The Efimov Effect in Ultracold Gases Weakly Bounds Systems in Atomic and Nuclear Physics March , 2010 Institut für Experimentalphysik, Universität Innsbruck Martin Berninger, Francesca Ferlaino, Alessandro Zenesini, Walter Harm, Hanns-Christoph Nägerl, Rudi Grimm

The Efimov Puzzle (an experimentalists view...) Theory Experiment Efimov States in the molecules and nuclei, Rome 2009 Weakly-Bound Systems in Atomic and Nuclear Physics, Seattle 2010

Outline Introduction atomic few-body physicsIntroduction atomic few-body physics The Efimov scenarioThe Efimov scenario Experimental Efimov physics with CsExperimental Efimov physics with Cs Overview experimental Efimov physicsOverview experimental Efimov physics New results in caesium samples (preliminary)New results in caesium samples (preliminary) Collisions in Dimer-Dimer samplesCollisions in Dimer-Dimer samples Ultracold exchange reactionsUltracold exchange reactions

last bound level  r  halo dimer kHz 2-body Cs 4-body Cs 2 Cs Cs 3 Cs Few-body physics 3-body Cs 2 Cs In general complex problem: strong dependence on potential many vib. levels non-universal dimer U(r)~1/r 6 r U(r) schematic drawing THz Universal regime scattering length a>>r 0 r 0 : range of the potential r 0 ~ l vdW ~ 100a 0 for Cs s­wave scattering length: dimers trimers tetramers Universal connection:  ? Halo dimers Efimov trimers Universal tetramers

Ultracold atomic gases as a model system Quantum gas Classical gas T ~ 1µK – 20nK Temperature Control knobs Interactions Interaction strength a crossed- beam trap  y ≈  z ≈  x 3D 2D 1D Geometry optical lattice „pancake“ trap Mixtures different interactions different mass ratios Bosonic / Fermionic systems State m F =3 F=3 m F =4 F=4 3 2 MW transfer caesium

magnetic moment of bound state differs from the magnetic moment of the incident channel B a a bg B0B0 F=3+F=3 F=3+F=4 F=4+F=4 (example Cs) r U(r) incident channel bound state Tunable interaction: Feshbach resonance Magnetic tunability of the scattering length

energy a < 0 a > 0 Two-particle picture attractive repulsive halo dimer s-wave resonances for Cs in F 1 =3 F 2 =3 channel 50 G100 G magnetic field (G) scattering length (a 0 ) 0150 G s-wave + d-wave resonances in Cs bound state in open channel: E B ~10kHz background scattering length a bg ~2000a 0 EbEb B 44(6) 34(7) 34(6) F1 F2 (F1+F2) E. Tiesinga et al.

energy a < 0 a > 0 The Efimov scenario „Efimov – states“ halo dimer ×22.7 ×(22.7) 2...there exists an infinite series of weakly bound trimer states for resonant two-body interaction... V. Efimov, Phys. Lett. B 33, (1970) weakly bound trimer even more weakly bound trimer

a < 0 deeply bound dimer Trap loss energy

3-atomic Efimov resonance OFF resonance ON resonance new decay channel  Enhancement of losses 10nK 200nK 3-Atomic Efimov resonance Kraemer et al., Nature 440, 315 (2006) three-body recombination rate  a 4 recombination length: energy Ultracold sample of 133 Cs atoms in atomic ground state: F=3, m F =3 N ~ 10 5 atoms T = 10/200nK

3-atomic Efimov resonance 10nK 200nK 3-Atomic Efimov resonance Kraemer et al., Nature 440, 315 (2006) three-body recombination rate  a 4 recombination length: energy for a<0, a   : C(a)=C(22.7a) Braaten & Hammer for a>0, a   : Atom-Dimer relaxation rate  : s 0 = Braaten-Hammer theory a AAA =-850 a 0 a min =210 a 0 L 3 max =5.7* cm 6 /s L 3 min =1.33* cm 6 /s

3-atomic Efimov resonance energy E for a<0, a   : C(a)=C(22.7a) Braaten & Hammer for a>0, a   : Atom-Dimer relaxation rate  : s 0 = a > 0 halo dimer

s-wave state d-wave state # dimer: ~ 4000 # atoms: (3-6)x10 4 T = nK Separate atoms and dimers by magnetic gradient field before imaging Measure the time-evolution & extract atom-dimer relaxation rate coefficient  Production of 6s-molecules via Feshbach association Atom-dimer Efimov resonance

