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									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
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
                 Efimov scenario



                                   This minimum




This resonance
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:


                                   14
                         mC6 
                   r0      2 
                                         31a0
                         16 

      Thus it is easier to fulfill the requirement: |a| >> r0
Experimental system: bosonic lithium
                What’s lithium?



                  Bulk metal – light and soft




    MOT setup




                                    Magneto-optically
                                     trapped atoms
   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
Experimental system: bosonic lithium
    Hyperfine energy levels of 7Li atoms in a magnetic field




 Absolute ground state           The one but lowest Zeeman state
  Experimental realization
      with 7Li atoms:

     all-optical way to
a Bose-Einstein condensate
                         Optical dipole trap
                            N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

                     Direct loading of an optical dipole trap from a MOT


                                                                                 (helping beam)     0 order


                                                                                (main trap)   +1 order

                     Ytterbium Fiber Laser
                           P = 100 W




w0 = 31 mm                                                                                    N=2x106
U = 2 mK                                                                                      T=300 mK
main trap
         Q = 19.50


      helping beam      w0 = 40 mm
                                                  * The helping beam is effective only
                                                   when the main beam is attenuated
        Feshbach resonances on F=1 state
                                                    Atoms are optically pumped to F=1 state

                          Theoretical predictions for Feshbach resonances
                                                                                            black: 11;11
                         200                                                                red: 10;11
                                                                                            green: 10;10
                         150                                                                yellow: 1-1;10
                                                                                            cyan: 1-1;1-1
                         100
Scattering length [a0]




                          50


                           0


                          -50


                         -100


                         -150


                         -200
                            0.060   0.065   0.070   0.075   0.080   0.085   0.090   0.095   0.100
                                                     Magnetic field [T]
                                                                                                             S. Kokkelmans, unpublished
   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.
          Spontaneous spin purification
Spin selective measurements
to identify where the atoms are.   Spin-flip collisions:

         |F=1, mF=0>
Feshbach resonances on mF=0 state




    Compared to Cs or 6Li the background scattering length is small: abg ~ 20 a0

    Straightforward approach is:      R *  40 a0  r0        sres  1
 Do we have a broad resonance? What is the extension of the region of universality ?
    Feshbach resonances on mF=0 state
                                                                                           1 Re k 2
Resonance effective range is extracted from the effective range expansion: k cot  (k )   
                                                                                           a  2

                                                        |Re| =2r0



                                                         40 G




     A narrow resonance – Re is very large         A broad resonance – Re crosses zero.
                                                    Far from the resonance – Re > r0
             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
                     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.
      Tree-body recombination rate
                                                                 a 4
       Theory:                                    K 3  3C a 
                                                                  m

                       Analytical results from the effective field theory:

a0                                                                    
      C a   67 .1e 2  cos 2 s0 ln a a   sinh 2    16 .8 1  e 4    

                                                                                4590 sinh 2  
                                               a0          C a  
                                                                        sin 2 s0 ln  a a   sinh 2  
Tree-body recombination rate
Experiment:                 
                            N   K3 n 2 N  N 

      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%.
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




                          sres  0.4




  N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
                  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                  UT prediction: a+/|a-| = 0.96(0.3)

                                    + = 0.232(0.036)
                                    - = 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)
 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                  UT prediction: a+/|a-| = 0.96(0.3)

                   + = 0.232(0.036)
                   - = 0.223(0.036)


The position of features may shift for lower temperature.
                How much do they shift?
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).
          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
         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 K3 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     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
Feshbach resonance on the
  absolute ground state

            |Re| =2r0



           40 G
Preliminary results for the absolute
           ground state
                  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.
  Who was in the lab and beyond?

Bar-Ilan University, Israel            Eindhoven University of
                                     Technology, The Netherlands


                        Noam Gross
                        Zav Shotan
                        L. Kh.



                                          Servaas Kokkelmans

								
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