feshbach resonances
Atoms are optically pumped to F=1 state.
Positions of Feshbach resonances from atom loss measurements:
Narrow resonance: 845.8(7) G
Wide resonance: 894.2(7) G
From the whole zoo of possible resonances only two were detected.

9. Spontaneous spin purification
Spin selective measurements
to identify where the atoms are.
Spin-flip collisions:
|F=1, mF=0>
N. Gross and L. Khaykovich, PRA 77, (2008)

10. Feshbach resonances on mF=0 state
Theoretical prediction for Feshbach resonances
This is not the absolute ground state!

11. Experimental playground
Absolute ground state
The one but lowest Zeeman state

12. Three-body universality: Efimov qunatum states

13. Quantum states near two-body resonance (Efimov scenario)

14. Universal three-body bound states
even more
weakly bound
trimers
weakly bound
trimers

15. Universal three-body bound states
Position of an Efimov state is nonuniversal.
It is defined by a three-body parameter.

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

17. Three-body recombination
Release of binding energy causes loss which probes 3-body physics.

18. Manifistation of Efimov resonances
One atom and a dimer
couple to an Efimov trimer
Three atoms couple
to an Efimov trimer
Enhanced three-body loss: collisions at much larger distance

19. Experimental observables – suppressed three-body recombination
There are two paths for the 3- body recombination
towards deeply bound state

20. Suppressed three-body recombination
deeply bound molecule
Two paths interfere destructively a certain scattering lengths – recombination minima.

21. Three-body recombination theory
Loss rate from a trap:
K3 – 3-body loss coefficient [cm6/sec]
Dimension analysis:
Full treatment:

22. Effective field theory
Loss into deeply bound molecules
Loss into shallow dimer
Recombination minima
Efimov resonances
Braaten & Hammer, Phys. Rep. 428, 259 (2006)

23. Experimental results mf = 1; Feshbach resonance ~740G.
a > 0: T= 2 – 3 mK
a < 0: T= 1 – 2 mK
mf = 1; Feshbach resonance ~740G.
N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, (2009); PRL 105, (2010).

24. Experimental results mf = 1; Feshbach resonance ~740G.
a > 0: T= 2 – 3 mK
a < 0: T= 1 – 2 mK
mf = 1; Feshbach resonance ~740G.
mf = 0; Feshbach resonance ~895G.
N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, (2009); PRL 105, (2010).

25. Experimentally demonstrated Efimov features
This resonance
This minimum

26. Experimentally demonstrated Efimov features
Theses two resonances
are related by 22.7

27. Experimentally demonstrated Efimov features
Theses two resonances
are related by 22

28. Experimentally demonstrated Efimov features
This resonance
This minimum
This resonance

29. Summary of the results Fitting parameters to the universal theory:
UT prediction:
a+/|a-| = 0.96(0.3)
The universal factor of 22.7 is confirmed across the region of
Three-body parameter is the same (within the experimental errors) for both nuclear-spin subleves.
N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, (2009); PRL 105, (2010).

30. the scattering length And the applied magnetic field
Mapping between
the scattering length And
the applied magnetic field

31. Mapping between the scattering length and the applied magnetic field
Bare state (non-universal) dimer:
Feshbach molecule (universal dimer):

32. Universal two-body bound state
There is only a small fraction of the wave function in the bound state. The size of the bound state increases.
“Quantum halo states”
The size of the bound state is that of a singlet potential: ~1.5 nm
Progressive contamintion by the atomic continuum

33. Experimental probe
Loss mechanism from the trap (release of binding energy):
Deeply bound molecule

34. Mapping between the scattering length and the applied magnetic field
Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.
A typical RF spectrum
N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:

35. Mapping between the scattering length and the applied magnetic field
Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.
Solid (dashed) line – local (global) analysis
N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:

36. Mapping between the scattering length and the applied magnetic field
Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.
Improved characterization of Li inter-atomic potentials.
N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:

37. Conclusions
For two different Fesbach resonances on two different nuclear-spin sublevles of the same atomic system we demonstrate:
Universal scaling factor of 22.7 across the region of .
Same positions of the Efimov features (within the experimental errors).
First experimental indication that the nonuniversal part of the universal theory – the three-body parameter – might have some “universal” properties.
New insight from Innsbruck group – for three different Feshbach resonances the Efimov features are the same!

38. People Bar-Ilan University, Israel Eindhoven University of
Technology, The Netherlands
Servaas Kokkelmans