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