Evidence for Efimov Quantum states

Transcription

1 KITP, UCSB, Evidence for Efimov Quantum states in Experiments with Ultracold Cesium Atoms Hanns-Christoph Nägerl bm:bwk University of Innsbruck TMR network Cold Molecules

2 ultracold.atoms Innsbruck two teams working on cesium dimers and Efimov physics T. Kraemer, M. Mark, J. Danzl, H. Schöbel, S. Knoop, F. Ferlaino B. Engeser, K. Pilch, A. Lange, A. Prantner R. Grimm, HCN collaborators and contributors E. Cs Braaten, lattice team C. Chin, O. Dulieu, C. Koch, H. Hammer, B. Esry, P. Julienne, T. Köhler, M. Gustavsson, H. Ritsch, E. E. Haller, Tiesinga G. Rojas-Kopeinig, M. Mark, HCN

3 Outline resonant scattering: weakly bound dimer molecules and the appearance of Efimov states three-body recombination theory our system: ultracold gases of Cs atoms experimental results for three-body recomb. atom-dimer scattering Cs atoms in optical lattices

4 molecular structure: resonant scattering U(r) last bound level E b many vibrational levels incident channel r the s-wave scattering length a, i.e. the scattering radius, is determined by the binding energy of the last bound level: E b binding energy E b elastic cross section ma σ = 8π a

5 relevance of resonant scattering to BEC Gross-Pitaevskii equation ψ 2 2 d 2 i = ψ + V( r) ψ + dt 2m with g a scattering length g ψ ψ Bose-Hubbard Hamiltonian site hopping with U on-site interaction a scattering length external confinement

6 molecular structure: resonant scattering U(r) U(r) last bound level above threshold level a > 0: stable BEC r a < 0: unstable BEC r Is there a way to tune a through resonance?

7 molecular structure: resonant scattering U(r) last bound level incident channel a r a bg (constant) background scattering length magnetic field B

8 molecular structure: resonant scattering now add a second channel U(r) bound state closed channel coupling incident channel a r a bg magnetic field B

9 Fano-Feshbach resonance U(r) bound state in resonance s-wave scattering length a as a function of magnetic field B coupling incident channel a a = a bg 1 B Δ B 0 magnetic moment of bound state differs from the magnetic moment of the incident channel r a bg B0 Δ coupling magnetic field induced scattering resonance magnetic field B

10 molecular structure: single channel description for sufficiently strong coupling: single channel approach possible U(r) energy E bare state B 0 last bound level resonance state r E b 1 a B 2 ( B B 2 0) T. Koehler, K. Goral, P. S. Julienne, Rev. Mod. Phys. 78, 1311 (2006).

11 molecular structure: wavefunction U(r) quantum halo states : deuteron, He 2, Feshbach molecules!!! ψ(r) U(r) ψ(r) r 0 r r 0 = range of potential r 0 r states with universal properties for r >> r 0 E b = ma 2 2 with bond length r = a / 2

12 The quantum generic states two-body near two-body resonance resonance a < 0 energy a > 0 1/ a B finally, the molecule will break apart weakly bound dimer E b ma 2 2

13 Quantum quantum states near a two-body resonance a < 0 energy a > / a even more weakly bound trimer Efimov 1971 (22.7) 2 weakly bound trimer infinite series of weakly bound trimer states for resonant two-body interaction Efimov states

14 Effective 1/R 1/R 2 2 -potential for the 3-body problem effective radial Schrödinger equation for r 0 << R << a hyperspherical wave function as a function of hyperradius E r 0 a 2 nd Efimov state R number of Efimov states 1 st Efimov state 1/( / s0 e π ) 2 = 1/(22.7) 2 1/515 review: E. Braaten and H. Hammer Physics Reports 428, 259 (2006)

15 Efimov states Efimov states: properties a < 0 energy a > 0 three atoms couple to an Efimov trimer: Tri-atom Efimov resonance one atom and a dimer couple to an Efimov trimer: 1/ a Atom-dimer Efimov resonance in analogy to Feshbach resonances

16 candidate systems for Efimov states Candidate systems for Efimov states nuclear physics halo nuclei with many neutrons: e.g. 14 Be, 18 C, 20 C best candidates: core + n + n simplest case: triton Review: A. S. Jensen et al., RMP 76, 215 (2004)

