BEC and superfluidity in ultracold Fermi gases

Transcription

1 Collège de France, 11 Apr 2005 BEC and superfluidity in ultracold Fermi gases Rudolf Grimm Center of Quantum Optics Innsbruck University Austrian Academy of Sciences

2 two classes Bosons integer spin Fermions half-integer spin trapped atoms at T=0 all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

3 two classes Bosons integer spin Fermions half-integer spin trapped atoms at T=0 all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

4 ultracold Fermi gases 1999: first degenerate Fermi gas ( 40 K) Debbie Jin group at JILA, Boulder degenerate Fermi gases now playing in nine labs: 40 K: JILA (1999) Florence (2002) Zurich (2004) Hamburg (2004) 6 Li: Rice (2001) ENS (2001) Duke (2001) MIT (2002) Innsbruck (2003) 2003 making molecules (bosons!) BEC of molecules at Innsbruck, JILA, MIT, ENS Paris, Rice 2004 BEC-BCS crossover, creation of fermionic superfluids

5 6 Li spin mixture Feshbach resonance prediction: M. Houbiers et al., PRA 57, R1497 (1998). a (1000 a 0 ) spin mixture -2 of two lowest states stable against -4 two-body decay weakly bound dimers: it s a kind of magic! magnetic Field [G]

6 three-body recombination molecules made by collisions three atoms three- body large positive scattering length U(r) and last bound level many states E b = h 2 /(ma 2 ) process atom Ekin = 2E b /3 r E kin = E b /3 molecule (binding energy E b )

7 weakly bound dimers are huge! they are incredibly stable!! (when (whenmade madeof of fermionic fermionicatoms) theory: theory: Petrov, Petrov, Salomon, Salomon, Shlyapnikov, Shlyapnikov, PRL PRL 93, 93, (2004) (2004) expt.: expt.: Cubizolles Cubizolleset et al., al., PRL PRL 91, 91, (2003) (2003) Jochim Jochim et et al., al., PRL PRL 91, 91, (2003) (2003) normal dimer size ~1nm weakly bound dimer size ~100nm

8 optical trap for evaporative cooling U magn special feature #1 precise control of laser power 10 W few 100µW special feature #2: axial magnetic confinement - spatial compression at very weak optical traps - perfectly harmonic!! - precisely known trap frequency for weak optical trap ν z = kG

9 apparatus Science (Aug 04): The Chamber of Secrets

10 6 Li team Johannes Hecker Denschlag U Chicago USA Jan. 05 Cheng U Chicago Chin Alexander Altmeyer Selim Jochim IBM res. labs Switzerland Sept. 04 Reece Geursen Stefan Riedl Markus Bartenstein 05 May U Melbourne Australia

11 axial profiles phase transition partially condensed almost pure excellent starting point for further experiments final trap power 28mW 3.8mW number of molecules temperature 430nK few 10nK condensate fraction ~20% >90%

12 6 Li 2 ENS Paris, Salomon et al. molecular BEC gallery 40 K 2 JILA, Jin et al. MIT, Ketterle et al. 6 Li 2 Rice Univ., Hulet et al. 6 Li 2

13 the BEC-BCS BCS crossover

14 two classes Bosons integer spin Fermions half-integer spin trapped atoms at T=0 these two worlds are connected! all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

15 two classes Bosons integer spin Fermions half-integer spin trapped atoms at T=0 pairing is the key all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

16 two classes Bosons integer spin Feshbach resonance Fermions half-integer spin trapped atoms at T=0 interaction control!!! all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

17 two classes Bosons integer spin Fermions half-integer spin superfluidity? all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

18 two classes Bosons integer spin neutron star Fermions half-integer spin exotic states of matter all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

19 exploring the crossover molecular BEC na 3 = 0.04

20 exploring the crossover na 3 = 0.28 molecular BEC na 3 = 0.04

21 exploring the crossover Bosons Fermions na 3,k F a = na 3 = 0.28 molecular BEC na 3 = 0.04

22 exploring the crossover Bosons Fermions na 3,k F a = na 3 = 0.28 k F a = 6 molecular BEC na 3 = 0.04

23 exploring the crossover Bosons Fermions na 3,k F a = na 3 = 0.28 fully reversible no loss, no heating!!! (isentropic) k F a = 6 molecular BEC na 3 = 0.04 k F a = 1 degenerate Fermi gas

