Three-Body Recombination in Ultracold Atoms: Studies and Observations

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Investigating three-body recombination in ultracold atoms, this study explores the Efimov scenario, experimental setups with ultracold 7Li atoms, and the implications of three-body inelastic collisions. The research delves into universality windows, real molecule comparisons, and the loss rate from traps, shedding light on the intriguing physics of ultracold atomic systems.

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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 atoms Magneto-optical trap of Li atoms Close to the resonance (orbital electronic states) visible (laser) light 671 nm (~2 eV) Magnetic fields Ultrahigh vacuum environment Dissipative trap N ~ 5x108 atoms n ~ 1010 atoms/cm3 Dilute gas of atoms:

Experimental setup: ultracold 7Li atoms Cooling: Trapping: conservative atom trap (our case: focus of a powerful infrared laser) Zeeman slower Crossed-beam optical trap Evaporation: ~2x104 atoms ~1.5 K MOT ~109 atoms Typical numbers: Temperature: Relative velocities CMOT few cm/sec ~5x108 atoms Collision energies few peV N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

Study of Efimov scenario with ultracold atoms

Efimov scenario universality window k 1 r 1 r 1 0 a 0 22 7 . 1 22 7 . 1 first excited level 22 7 . 1 lowest level Borromean region: trimers without pairwise binding ) ( ln ) ( = N s a r 0 0 ( ) + 1 n T n T exp 2 E E s 0

Efimov scenario and real molecules a < 0 a > 0 No 2-body bound states Energy Energy One 2-body bound state Vbg(R) Vbg(R) Atomic separation R Atomic separation R Energy Real molecules: many deeply bound states Vbg(R) Atomic separation R

Three-body recombination Three body inelastic collisions result in a weakly (or deeply) bound molecule. 2Eb/3 Eb/3 U0 Release of the binding energy causes loss of atoms from a finite depth trap which probes 3-body physics. Loss rate from a trap: N = 2 3 K3 3-body loss rate coefficient [cm6/sec] K n N 3

Experimental observables k 1 r 1 a 1 a 1 r 1 0 a * 0 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 1 r 1 a 1 a* 1 r 1 0 a 0 0 Three atoms couple to an Efimov trimer Two paths for the 3- body recombination towards weakly bound state interfere destructively. Experimental observable recombination minimum.

Experimental observables 1 4 mK 3 ) = Recombination length: 3 3 ( C a 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 Efimov physics (and beyond) with ultracold atoms: 2006 - 133Cs Innsbruck 2008 2010 6Li 3-component Fermi gas in Heidelberg, Penn State and Tokyo Universities 2009; 2013 39K in Florence, Italy 2009 41K - 87Rb in Florence, Italy 2009; 2013 7Li in Rice University, Huston, TX 2009 - 7Li in BIU, Israel 2012 - 85Rb and 40K - 87Rb JILA, Boulder, CO 2014 - 133Cs - 6Li in Chicago and Heidelberg* Universities *Eva Kuhnle s talk on Friday.

Experimental playground - 7Li 3 identical bosons on a single nuclear-spin state. Absolute ground state Next to the lowest Zeeman state

Experimental playground - 7Li Absolute ground state The one but lowest Zeeman state Feshbach resonance Feshbach resonance N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011).

Experimental results - 7Li a > 0: T= 2 3 K a < 0: T= 1 2 K mf = 1; Feshbach resonance ~738G. mf = 0; Feshbach resonance ~894G. 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 Purely academic.

Motivation 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 the thermal equilibrium; - Good collisions: elastic; - Bad collisions: three-body recombination (heating); el - optical trap weakens during evaporation; n which can be compensated by increasing a. But: 3 3 K n b 2 2 4 n a

Zero-crossings 7Li lower hyperfine level. Feshbach resonance mF state. 400 300 200 100 a [a0] 0 -100 850 G -200 412 G 575 G -300 -400 0 200 400 Magnetic field [G] 600 800 1000

Early observations Same scattering length different three-body recombination rates.

Early observations Universal region. K 4 a 3

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 zero-crossing Effective range expansion of the scattering phase shift: 1 B 1 ( ( ) k ) = 0 2 a cot + ( ) k R B k Inconvenient when e ( ) 2 a Inverted expression: ( ( ) k ) tan 1 = 2) 2 + ( a R a k 0 a Well defined when e 2 k = 2 2 V R a Effective volume: e e See also: C. L. Blackley, P. S. Julienne and J. M. Hutson, PRA 89, 042701 (2014).

Feshbach resonances and zero-crossings Scattering length and effective range: 40 400 30 200 20 a, Re[a0] 0 10 -200 0 -400 -10 500 550 600 Magnetic field [G] 650 700 750 800 800 820 840 860 880 900 920 940 Magnetic field [G] N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).

Two-body physics near zero-crossing Energy dependent two-body collisional cross-section: ( ) 2 2 8 8 k V k a ( ( ) k ) = = 2 ( ) sin e k ( ) 2 2 2 2 1 + V k a k e Condition for vanishing collisional cross-section: 2 k e 2 = = a V k = a ( ) 0 k e 2 R The zero-crossing position is well defined now by precise characterization of Feshbach resonances: N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011). 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 cross-section evaporative cooling around zero-crossing. S. Jochim et. al. , Phys. Rev. Lett. 89 273202 (2002). K. O Hara et. al. , Phys. Rev. A 66 041401(R) (2002). Zero-crossing of 6Li resonance.

Evaporative cooling near zero-crossing Evaporation during 500 ms Initial temperature: 31 K Zero-crossing is at 849.9G Maximum is at 850.5G Two-body collisions show energy dependence. Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

Three-body physics near zero-crossing 4 = 3 ( ) K C a a Universal limit: 3 m 4 m = 3 K C L Formal definition: 3 max m C = 54.7 The universal limit maximal value(*): max 1 4 mK 3 = Lm Recombination length: 3 C max B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999). We measure K3 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 zero-crossing Three-body recombination length: 600 500 Recombination length, a[a0] 400 Van der Waals length: 300 1 4 mC = 6 32 5 . r a 0 0 2 16 200 100 0 850 860 Magnetic field [G] 870 880 890

Effective recombination length 1 4 mK = 3 Lm Measured recombination length: 3 C max From the effective range expansion the leading term is proportional to the effective volume. 1 3 2 R a 1 3 Effective recombination length: = = e L V e e 2 Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

Three-body physics near zero-crossing Black: T 2.5 K Red: T 10 K Three-body recombination shows no energy dependence. 2 = L V k Rules out other possibilities to construct Le such as (in analogy to two-body collisions) e e Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).

Three-body physics near zero-crossings Prediction for the recombination length in the resonances region. Low field zero-crossing. B [G] Experimental resolution limit is 100 a0. 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 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?