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Observation of universality in 7 Li 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.
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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: 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 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
Feshbach resonances on F=1 state Atoms are optically pumped to F=1 state Theoretical predictions for Feshbach resonances S. Kokkelmans, unpublished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: Do we have a broad resonance? What is the extension of the region of universality ?
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
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 Theory: Analytical results from the effective field theory:
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%.
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).
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)
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?
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 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
Feshbach resonance on the absolute ground state |Re| =2r0 40 G
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? Eindhoven University of Technology, The Netherlands Bar-Ilan University, Israel Noam Gross Zav Shotan L. Kh. Servaas Kokkelmans