Superfluidity in interacting Fermi gases

Transcription

1 Superfluidity in interacting Fermi gases Quantum many-body system in attractive interaction Molecular condensate BEC Cooper pairs BCS Thomas Bourdel, J. Cubizolles, L. Khaykovich, J. Zhang, S. Kokkelmans, M. Teichmann, L. Tarruell, J. McKeever, F. Chevy, C. Salomon Laboratoire Kastler Brossel, Ecole Normale Supérieure Collège de France

2 Superfluidity in interacting Fermi gases Molecular condensate BEC Superfluid 4 He Fermions close to a Feshbach resonance HTc Supra. Std supra. Cooper pairs BCS Pair binding energy [E F ] Alkali atom condensates

3 Outlook Molecule Formation Interaction control: Feshbach resonance Reversible process Bose-Einstein Condensation of molecules Measurement of a mol-mol BEC-BCS Crossover Decription Expansion of the gas

4 E Feshbach resonance: 1/2,-1/2>+ 1/2,1/2> Open channel: triplet potential Closed channel: singlet potential Different magnetic moments Bound state: Eb=! ~a h2 ma 2 scattering length [nm] ares~1/(b-b0) 0,0 0,5 1,0 1,5 2,0 magnetic field [kg] No bound state

5 Experimental approch Glass cell 2 isotopes MOT Ioffe- Pritchard Magnetic trap Sympathetic cooling of 6 Li by evaporation of 7 Li T=1 mk T=10 µk Optical trap power: 3W waists ~25 µm RF tranfers: mixture at 1060 G: T < 1 µk T F = 5 µk T/T F < 0.2 N total =

6 Formation and detection of molecules E B 0 2 E B= ma 2 B

7 Formation and detection of molecules E E B= ma 2 2 B 0 Formation of molecules is energetically favorable 50 ms B

8 Formation and detection of molecules E 2 E B= ma 2 Molecular fraction at 700 G: E B ~10 µk B 0 T=4.7 µk TF=11 µk B -Conversion efficiency close to 100% (10%) -Lifetime: ~ 1 s (1ms) - slow sweep though resonance (fast) Reversing the ramp: back to initial conditions ~10 a>0-9 ev a<0 Process is reversible Quasi-static thermodynamic equilibrium between atoms and molecules during the ramp Magnetic field [kg]

9 A simple thermodynamic model No heat transfert, reversible Entropy conservation E b E E b B 0 T~0.4 TF B E b T<0.2 TF

10 Bose-Einstein condensate of 6 Li 2 molecules 6 Li mmanm+!= 7 Li 70.65(10)anm= B=770 G N= molecules B=610 G N= atoms From pure condensates: mmanm+!= Scattering length measurement at 770 G: In agreement with a mm =0.6 a (Petrov, Salomon, Shlyapnikov, PRL, 2004)

11 a BEC-BCS Crossover Molecular condensate Size a << n -1/3 n -1/3 : mean interparticule distance a>0 Close to resonance na 3 > 1 or k F a > 1 Paires are overlapping They are stabilized by the Fermi sea BCS Regime: k F a <<1 Cooper pairs: k, -k Large compared to interparticule distance a<0

12 BEC-BCS Crossover a BEC BCS E B = 2 ma 2 Tc!0. 22TF T C / T F ? & Tc) 0.3TF( exp $ ' * % 2kFa #! " /k F a 1

13 BEC-BCS Crossover: images after expansion mol., N 0 /N 60% Slow change of B: 1-2 G/ms Images after time of flight Aspect ratio: λ =0.3 a < 0 a < 0 a > 0 Optical density Feshbach resonance peak 834 G a > 0 Axial: X Radial:Y

14 BEC-BCS Crossover: images after expansion mol., N 0 /N 60% Slow change of B: 1-2 G/ms Images after time of flight Aspect ratio: λ =0.3 a < 0 a < 0 a > 0 Optical density Feshbach resonance peak 834 G a > 0 Axial: X Radial:Y

15 BEC-BCS Crossover: release energy From Gaussian fits: 222(2)/2RyxEm!!"=+ NIFG -1/k F a

16 BEC-BCS Crossover: release energy From Gaussian fits: 222(2)/2RyxEm!!"=+ NIFG -1/k F a at resonance: unitarity limit We find: µ = ( 1+!)EF 0.64(15)!=" In agreement with quantum Monte-Carlo calculations (Carlson 02, Giorgini 04): -0.56(1) and with R.Gimm s experiment in Innsbruck.

