Experimental study of Efimov scenario in ultracold bosonic lithium

Lev Khaykovich

Physics Department, Bar-Ilan University,

52900 Ramat Gan, Israel

FRISNO-11, Aussois, 28/3/2011

Outline

Experimental approach - all optical BEC of lithium Exploring Feshbach resonances on F=1 state. Spontaneous spin purification.

Universal quantum states in three body domain (scattering length a is the largest length scale in the system)

Weakly bound Efimov trimers. Log periodic behavior of three-body recombination. Evidence of spin independent short range 3-body physics.

Mapping between the scattering length and the applied magnetic field – direct association of Feshbach molecules.

Conclusions – is the nonuniversal part of the theory nonuniversal?

Experimental system: bosonic lithium

Compared to other atomic species available for laser cooling, lithium has the smallest range of van der Waals potential:

0

41

26

0 3116

amC

r

Thus it is easier to fulfill the universal physics requirement: |a| >> r0

Why lithium?

Experimental system: bosonic lithium

Bulk metal – light and soft

What’s lithium?

Magneto-optically trapped atoms

All optical BEC: optical dipole trapDirect loading of an optical dipole trap from a MOT

0 order (helping beam)

+1 order (main trap)

main trap

helping beam * The helping beam is effective only when the main beam is attenuated

Ytterbium Fiber LaserP = 100 W

w0 = 31 mU = 2 K

= 19.50

w0 = 40 m

N=2x106

T=300 K

N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

Tuning the s-wave scattering length

0

1BB

aa bg

Feshbach resonance

A weakly bound state is formed for positive a – Feshbach molecule

Feshbach resonances on F=1 state

0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100-200

-150

-100

-50

0

50

100

150

200

Sca

tteri

ng

len

gth

[a0]

Magnetic field [T]

black: 11;11red: 10;11green: 10;10yellow: 1-1;10cyan: 1-1;1-1

Theoretical prediction for Feshbach resonances

S. Kokkelmans, unpublished

Search for Feshbach resonances

Positions of Feshbach resonances from atom loss measurements:

Narrow resonance: 845.8(7) G Wide resonance: 894.2(7) G

From the whole zoo of possible resonances only two were detected.

Atoms are optically pumped to F=1 state.

Spontaneous spin purificationSpin selective measurements

to identify where the atoms are. Spin-flip collisions:

|F=1, mF=0>

N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

Feshbach resonances on mF=0 stateTheoretical prediction for Feshbach resonances

This is not the absolute ground state!

Experimental playground

The one but lowest Zeeman stateAbsolute ground state

Three-body universality: Efimov qunatum states

Quantum states near two-body resonance (Efimov scenario)

Universal three-body bound states

weakly bound trimers

even moreweakly bound

trimers

Universal three-body bound states

Position of an Efimov state is nonuniversal. It is defined by a three-body parameter.

Experimental observables – Efimov resonances

Three atoms coupleto an Efimov trimer

One atom and a dimer couple to an Efimov trimer

Experimental observable - enhanced three-body recombination

Three-body recombination

Release of binding energy causes loss which probes 3-body physics.

Manifistation of Efimov resonances

Three atoms coupleto an Efimov trimer

One atom and a dimer couple to an Efimov trimer

Enhanced three-body loss: collisions at much larger distance

Experimental observables – suppressed three-body recombination

There are two paths for the 3- body recombinationtowards deeply

bound state

Suppressed three-body recombination

deeply bound molecule

Two paths interfere destructively a certain scattering lengths – recombination minima.

Three-body recombination theory

NnKN 23 K3 – 3-body loss coefficient [cm6/sec]

Loss rate from a trap:

Dimension analysis: m

aK

4

3

Full treatment: m

aaCK

4

3 3

Effective field theory

42

022 18.16sinhlncos1.67 eaaseaC

2

02 sinhlnsin

2sinh4590

aasaC

0a

0a

Loss into shallow dimer Loss into deeply bound molecules

Efimov resonancesRecombination minima

Braaten & Hammer, Phys. Rep. 428, 259 (2006)

Experimental results

N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

a > 0: T= 2 – 3 K

a < 0: T= 1 – 2 K

mf = 1; Feshbach resonance ~740G.

Experimental resultsa > 0: T= 2 – 3 K

a < 0: T= 1 – 2 K

mf = 1; Feshbach resonance ~740G.mf = 0; Feshbach resonance ~895G.

N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

Experimentally demonstrated Efimov features

This resonance

This minimum

Experimentally demonstrated Efimov features

Theses two resonancesare related by 22.7

Experimentally demonstrated Efimov features

Theses two resonancesare related by 22

Experimentally demonstrated Efimov features

This resonance

This minimum

This resonance

Summary of the results

The universal factor of 22.7 is confirmed across the region of

Three-body parameter is the same (within the experimental errors) for both nuclear-spin subleves.

a+/|a-| = 0.96(0.3)

Fitting parameters to the universal theory:

a

UT prediction:

N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

Mapping between the scattering length And the applied magnetic field

Mapping between the scattering length and the applied magnetic field

0BBEb

2

2

maEb

Bare state (non-universal) dimer:

Feshbach molecule (universal dimer):

Universal two-body bound state

The size of the bound state is that of a

singlet potential: ~1.5 nm

Progressive contamintion by

the atomic continuum

There is only a small fraction of

the wave function in the bound

state. The size of the bound state

increases.

“Quantum halo states”

2

2

maEb

Experimental probe

Deeply bound molecule

Loss mechanism from the trap (release of binding energy):

Mapping between the scattering length and the applied magnetic fieldPrecise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.

A typical RF spectrum

N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Mapping between the scattering length and the applied magnetic fieldPrecise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.

Solid (dashed) line – local (global) analysis

N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Mapping between the scattering length and the applied magnetic field

0)2(33.34 aaS

0)8(87.26 aaT

Improved characterization of Li inter-atomic potentials.

Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers.

N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Conclusions For two different Fesbach resonances on two different

nuclear-spin sublevles of the same atomic system we demonstrate: Universal scaling factor of 22.7 across the region of

. Same positions of the Efimov features (within the

experimental errors). First experimental indication that the nonuniversal part

of the universal theory – the three-body parameter – might have some “universal” properties. New insight from Innsbruck group – for three different Feshbach

resonances the Efimov features are the same!

a

People

Eindhoven University ofTechnology, The Netherlands

Servaas Kokkelmans

Bar-Ilan University, Israel