17 candidate systems for Efimov states Candidate systems for Efimov states atomic physics: 4 He 3 Beams with He, He 2, He 3,... He 2 : binding energy 1.1 mk, <r> = 5.2 nm He 3 : binding energy 126 mk, <r> = 0.96 nm Efimov-He 3 : binding energy 2.3 mk, <r> = 7.8 nm J. P. Toennies et al, PRL 95, (2005)

18 the probe ultracold atomic gases: signature of Efimov states three-body recombination for positive scattering lengths: formation of the weakly bound dimer for negative scattering lengths: population of deeply bound dimers states

19 Three-body Efimov states recombination a < 0 energy a > 0 1/ a deeply bound dimer

20 three-body recomb. theory basics Three-body recombination: theory basics L 3 : three-body loss coefficient [cm 6 /s] Fedichev et al., PRL 77, 2921 (1996) prediction of a 4 scaling a >> r 0, C ~ 4 Nielsen & Macek, PRL 83, 1566 (1999) Esry et al., PRL 83, 1751 (1999) Bedaque et al., PRL 85, 908 (2000) Braaten & Hammer, PRL 87, (2001) C = C(a) with upper limit ~70 for a > 0 oscillatory behavior e π ~ 22.7

21 Esry-Greene theory Esry-Greene theory PRL 83, 1751 (1999) numerical calculations for model potentials definition of a recombination length Efimov resonance! L 3 ~a 4 L 3 ~a 4 destructive interference effect

22 Braaten-Hammer theory theory Three-body loss coefficient 4 a L 3 = 3 C with C = C( a) m mostly loss into shallow dimer C( a) = sin sinh(2η *) ( s ln( a Λ ) ) + sinh 0 * 2 η * C( a) = 67.1e 2η * (1 e (cos 4η * 2 ) ( s ln( aλ ) ) + sinh 0 * 2 η ) * loss into deeply bound molecules only Efimov resonances a < 0 also loss into deeply bound molecules a > 0 C(a) C(a) a Λ * a Λ *

23 Molecular energy structure for Cs 2 : the weakly bound dimer binding energy (MHz) 6l magnetic field (G) P. Julienne, E. Tiesinga

24 Cs molecular structure simplified Cs molecular structure simplified -12 G E 0 20 G B 20 khz 70 MHz two-channel problem

25 Cs molecular structure simplified Where do the Efimov states show up? E B not to scale T. Köhler, see next talk

26 magnetic tunability of Cs accessible range for the scattering length scattering length (a 0 ) some F=3, chance m F =3 to find an atom-dimer Efimov resonance! G 100 G 150 G magnetic field (G) good chance to find a tri-atom Efimov resonance! E. Tiesinga et al.

27 scattering length a (a 0 ) F=3, m F = Cs BEC 50 G 100 G magnetic field (G) BEC-implosion at slightly negative a gives a thermal ensemble at 10 nk 150 G

28 Three-body loss measurement anti-evaporation and recombination heating particle number temperature Fit γ ~ L 3 trap hold time trap hold time

29 exp. results! experimental results Recombination length (1000 a 0 ) 25 L 3 =6*10-22 cm 6 /s T = 10nK 200nK Braaten-Hammer theory Λ*=1/230 a 0, η*=0.08 L 3 =1*10-28 cm 6 /s Scattering length (1000 a 0 ) Nature 440, 315 (2006)

30 loss minimum three-body loss minimum three-body loss after 200ms storage in recompressed trap minimum at 210a 0! half Efimov period (22.7 1/2 ) observed: min.-max. loss! optimization of evaporative cooling towards BEC -> a 0

31 continuum resonance Continuum resonance E 200 nk nk 50 nk 1/a a<0 Efimov-resonance Efimov-trimer

32 Resonance resonance shift

33 Efimov states: connection to atom-dimer scattering a < 0 energy a > 0 1/ a

34 State preparation for Cs 2 BEC binding energy (MHz) 6l magnetic field (G) P. Julienne, E. Tiesinga

35 State preparation for Cs 2 binding energy (MHz) 10% efficiency for molecule production, nearly 100% efficiency for molecule transfer