24 cloud size interaction energy comparison with theory BEC mean-field with a mol = 0.6a M. Bartenstein et al. PRL 92, (2004); updated in Procs. ICAP-2004 (Petrov et al. prediction) quantum Monte Carlo (Carlson et al. Astrakharchik et al.) ζ 0 =0.810(3) normalized to non-interacting Fermi gas ( β = ζ 04 1 )

25 collective modes in the BEC-BCS crossover M. Bartenstein et al., PRL 92, (2004)

26 collective modes S. Stringari, Europhys. Lett. 65, 749 (2004): interesting behavior of collective modes in the crossover!!! axial our cigar-shaped trap ν r = 755(10) Hz, ν z 22 Hz radial

27 axial mode M. Bartenstein et al., PRL 92, (2004), updated data analysis: PhD thesis M. Bartenstein frequency (normalized to sloshing mode) damping rate hydrodynamic behavior

28 axial mode: resonance region M. Bartenstein et al., PRL 92, (2004), updated data analysis: PhD thesis M. Bartenstein frequency (normalized to sloshing mode) Ω unitarity point: z / ω = z 12 / 5 confirms equation of state µ n 2 / 3 damping rate extremely weak damping in resonance region!! superfluidity?

29 radial coll. excitation M. Bartenstein et al. PRL 92, (2004) frequency (normalized to sloshing mode) Ω r /ω r 2,2 2,0 1,8 BEC limit collisionless limit 1,6? damping Γ r /ω r 1,4 0,8 0,6 0,4 hydrodynamic collisionless 0,2 0, magnetic field (G)

30 comparison with theory Hu et al., PRL 93, (2003) based on Leggett s mean-field model Manini et al., cond-mat/ based on Giorgini s qu.mc calculation γ µ ~ n hydrodynamic

31 comparison with theory cond-mat/ ? how good is our experiment? axial trap very well known! radial trap freq. meas d only in one direction: ellipticity of laser beam???

32 in progress: upgrade of apparatus new new imaging beam acousto-optical scanning system dichroic mirror glass cell CCD camera dichroic mirror new mol. BEC / Fermi gas trapping beam new possibilities precise studies of radial modes (compression and surface mode) rotating ellipse stirring up vortices

33 measurement interpretation something(b) something(1/k F a)

34 measurement interpretation something(b) something(1/k F a) precise knowledge of a(b) through rf spectroscopy on ultracold molecules Bartenstein et al., PRL 94, (2005) (collaboration Innsbruck NIST)

35 radio-frequency spectroscopy meas. of mol. bind. energy in 40 K Regal et al., Nature 424, 47 (2003) rf spectroscopy of 6 Li: Gupta et al., Science 300, 1723 (2003) ~80MHz rf m I = loss signal ~200Hz rf frequency high B-field

36 radio-frequency spectroscopy meas. of mol. bind. energy in 40 K Regal et al., Nature 424, 47 (2003) rf spectroscopy of 6 Li: Gupta et al., Science 300, 1723 (2003) rf ~80MHz m I = breaking molecules costs energy molecular signal up-shifted high B-field

37 radio-frequency spectroscopy meas. of mol. bind. energy in 40 K Regal et al., Nature 424, 47 (2003) rf spectroscopy of 6 Li: Gupta et al., Science 300, 1723 (2003) ~80MHz atoms molecules rf m I = fractional loss atoms 720 G rf offset (khz) high B-field E b /h binding energy

38 bound-free dissociation spectra (4) G (4) G binding energy 134(2) khz 277(2) khz lineshape of dissociation signal: C. Chin and P. Julienne PRA 71, (2005)

39 rf spectroscopy on 6Li2

40 bound-bound transition second data point (2) (2) G (5) (3) G exp. data NIST theory group: multi-channel quantum scattering model a s = (8) a 0 a t = (18) a 0

41 s-wave scattering lengths simple fit formulae available!