Atom-dimer resonance at B=25 G a AD =+400 a 0 universality a>0 and a<0 via a=0 ? transition universal to non-universal ? (r 0 ~100a 0 ) any relation to Efimov physics at different Feshbach resonances Universal relation via pole: for n=0, n‘=1  a AD /a AAA = 0.47 Knoop et. al., Nature Physics 5, 227 (2009) 1/a a < 0a > 0 Atom-dimer Efimov resonance

energy a < 0 a > 0 Tetra1 Tetra2 The extended Efimov scenario Prediction of two universal 4-body states tied to each Efimov trimer! H. Hammer and L. Platter, Eur. Phys. J. A 32, 113 (2007) J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Physics 5, (2009)

F. Ferlaino et. al., PRL 102, (2009) Tetra1 Tetra2 t hold =250ms t hold =8ms Four-body states - experimental results Experiment ~ 0.47 a* T ~ 0.84 a* T Position of the universal 4-body states Theory a* Tetra1 ~ 0.43 a* T a* Tetra2 ~ 0.9 a* T 4-body mixed 3-body Fitting function simple 3 body simple 4 body body

F. Ferlaino et. al., PRL 102, (2009) Tetra1 Tetra2 t hold =250ms t hold =8ms Four-body states - experimental results Experiment ~ 0.47 a* T ~ 0.84 a* T Position of the universal 4-body states Theory a* Tetra1 ~ 0.43 a* T a* Tetra2 ~ 0.9 a* T

Overview experimental Efimov physics Barontini et al., Phys. Rev. Lett. 103, (2009) Ottenstein et al., Phys. Rev. Lett. 101, (2008) Huckans et al., Phys. Rev. Lett. 102, (2009) Williams et al., Phys. Rev. Lett. 103, (2009) Wenz et al., Phys. Rev. A 80, (R) (2009) 41 K + 87 Rb 6 Li Fermionic systems Bosonic mixtures Bosonic systems Zaccanti et al., Nature Physics 5, (2009) Pollack et al., Science 326 (2009) Gross et al., Phys. Rev. Lett 103, (2009) Kraemer et al., Nature 440, 315 (2006) Knoop et. al., Nature Physics 5, 227 (2009) F. Ferlaino et. al., Phys. Rev. Lett. 102, (2009) 133 Cs 39 K 7 Li F=1, m F =1 F=1, m F =0

Successive Efimov Features – bosonic system ( 39 K) Zaccanti et al., Nature Physics, Vol. 5 (2009) Florence-Group Comparison with universal theory: Valid only for |a|>>r 0  Model for finite-range interactions? Res: second order process: A+A+A  D*+A a AD*   losses in an atom sample due to elastic scattering Lossa (a 0 ) a<0 3B Maxa1-a B MaxaT*aT*-650 a>0 3B Min a1+a a2+a AD Max a1*a1*30 a2*a2*930 Experiment with 39 K atomic sample across Feshbach resonance, r 0 =64a 0  atomic threshold

Usually, in the three-body process 3 particles are lost Efimov physics in 39K: AD resonances Thanks to M. Zaccanti & Co-Workers for the slides!

…but if AD cross section is large particle losses can be >>3!!! Efimov physics in 39K: AD resonances Thanks to M. Zaccanti & Co-Workers for the slides!

( 7 Li – F=1,m F =1 ) Successive Efimov Features – bosonic system ( 7 Li – F=1,m F =1 ) Rice-Group atomic sample 7 Li (F=1,m F =1) across Feshbach resonance, r 0 =33a 0 Pollack et al., Science 326 (2009) Comparison universal theory Valid only for each side, systematic discrepancy (factor 2)  Variation in the short range phase across the Feshbach resonance? Lossa (a 0 ) a<0 3B Max a1-a a2-a B Max a T 1,1 -120a T 1, a T 2, a T 2, a>0 3B Min a1+a a2+a AD Max indirect a2*a2*608 DD Max debate a* 2, a* 2, Res: a>0 a<0 a 

Ottenstein et al., PRL 101, (2008) Huckans et al., PRL 102, (2009) Williams et al., PRL 103, (2009) Wenz et al., PRA 80, (R) (2009) Braaten et al., PRL 103, (2009) Naidon et al., PRL 103, (2009) Floerchinger et al., PRA 79, (2009) Braaten et al., PRA 81, (2010) Jochim & O‘Hara 6 Li 3 component Fermi-Spin-mixture: |3> m F = -3/2 |2> m F = -1/2 |1> m F = 1/2 Comparison with universal theory Using fit results for high field resonance (895G)reproduces low field resonances accurately: 125(3)G & 499(2)G  No change in the three body parameter for  B ~ 750G? for a ij ~ l vdw ? Efimov features in fermionic spin mixtures ( 6 Li) LossstateB(G) a<03B Max n=0127 n=0500 n‘=1895 Res:

