few-body physics with ultracold atoms: efimov states and

ultracold.atomsFRISNOFRISNO--10, Ein Gedi, 09 Feb 0910, Ein Gedi, 09 Feb 09

few-body physics with ultracold atoms:Efimov states and beyond


Rudolf GrimmRudolf Grimm

“Center for Quantum Optics” in Innsbruck“Center for Quantum Optics” in Innsbruck

Austrian Academy of SciencesAustrian Academy of SciencesUniversity of Innsbruck University of Innsbruck

2718 m2718 m 2505 m2505 m

574 m574 m

ultracold.atomsFRISNOFRISNO--10, Ein Gedi, 09 Feb 0910, Ein Gedi, 09 Feb 09



Rudolf GrimmRudolf Grimm

“Center for Quantum Optics” in Innsbruck“Center for Quantum Optics” in Innsbruck

Austrian Academy of SciencesAustrian Academy of SciencesUniversity of Innsbruck University of Innsbruck

3118 m3118 m 2925 m2925 m

994 m994 m

ultracold.atomswelcome to the cold-atom world

atom trap: electromagnetic field(our case: focus of powerful infrared laser)

cooling to nanokelvin:laser cooling & subsequent evaporative cooling

atomic species:bosons and fermionsnKnK





CsBEC





collision energies: few peVtypical numbers

relative velocities: few mm/s

scattering completely s-wave dominated:s-wave scattering length a !





1995: Bose-Einstein condensation 1999: degenerate Fermi gas

milestones in the field

BEC

2003: molecular condensates 2004/05: fermionic condensates

2002/03: ultracold dimers

2006: Efimov states

2002: Mott insulator

2007: dipolar quantum gas2008: ultracold ground-state molecules

interaction tuning through Feshbach resonances !interaction tuning through Feshbach resonances !

ultracold.atomsmolecular structure: scattering length

r

U(r)

incident channel

B

a

s-wave scattering length adetermined by last bound level

abg

last boundlevel many

vib.levels

ultracold.atomsmolecular structure: scattering length

B

a

abg

r

U(r)

incident channel

bound state

coupling

ultracold.atomsFeshbach resonance

r

U(r)

incident channel

bound state

magnetic moment of bound statediffers from the magnetic moment of the incident channel

B

a

s-wave scattering length aas a function of magnetic field B

abg

B0

⎟⎟⎠

⎞⎜⎜⎝

⎛−Δ

−=0

1BB

aa bg

coupling

ultracold.atomsultracold.atoms Innsbruck

HCNFS

RG

JHD

6Li2 (RG & JHD)

Rb lattice (JHD & RG)

Cs-Rb mixture (RG & HCN)

Cs few-body physics (RG, FF, HCN)Cs III (HCN) Li-K-Sr mixture (RG & FS)

Ca+ Rb (JHD)

Sr BEC (FS)

FF

ultracold.atoms

exotic trimer states:exotic trimer states:„„EfimovEfimov““ quantum statesquantum states

ultracold.atomsuniversality

rr0

U(r)

ψ(r)

„quantum halo states“:deuteron, He2, Feshbach molecules !!!

weakly bound last level:

scattering length a>>r0binding energy Eb = - h2/(ma2)

a system with universal properties !!!

weakly bound last level:

scattering length a>>r0binding energy Eb = - h2/(ma2)

a system with universal properties !!!

ultracold.atoms

energy1/a

quantum states near two-body resonance

a < 0 a > 0

Edimer = − h2/(ma2)

weaklybounddimer

ultracold.atoms

energy1/a


a < 0 a > 0

ultracold.atoms39 years ago ...

ultracold.atoms

energy1/a


weakly bound trimer

a < 0 a > 0

even more weaklybound trimer

×22.7

×(22.7)2

infinite series of weakly bound trimer statesfor resonant two-body interaction

„Efimov states“

infinite series of weakly bound trimer statesfor resonant two-body interaction

„Efimov states“

ultracold.atoms

Borromean regionBorromean regiontrimers withouttrimers without

pairwise bindingpairwise binding

energy1/a

a < 0 a > 0

Borromean region

ultracold.atoms

Borromean ringsBorromean rings(symbol of Borromeo family, Northern Italy)(symbol of Borromeo family, Northern Italy)

ultracold.atomsobservations in nuclear and molecular physics

(an elusive goal for more than 3 decades)

ultracold.atoms

energy1/a

Efimov resonancesEfimov resonances

a < 0 a > 0

three atoms couple to anEfimov trimer:

