Three-body recombination at vanishing scattering lengths in ultracold atoms
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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
Ultrahigh vacuum environment
Dissipative trapN ~ 5x108 atoms
n ~ 1010 atoms/cm3
T ~ 300 mK
Close to the resonance (orbital electronic states) visible (laser) light – 671 nm (~2 eV)
Magnetic fields
Magneto-optical trap of Li atoms
Dilute gas of atoms:
Experimental setup: ultracold 7Li atoms
Zeemanslower
MOT~109 atoms
CMOT~5x108 atoms
(300 mK)
~2x104 atoms~1.5 mK
Crossed-beam optical trap
Trapping: conservative atom trap(our case: focus of a powerful infrared laser)
Temperature: ~ mK
Typical numbers:
Relative velocities: few cm/sec
Collision energies: few peV
N. Gross and L. Khaykovich, PRA 77, 023604 (2008)
Evaporation:
Cooling:
Study of Efimov scenario with ultracold atoms
Efimov scenario – universality window
01 r
k
1a 01 r
lowest level
first excited level
17.22 17.22
17.22
Borromean region:trimers without pairwise binding
01 2exp sEE n
TnT
00 ln rasN
Efimov scenario and real molecules
Vbg(R)
Ene
rgy
Atomic separation R
Vbg(R)
En
erg
y
Atomic separation R
No 2-body bound states
One 2-body bound state
Real molecules:many deeply bound states
Vbg(R)
Ene
rgy
Atomic separation R
a < 0 a > 0
Three-body recombination
Eb/32Eb/3
Release of the binding energy causes loss of atoms from a finite depth trapwhich probes 3-body physics.
Three body inelastic collisions result in a weakly (or deeply) bound molecule.
NnKN 233 K3 – 3-body loss rate coefficient [cm6/sec]
Loss rate from a trap:
U0
Experimental observables
01 r
k
1a *1 a a1 01 r
Experimental observable - enhanced three-body recombination.
One atom and a dimer couple to an Efimov trimer Three atoms couple
to an Efimov trimer
Experimental observables
01 r
k
1a a1 01 ra*0
1
Experimental observable – recombination minimum.
Two paths for the 3- body recombination
towards weakly bound state interfere
destructively.
Three atoms coupleto an Efimov trimer
Experimental observables
B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999).
41
33 )(3
=
aC
mKRecombination length:
Efimov resonance
Recombinationminimum
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
Absolute ground state
Next to the lowest Zeeman state
3 identical bosons on a single nuclear-spin state.
Experimental playground - 7Li
Feshbachresonance
Feshbachresonance
Absolute ground state The one but lowest Zeeman state
N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011).
Experimental results - 7Lia > 0: T= 2 – 3 mK
a < 0: T= 1 – 2 mK
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);
- optical trap weakens during evaporation;
which can be compensated by increasing a.
But:
nel
423
23 anKnb
Zero-crossings 7Li lower hyperfine level.
Feshbach resonance mF =0 state.
0 200 400 600 800 1000-400
-300
-200
-100
0
100
200
300
400
a [a
0]
Magnetic field [G]
850 G
575 G
412 G
Early observations
Same scattering length – different three-body recombination rates.
Early observations
43 aK
Universal region.
Early observations
N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Saturation of the three-body recombination rate.
Two-Body Physics
Scattering phase shift at zero-crossing
2)(2
1+
)(
1cot kBR
Bakk e
Effective range expansion of the scattering phase shift:
Inconvenient when
0a
22 )(2
1+
tankaRa
k
ke
22aRV ee Effective volume:
See also: C. L. Blackley, P. S. Julienne and J. M. Hutson, PRA 89, 042701 (2014).
Inverted expression:
Well defined when
0a
Feshbach resonances and zero-crossings
800 820 840 860 880 900 920 940
-400
-200
0
200
400
Magnetic field [G]
Scattering length and effective range:
N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
500 550 600 650 700 750 800-10
0
10
20
30
40
a, R
e [a
0]
Magnetic field [G]
Two-body physics near zero-crossingEnergy dependent two-body collisional
cross-section:
222
222
2+1
8sin
8)(
kakV
akVk
kk
e
e
0)( k 2= kVa e 2
2=
kRa
e
Condition for vanishing collisional cross-section:
The zero-crossing position is well defined now by precise characterizationof 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
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Zero-crossing is at 849.9GMaximum is at 850.5G
Evaporation during 500 msInitial temperature: 31 mK
Two-body collisions show energy dependence.
Three-body physics near zero-crossing
43 )(3= a
maCK
Universal limit:
Recombination length:
41
max
3
3=
C
mKLm
We measure K3 and represent the results as Lm.
B. D. Ezry, C. H. Greene and J. P. Burke Jr., Phys. Rev. Lett. 83 1751 (1999).
4max3 3= mL
mCK
Formal definition:
The universal limit maximal value(*):
54.7=maxC
(*) N. Gross, Z. Shotan, S.J.J.M.F. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009).
Three-body physics near zero-crossing
850 860 870 880 8900
100
200
300
400
500
600
Rec
ombi
natio
n le
ngth
, a
[a0]
Magnetic field [G]
Three-body recombination length:
0
41
26
0 5.3216
amC
r
Van der Waals length:
Effective recombination length
41
max
3
3=
C
mKLmMeasured recombination
length:
31231
2==
aRVL e
ee
From the effective range expansion the leading term is proportional tothe effective volume.
Effective recombination length:
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body physics near zero-crossing
Black: T=2.5 mKRed: T=10 mK
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Three-body recombination shows no energy dependence.
Rules out other possibilities to construct Le such as(in analogy to two-body collisions)
2= kVL ee
Three-body physics near zero-crossings
Low field zero-crossing.
Prediction for the recombination length in the resonances’ region.
B [G]
Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, PRL 113 , 053202 (2014).
Experimental resolution limit is 100 a0.
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?
People
Eindhoven University ofTechnology, The Netherlands
Servaas Kokkelmans
Bar-Ilan University, Israel
Zav Shotan, Olga Machtey
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