42 rf spectroscopy in the strongly interacting Fermi gas observation of the pairing gap C. Chin et al., Science 305, 1128 (2004)

43 radio-frequency spectroscopy meas. of mol. bind. energy in 40 K Regal et al., Nature 424, 47 (2003) rf spectroscopy of 6 Li: Gupta et al., Science 300, 1723 (2003) rf ~80MHz m I = -1 0 breaking molecules costs energy molecular signal up-shifted 1 two-body physics high B-field

44 radio-frequency spectroscopy meas. of mol. bind. energy in 40 K Regal et al., Nature 424, 47 (2003) rf spectroscopy of 6 Li: Gupta et al., Science 300, 1723 (2003) rf ~80MHz m I = -1 0 breaking pairs costs energy pair signal up-shifted 1 many-body physics high B-field

45 rf spectra in molecular limit evaporation at 764G, then ramp field to 720G no evaporation atoms only moderate evaporation loss signal atom-molecule molecule mixture deep evaporation pure molecular sample (BEC) rf offset

46 rf spectra in crossover regime evaporation at 764G, then ramp field on resonance a ± loss signal T 0.2 T F double-peak structure: atoms and pairs the pairing gap rf offset T = 0.0? T F pairs only! shift decreases with Fermi energy

47 rf spectra in crossover regime evaporation at 764G, then ramp field to BCS side BCS side loss signal T/T F 0.2 gap!! T/T F 0.0? rf offset

48 gap vs. coupling strength BEC unitary BCS T F = 3.6µK 1.2µK molecular limit (two-body physics)

49 gap vs. coupling strength collective oscillation couples to pairs molecular limit (two-body physics) explanation for abrupt change!! radial osc. frequency T F = 3.6µK 1.2µK

50 temperature dependence 0,4 T 0.8 (a) T F 837 G (unitarity) controlled heating: same T F, N fractional loss in 2> 0,0 0,4 0,0 0,4 0,0 0, (b) T F 0.45 (c) T F < 0.2 (d) T F thermodynamics of interacting temperature fermions T measured Chen et al. in cond-mat/ BEC regime (1/k T F a T 3) true temperature 0, RF frequency offset (khz)

51 temperature dependence 0,4 T 0.3 (a) T F 837 G (unitarity) controlled heating: same T F, N fractional loss in 2> 0,0 0,4 0,0 0,4 0,0 0, (b) T F 0.22 (c) T F < 0.1 (d) T F thermodynamics of interacting temperature fermions T measured Chen et al. in cond-mat/ BEC regime T T true temperature 0, RF frequency offset (khz)

52 comparison with theory 0,4 Kinnunen, Rodriguez, Törmä, Science 305, 1131 (2004) T 0.3 (a) T F T/T F = 0.27 K. Levin, priv. comm. fractional loss in 2> 0,0 0,4 0,0 0,4 0, (b) T F 0.22 (c) T F ,4 < 0.1 (d) T F , RF frequency offset (khz)

53 phase diagram 1 T/T F 0.8 molecules T * Perali, Pieri, Pisani, Strinati PRL 92, (2004) harmonic trap (inhomog. system) Li T C Li BEC paired superfluid 6 Li Cooper pairs BCS /k F a

54 conclusion creation of a molecular BEC with 6 Li 2 excellent starting point for further experiments funding TMR network cold molecules

55 conclusion creation of a molecular BEC with 6 Li 2 excellent starting point for further experiments studies on the BEC-BCS crossover cloud size collective modes pairing gap strong case for superfluidity funding TMR network cold molecules

56 ultracold.atoms 2D BEC in a surface trap B. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl Innsbruck BEC of cesium, ultracold molecules T. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl fermionic Li-6 & molecular BEC A. Altmeyer, S. Riedl, M. Bartenstein, R. Geursen S. Jochim, C. Chin, J. Hecker Denschlag Cheng Chin Lise-Meitner fellow Li-K/Sr mixtures E. Wille,G. Kerner, NN Florian Schreck Johannes Hecker Denschlag quantum matter in optical lattices M. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid Hanns-Christoph Nägerl START 2nd generation cesium BEC M. Gustavsson, P. Unterwaditzer, A. Flir

57 ultracold.atoms 2D BEC in a surface trap B. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl Innsbruck BEC of cesium, ultracold molecules T. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl fermionic Li-6 & molecular BEC A. Altmeyer, S. Riedl, M. Bartenstein, R. Geursen S. Jochim, C. Chin, J. Hecker Denschlag fermions Cheng Chin Lise-Meitner fellow Li-K/Sr mixtures E. Wille,G. Kerner, NN Florian Schreck Johannes Hecker Denschlag quantum matter in optical lattices M. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid Hanns-Christoph Nägerl START 2nd generation cesium BEC M. Gustavsson, P. Unterwaditzer, A. Flir