Gross et al., PRL 103, (2009) Khaykovich-Group atomic sample 7 Li (F=1,m F =0) across Feshbach resonance Comparison with universal theory: a + /|a - | = 0.92(14) (Theory=0.96(3))  Why does 7 Li agree so nicely in (F=1,m F =0) and not in (F=1,m F =1)? ( 7 Li – F=1,m F =0 ) Bosonic system showing universality ( 7 Li – F=1,m F =0 ) Lossa (a 0 ) a<03B Maxa-a a>03B Mina+a Results:

Barontini et al., Phys. Rev. Lett. 103, (2009) Efimov Resonances – Heteronuclear systems ( 41 K + 87 Rb) Florence-Group System composed of distinguishable particles with different masses Experiment with bosonic mixture of 41 K and 87 Rb at a interspecies Feshbach resonance  Two resonantly interacting pairs are sufficient for Efimov physics  Existence of two Efimov series: KRbRb: exp  (  /s 0 ) = 131 KKRb: exp  (  /s 0 ) = 3.51  10 5 Results: KKRb-resonance Lossa (a 0 ) a<0 3B Max KRbRb-246 3B Max KKRb a>0 AD Max indirect a*667 No oscillations for a>0 observed

6d6 B (Gauss) preliminary K3 preliminary Lifetime high magnetic fields Recombination 6s6 resonance ~ 800G, width ~ 90G T~200nK Resonance! Unitarity limit: Another piece to the puzzle! L3L3 L3L3 f l m f

n D = -L 2 n D 2 Measuring relaxation rate L 2 : Ferlaino et al., PRL 101, (2008) Experimental results: dimer-dimer collisions s-wave state d-wave state 2 atoms in F=3, m F =3 microwave Sample of universal dimers in 6s-state: crossed dipole trap (1060nm) crossed dipole trap (1060nm) N D ~ 4000 N D ~ 4000 T ~ 40 – 350 nK T ~ 40 – 350 nK k B T << E B ~ h  50kHz << E vdW ~ h  2.7MHz k B T << E B ~ h  50kHz << E vdW ~ h  2.7MHz 10 5 ultracold 133 Cs atoms (40nK)  Feshbach association  Removal of atoms with microwave  Sample of ultracold dimers scattering length (a 0 ) 2-body reaction cross section (Wigner 1948) energy a < 0 a > 0 Tetra1 Tetra2 ?

Exchange reactions with distinguishable particles B + A 2 F=4, m F =2, 3 or 4 Feshbach molecule / halo dimer 2x (F=3, m F =3) m F =3 F=3 F=4 2 m F =4 3 MW transfer A + A 2 F=3, m F =3 ?

total loss exchange T=50 nK  : atom-dimer loss rate coefficient Exchange reactions loss rates Knoop et al., Phys. Rev. Lett. 104, (2010) Theory: Jose D’Incao & Brett Esry B E A+A+B A 2 +B A+AB EE new decay channel m F =4 m F =3 m F =2 35 G: opening exchange channel B E A+B A+A AB A2A2

A 2 (v=-1) +B → A+AB (v=-1) Closer look around 35 G appearance of trapped atoms in state A! Ultracold exchange reaction controlled by magnetic field T=100 nK, t hold =22ms m F =4 m F =3 m F =2

Role of the large scattering length A 2 (v=-1) +B A+AB (v’<v) A+AB (v=-1) A 2 (v’<v) +B A+A A+B(m F =2) A+B(m F =3) A+B(m F =4)  r 

Theory Experiment Experimentalists wish list for Theory  Is there any relation for Efimov physics at different Feshbach resonances ( 133 Cs low fields and Feshbach 800G)?  Model for finite-range interactions, transition universal to non-universal ( 39 K & 133 Cs)?  Variation in the short range phase across the Feshbach resonance ( 7 Li) – Factor 2?  Why does 7 Li agree so nicely in (F=1,m F =0) and not in (F=1,m F =1)?  Why there is no change in the three body parameter in 6 Li spin mixture for   B ~ 750G and/or for a ij ~ l vdw ? Coming soon: Cs data for 800G resonance  Any connection of Efimov physics from a>0 to a 0 to a<0 via a=0 ( 133 Cs)? – Factor 1/2?  Temperature dependence in 133 Cs halo molecules? a <<  a 

The Caesium-Efimov-Team M.B. RudiGrimm FrancescaFerlaino AlessandroZenessini Hanns- Christoph Nägerl WalterHarm