„triatomic Efimov resonance“

three atoms couple to anthree atoms couple to anEfimov trimer:Efimov trimer:

„„triatomictriatomic Efimov resonanceEfimov resonance““one atom and a dimer couple to anEfimov trimer:

„atom-dimer Efimov resonance“

one atom and a dimer couple to anone atom and a dimer couple to anEfimov trimer:Efimov trimer:

„„atomatom--dimer Efimov resonancedimer Efimov resonance““

resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

ultracold.atoms

energy1/a

universalityuniversality

a < 0 a > 0

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

ultracold.atoms

energy1/a

universalityuniversality

a < 0 a > 0

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

locations of Efimov states / resonance positionsnot universal !!!

addtl. three-body parameter needed

locations of Efimov states / resonance positionsnot universal !!!

addtl. three-body parameter needed

ultracold.atoms

real-world molecules (e.g. Cs2)

U(r)

ψ(r)

another issue

U(r)

ψ(r)

single or no two-body bound state many two-body bound states

ultracold.atoms

threethree--body recombinationbody recombinationatomic systems feature deeply bound dimer states

Eb/3

2Eb/3

release of binding energy -> loss

loss probes threeloss probes three--body physics !body physics !

ultracold.atomsthree-body recomb. theory basics

L3: three-body loss coefficient [cm6/s]

Fedichev et al., PRL 77, 2921 (1996)prediction of a4 scaling, C = 3.9

Nielsen & Macek, PRL 83, 1566 (1999)Esry et al., PRL 83, 1751 (1999)Bedaque et al., PRL 85, 908 (2000)Braaten & Hammer, PRL 87, 160407 (2001)

CC((aa) = ) = CC(22.7(22.7aa))with upper limit with upper limit ~~70 for 70 for aa>0>0

oscillatory behavioroscillatory behavior×× eeππ ~~ 22.722.7

ultracold.atomsEsry-Greene-Burke theory

PRL 83, 1751 (1999) calculations for a sech2(rij/r0) model potential

definition ofa recombination length

L3~a4L3~a4

destructiveinterference effect

destructiveinterference effect

Efimov resonance !Efimov resonance !

ultracold.atoms

)( with 34

3 aCCmaCL ==

0<a

*|| Λa

*22

*

sinh)72.1)*|ln(|0(sin)2sinh( 4590)(

ηη

++Λ=

asaC

)(aC

Three-body loss coefficient

)(aC

* Λa

0>a

)1( 8.16

)sinh)76.1)*ln(0((cose 1.67)(

*4

*2

*22

η

ηη

−

−

−+

++Λ=

e

asaC

loss into deeply bound molecules

loss into shallow dimer

effective field theory (Braaten & Hammer)


Phys. Rep. 428, 259 (2006)

ultracold.atomsCs I team

FrancescaFrancescaFerlainoFerlaino

JohannJohannDanzlDanzl

StevenStevenKnoopKnoop

MichaelMichaelMarkMark

HaraldHaraldSchSchööbelbel

MartinMartinBerningerBerninger

AlmarAlmarLangeLange

BastianBastianEngeserEngeser

KarlKarlPilchPilch

AndreaAndreaPrantnerPrantner

ChengChengChinChin

TobiasTobiasKraemerKraemer

HH--CCNNäägerlgerl

ultracold.atomsmagnetic tunability of Cs

150 G50 G 100 G

-1000

1000

2000

-2000

3000

0

magnetic field (G)

scat

terin

g le

ngth

(a 0

)

F=3, mF=3F=3, mF=3

0

there should be an Efimov resonance !there should be an Efimov resonance !there should be an Efimov resonance !

ultracold.atoms

CsBEC

ultracold.atomsexp. results !

Braaten-HammertheoryΛ*=1/230a0, η*=0.08

T = 10nK

200nK

Efimov resonanceEfimov resonance

ultracold.atomsexp. results !