36 Atom-dimer mixture s 8000 Energy (MHz) No blast beam 2 x 10 5 atoms 3-5 x 10 3 dimers N d (x2) Magnetic field (G) time (ms) n = Rn D A n D n A(D) : atom(dimer) density R: atom-dimer collisional loss rate Dependence on scattering length? Na-Na 2 : Mukaiyama et. al., PRL 2004, 87 Rb- 87 Rb 2 : Syassen et. al., PRA 2006

37 Atom-dimer inelastic collision rate atom-dimer collision rate (10 ( cm cm 3 /s) 3 /s) a scattering Magnetic length field (10 (G) 3 a 0 ) scattering length (a 0 ) G 100 G Magnetic field (G) Braaten & Hammer, cond-mat/ energy a < 0 a > G 1/a Resonant enhancement!!! Coupling to a trimer state? Efimov physics? Universal regime? a>>r 0 Cs: r 0 ~100 a 0 Temperature dependence?

38 Optical lattices 87 Rb Munich Mainz Nature (2002) 23 Na (MIT) 40 Ka (ETH) Mixture 87 Rb / 40 Ka (Hamburg, ETH, Mainz) Molecules 87 Rb (Munich, Innsbruck) Phys. Rev. Lett. 96, (2006) Nature 441, 854 (2006) Phys. Rev. Lett. 96, (2006) cond-mat/

39 Tunability scattering length (a 0 ) Feshbach resonances: Cs F=3, m F =3 repulsive null attractive 50 G 100 G magnetic field (G) 150 G

40 Tunability scattering length (a 0 ) Feshbach resonances: Cs F=3, m F =3 50 G 100 G magnetic field (G) 87 Rb 150 G

41 Tunability and abundance of molecular states scattering length (a 0 ) Feshbach resonances: Cs F=3, m F =3 50 G 100 G magnetic field (G) 87 Rb 150 G Feshbach 0 molecules: Energy (MHz) -4-8 M. Mark et al., in preparation 10 G 20 G magnetic field (G) 50 G

42 Experimental setup 25 beams oven section Zeeman slower glass cell & coils glass cell gradient+offset coils offset field gradient field dipole trap atoms

43 Experimental setup oven section Zeeman slower glass cell & coils BEC: levitated expansion levitated at 100 aa 0 0 BEC 10 a 0

44 Optical lattice fiber amplifier 1064nm 1 khz linewidth (design H.Zellmer IAP Jena) beams -110 MH z waist 500μm +105 MHz +110 MHz -110 MH z external confining potential not modified due to lattice

45 Mott-insulator transition: ramping the lattice depth Lattice depth 16 E r time a = 100a 0 a = 210a 0 a = 400a 0 0E r 8E r 16E r 8E r 0E r

46 Mott-insulator transition: ramping the lattice depth 40 a 0 visibility (a.u.) 140 a a a 0 lattice depth (E r )

47 Excitation spectrum lattice depth modulation lattice depth 13 E r

48 Mott-insulator transition: ramping the interactions 70 a a a 0 70 a 0 no lattice70 a 0 larger scattering lengths: requires jump across a narrow Feshbach resonance 190 a a a a 0 for larger scattering lengths: we do not recover interference. Heating?

49

50 outlook I Outlook 1 taking full advantage of Cs tunability the ideal Feshbach resonance for Efimov physics?! our expts so far can we see the full Efimov period (x22.7)?

51 outlook III Outlook 2 Few-body physics & Efimov states in an optical lattice λ/2 making Efimov trimers in an optical lattice 85 Rb association and detection of Efimov trimers Stoll & Köhler, PRA 71, (2005)

52 ultracold.atoms funded by and Innsbruck bm:bwk 3 Cs teams Cs BEC & ultracold molecules: Rb-Cs mixtures: Cs in optical lattices: the Cs coolers T. Kraemer, M. Mark, J. Danzl, H. Schöbel, S. Knoop, F. Ferlaino, HCN, R. Grimm B. Engeser, K. Pilch, A. Lange, A. Prantner, HCN, R. Grimm M. Gustavsson, E. Haller, G. Rojas-Kopeinig, M. Mark, HCN