Threebody recombination at vanishing scattering lengths in ultracold
Three-body recombination at vanishing scattering lengths in ultracold atoms Lev Khaykovich Physics Department, Bar-Ilan University, 52900 Ramat Gan, Israel Critical Stability workshop, Santos Brasil 10/14/2014
System: dilute gas of ultracold Magneto-optical trap of Li atoms Close to the resonance (orbital electronic states) visible (laser) light – 671 nm (~2 e. V) Magnetic fields Ultrahigh vacuum environment Dilute gas of atoms: Dissipative trap N ~ 5 x 108 atoms n ~ 1010 atoms/cm 3 T ~ 300 m. K
Experimental setup: ultracold 7 Li Trapping: conservative atom trap atoms. Cooling: (our case: focus of a powerful infrared laser) Zeeman slower Crossed-beam optical trap Evaporation: ~2 x 104 atoms ~1. 5 m. K MOT ~109 atoms Typical numbers: CMOT ~5 x 108 atoms (300 m. K) Temperature: ~ m. K Relative velocities: few cm/sec Collision energies: N. Gross and L. Khaykovich, PRA 77, 023604 (2008) few pe. V
Study of Efimov scenario with ultracold atoms
Efimov scenario – universality k window first excited level lowest level Borromean region: trimers without pairwise binding
Efimov scenario and real a<0 a>0 molecules No 2 -body bound states One 2 -body bound state Real molecules: many deeply bound states
Three-body recombination Three body inelastic collisions result in a weakly (or deeply) bound molecule. 2 Eb/3 U 0 Release of the binding energy causes loss of atoms from a finite depth trap which probes 3 -body physics. Loss rate from a trap: K 3 – 3 -body loss rate coefficient [cm 6/sec]
Experimental observables k One atom and a dimer couple to an Efimov trimer Three atoms couple to an Efimov trimer Experimental observable - enhanced three-body recombination.
Experimental observables k Two paths for the 3 body recombination towards weakly bound state interfere destructively. Three atoms couple to an Efimov trimer Experimental observable – recombination minimum.
Experimental observables Recombination length: Recombination minimum Efimov resonance B. D. Ezry, C. H. Greene and J. P. Burke Jr. , Phys. Rev. Lett. 83 1751 (1999).
Efimov scenario: a short overview n Efimov physics (and beyond) with ultracold atoms: q q 2006 - … 133 Cs Innsbruck 2008 – 2010 6 Li 3 -component Fermi gas in Heidelberg, Penn State and Tokyo Universities q 2009; 2013 39 K in Florence, Italy q 2009 41 K - 87 Rb in Florence, Italy q 2009; 2013 7 Li in Rice University, Huston, TX q 2009 - … 7 Li in BIU, Israel q 2012 - … 85 Rb and 40 K - 87 Rb JILA, Boulder, CO q 2014 - 133 Cs - 6 Li in Chicago and Heidelberg* Universities *Eva Kuhnle’s talk on Friday.
Experimental playground - 7 Li 3 identical bosons on a single nuclear-spin state. Absolute ground state Next to the lowest Zeeman state
Experimental playground - 7 Li Absolute ground state Feshbach resonance The one but lowest Zeeman state Feshbach resonance N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C. R. Physique 12, 4 (2011).
Experimental results - 7 Li a > 0: T= 2 – 3 m. K a < 0: T= 1 – 2 m. K mf = 1; Feshbach resonance ~738 G. mf = 0; Feshbach resonance ~894 G. N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010
Three body recombination at vanishing scattering lengths
Motivation n Purely academic.
Motivation n n Purely academic. Application: optimization of evaporative cooling in an optical trap. Evaporative cooling in a nutshell: - high energy atoms are evaporated due to final potential depth; - elastic collisions re-establish thermal equilibrium; - Good collisions: elastic; - Bad collisions: three-body recombination (heating); - optical trap weakens during evaporation; which can be compensated by increasing a. But:
Zero-crossings 7 Li lower hyperfine level. Feshbach resonance m. F =0 state. 850 G 412 G 575 G
Early observations Same scattering length – different three-body recombination rates.
Early observations Universal region.
Early observations Saturation of the three-body recombination rate. N. Gross, Z. Shotan, S. J. J. M. F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Two-Body Physics
Scattering phase shift at zerocrossing Effective range expansion of the scattering phase shift: Inconvenient when Inverted expression: Well defined when Effective volume: See also: C. L. Blackley, P. S. Julienne and J. M. Hutson, PRA 89, 042701 (2014).
Feshbach resonances and zero. Scattering length and effective range: crossings N. Gross, Z. Shotan, S. J. J. M. F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Two-body physics near zero. Energy dependent two-body collisional crossing section: Condition for vanishing collisional cross-section: The zero-crossing position is well defined now by precise characterization Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C. R. Physique 12, 4 (2011). of. N. Feshbach resonances: P. S. Julienne and J. M. Hutson, Phys. Rev. A 89 052715 (2014) (Data from Heidelberg, ENS, Rice and Bar Ilan). Experimental approach to test the temperature dependence of the crosssection – evaporative cooling around zero-crossing. S. Jochim et. al. , Phys. Rev. Lett. 89 273202 (2002). Zero-crossing of 6 Li resonance. K. O’Hara et. al. , Phys. Rev. A 66 041401(R) (2002).
Evaporative cooling near zeroduring 500 crossing Evaporation ms Initial temperature: 31 m. K Zero-crossing is at 849. 9 G Maximum is at 850. 5 G Two-body collisions show energy dependence. Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body physics near zerocrossing Universal limit: Formal definition: The universal limit maximal value(*): Recombination length: B. D. Ezry, C. H. Greene and J. P. Burke Jr. , Phys. Rev. Lett. 83 1751 (1999). We measure K 3 and represent the results as Lm. (*) N. Gross, Z. Shotan, S. J. J. M. F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Three-body physics near zerocrossing Three-body recombination length: Van der Waals length:
Effective recombination length Measured recombination length: From the effective range expansion the leading term is proportional to the effective volume. Effective recombination length: Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body physics near zerocrossing Black: T=2. 5 m. K Red: T=10 m. K Three-body recombination shows no energy dependence. Rules out other possibilities to construct Le such as (in analogy to two-body collisions) Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body physics near zerocrossings Prediction for the recombination length in Low field zerocrossing. the resonances’ region. B [G] Experimental resolution limit is 100 a 0. Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Optimization of evaporative cooling Scattering length compensation of the density decrease. Bad/Good collisions ratio:
Phase space density
Conclusions n n n Zero-crossing does not correspond to the minimum in 3 body recombination rates. Three-body recombination rate is different at different zero -crossings. We suggest a new lengthscale to describe the 3 -body recombination rates. Energy independent 3 -body recombination rate. We predict a minimum in 3 -body recombination in the non -universal regime. The question is how general the effective length is?
People Bar-Ilan University, Israel Eindhoven University of Technology, The Netherlands Servaas Kokkelmans Zav Shotan, Olga Machtey
- Slides: 35