Braaten-Hammertheory

Esry, Greene, Burketheory 1999

T = 10nK

200nK

Efimov resonanceEfimov resonance

ultracold.atoms

energy1/a


a < 0 a > 0









ultracold.atoms

how to make the dimers?how to make the dimers?

ultracold.atomsFeshbach ramp

r

U(r)

incident channel

bound state

magnetic moment of bound statediffers from the magnetic moment of the incident channel

B

a

s-wave scattering length aas a function of magnetic field B

abg

B0

⎟⎟⎠

⎞⎜⎜⎝

⎛−Δ

−=0

1BB

aa bg

coupling

association of a “Feshbach molecule”

association of a “Feshbach molecule”

ultracold.atomsmaking Feshbach molecules from BECs

breakthroughsbreakthroughs2002/032002/03

CsCs22

8787RbRb22 NaNa22

Innsbruck, Science 301, 1510 (2003)

MPQ, PRL 92, 020406 (2004) MIT, PRL 91, 210402 (2003)

8585RbRb22

JILA, Nature 417, 529 (2002)

Feshbach molecules from fermionic atoms JILA, ENS, Rice, Innsbruck 2003

Feshbach molecules from fermionic atoms JILA, ENS, Rice, Innsbruck 20034040KK22 66LiLi22

ultracold.atomscesium: magnetic field region of interest

xx xx xx xx

ultracold.atomsrelevant states

halo state !universal relationto scatt. length

halo state !universal relationto scatt. length

ultracold.atomscreation of “tunable” halo dimers

dimers

atoms

optional: subsequent purification – dimers only

mixtureat variable B-field

ultracold.atomsfast atom-dimer decay: an example

extract loss rate coefficient β

B = 35 G

expt. with trapped atom-dimer mixture

ultracold.atomsatom-dimer “Efimov” resonance

Knoop et al., Nat. Phys., in press; arXiv0807.3306

40 nK170nK

ultracold.atoms

energy1/a


a < 0 a > 0









ultracold.atomsdo things fit together ?

-850a0 +370a0

qualitatively, but not quantitatively !Hammer et al., PRA 75,032715 (2006)Thogersen et al., PRA 78,020501 (2008)

two possible explanations:• not fully in the universal regime (rvdw ≈ 100a0)

-> finite-range corrections ?• change of short-range physics (“three-body parameter”) ?

J. D‘Incao et al., cond-mat/0703206 (2007) still an open issue !

ultracold.atoms

ultracold.atomsprobing four-body physics

dimer-dimer relaxation

again, measure trap loss vs. halo dimer sizeagain, measure trap loss vs. halo dimer size

breakup

two halo dimers:four identical bosons

ultracold.atoms

Ferlaino et al., PRL 101, 023201

experimental results: loss vs. scatt. length

(2008)

ultracold.atomsexperimental results: loss vs. scatt. length

Ferlaino et al., PRL 101, 023201(2008)

ultracold.atomsexperimental results: loss vs. scatt. length

Ferlaino et al., PRL 101, 023201(2008)

losslossminimumminimum

universal fouruniversal four--body phenomenon?body phenomenon?

ultracold.atomsnew 4-body theory predictions

3A res.

AD res.

DD-4Ares.

4A res.

main message: each Efimov trimer stateis accompanied by two universal tetramer states !

no 4-body parameter

von Stecher et al, arXiv:0810.3876

3-body features

4-body features

ultracold.atomsobservation of four-body recombination

four-bodyresonance

preliminary!preliminary!

ultracold.atomsfew-body conclusions

atomic three-body recombinationKraemer et al., Nature 440, 315 (2006)

beyond Efimov: first insights (expt. and theo.) into universal 4-body states

first observations in the ultracold cesium gas (Innsbruck)atom-dimer collisionsKnoop et al., Nat. Phys., in press

Efimov resonances now observedin three other Feshbach-resonant systems

6Li three-component Fermi gas

39K Bose gas

41K – 87Rb Bose-Bose mixture gas

Jochim group, HeidelbergO‘Hara group, Penn. State Univ.

Inguscio, Modugno group, Florence

Inguscio, Minardi group, Florence

ultracold.atoms

Vitali Efimov in the 70´s

ultracold.atoms

Vitali Efimov Vitali Efimov at FB18, July 2006at FB18, July 2006

ultracold.atomsfewfew--body conclusionsbody conclusions

amazing progress in both experiment and theory !amazing progress in both experiment and theory !

fewfew--body physics:body physics:emerging subemerging sub--field of coldfield of cold--atom physicsatom physics

few-body physics with ultracold atoms: efimov states and

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