17 BEC-BCS Crossover: Anisotropy Superfluid or highly collisionnal hydrodynamic expansion η =1.7 At 730 G, on the BEC side, n m a m3 <<1 Measured anisotropy: η=σ Y / σ X =1.6 (1) NIFG Going toward a<0, the gas losses its hydrodynamic behavior Decrease of the superfluid fraction Another explaination: rapide loss of the superfluid character in the expansion

18 Perspectives: BEC-BCS Crossover Numerous experimental studies Expansion measurement (ENS) Collective modes (Duke, Innsbruck) Pair binding energy (Innsbruck, JILA) Condensation of fermionic pairs (JILA, MIT) Theory (Holland, Kokkelmans, Levin, Ohashi, Griffin, Strinati, Stoof, Bruun, Pethick, Combescot, Stringari, Shlyapnikov, Giorgini, ) Direct proof of superfluidity (vortex) Long range order, interference experiment

19 Perspectives p-wave pairing ( 3 He) Heteronuclear molecules Fermionic molecules Polar molecules (long range interaction) Simulation of hamiltonians from condensed matter (Fermions in an optical lattice)

20 Thanks Fred Merci Florian Julien Jing Christophe Josh Servaas Lev Leticia Martin Jason Christophe Fred à tous

21 Feshbach resonance Canal fermé Canal ouvert divergence de a

22 Feshbach resonance Canal ouvert Canal fermé a>0

23 Feshbach resonance Canal fermé Canal ouvert a<0 scattering length [nm] ,0 0,5 1,0 1,5 2,0 Magnetic field [kg]

24 Molecular states 543 Gauss FR Broad 830 Gauss FR used in resonance superfluidity

25 Dispositif expérimental Tube de pompage différentiel Faisceaux MOT Faisceau ralentisseur pompe pompe T=1 mk four à 800 K Ralentisseur Zeeman V cap = 1000 m/s Cellule en verre MOT T=1 mk

26 Transition BEC-BCS: Autres Résultats Condensation des paires de Fermions: (JILA, MIT) Mesure de l énergie des paires (Innsbruck, JILA) T / T F = Étude des modes d oscillation: (Duke, Innsbruck)

27 Quantum gases cooling d d 300 K 1000 m/s 1 µk 5 cm/s atom wave-function of size λ db = h/(2πmk B T) 1/2 Quantum regime in a dilute gas: n~10 13 cm -3 «Very clean» quantum many-body System Difference between bosons et fermions

28 Quantum statistics E Bose-Einstein Bose-Einstein Condensate T C = h! k B (0.83 N) 1/3 E Fermi-Dirac 7 Li E F =k B T F T << T = F h! k B (6N) 1/3 6 Li Fermi sea

29 Molecules velocity distribution Optical trap off: expansion of the molecular gas At the end of the time of flight: dissociation of pairs E E b B 0 B B Optical trap off 0.8 ms 0.2 ms 0.2 ms Detection

30 Pure Condensates: measurement of a mm By lowering the trap power, we optain a pure condensate Thomas-Fermi fit, no thermal cloud Hydrodynamic expansion Ellipticity: -mesured: 2.0 (1) -theory: 1.98 TOF=1.2 ms T<T C /3 λ=0.1 N=4x10 4 atoms Scattering length measurement mmanm+!= à 770 G: In agreement with a mm =0.6 a (Petrov, Salomon, Shlyapnikov, PRL, 2004)

31 Interaction control: Feshbach Resonance E Closed channel: singlet potential Open channel: triplet potential Different magnetic moments E Singlet bound state energy B 1 =550 G B 2 free atoms in states : 1/2,1/2>+ 1/2,-1/2>

32 Feshbach resonance E Closed channel: singlet potential Open channel: triplet potential Different magnetic moments B B0 Singlet bound state energy B 1 =550 G =834 G 2 free atoms in states : 1/2,1/2>+ 1/2,-1/2> E

33 2 body bound state B B0 Singlet bound state energy Purely singlet Size of the singlet potential : ~1.5 nm Progressive hybridation from the triplet continuum 2 free atoms in states : 1/2,1/2>+ 1/2,-1/2> E Allmost purely triplet The size of the bound states gets larger and larger

34 Fermonic Superfluid BCS HTc Super. superfluid 3 He Transition temperature [T F ] Superconductors Two types of superfluidity BEC Alkali atom condensates Superfluid 4 He Pair binding energy [k B T F ] Fermions au voisinage d une résonance de Feshbach

35 Formation and detection of molecules E 2 B 0 Formation of molecules is energetically favorable E B= ma 2 50 ms B E B 0 2 E B= ma 2 20 µs B Only free atoms are detected Presence of molecules is detected by a diminution of atomic signal

36 Formation and detection of molecules E B 0 E B= ma 2 50 ms 2 E 2 E B= ma 2 B 0 B B Only free atoms are detected Presence of molecules is detected by a diminution of atomic signal This is not due to losses

37 Molecular condensate lifetime Relaxation toward deeply bound states R e 2 identical fermions R e Fermions: β ~ a Experimentally β ~ a -1.9±0.8

38 Temperature of atom-molecule molecule mixture T at-mol Resonance Atoms Molecules : heating 3 body recombinaison: E B E C T aller-retour Molecular fraction Magnetic field [kg]

39 Temperature of atom-molecule molecule mixture T at-mol Resonance Atoms Molecules : heating 3 body recombinaison: E B E C T return Molecular fraction Molecules atoms : Cooling Process is reversible Entropie conservation Magnetic field [kg]

40 Temperature of atom-molecule molecule mixture T at-mol Atoms Molecules : heating 3 body recombinaison: E B E C T return Molecular fraction Magnetic field [kg] Molecules atoms : Cooling Process is reversible Entropy conservation Quasi-static thermodynamic equilibrium between atoms and molecules during the ramp