Quantum Quantum Optics Optics VII, VII, Zakopane Zakopane, 11 June 09, 11

Transcription

1 Quantum Optics VII, Zakopane, 11 June 09 Strongly interacting Fermi gases Rudolf Grimm Center for Quantum Optics in Innsbruck University of Innsbruck Austrian Academy of Sciences

2 ultracold fermions: species 6 Li 40 K more candidates: more candidates: non-alkali species

3 fermion + fermion = boson tunable s-wave interaction fermionic pairing, many-body physics

4 6 Li spin mixture Feshbach resonance prediction: Houbiers et al., PRA 57, R1497 (1998) precise characterization: Bartenstein et al., PRL 94, (2005) a ( a 0 ) spin mixture-2of two lowest states stable against -4 two-body decay interaction control knob weakly bound molecules magnetic Field [G]

5 apparatus

6 optical trap for evaporative cooling

7 BEC of molecules partially condensed almost pure final trap power 28mW 3.8mW number of molecules temperature 430nK few 10nK condensate fraction ~20% >90% mbec: excellent starting point for studies on BEC-BCS crossover

8 two classes Bosons Fermions integer spin 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

9 two classes Bosons Fermions integer spin 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

10 two classes Bosons Fermions Feshbach integer spin half-integer spin resonance interaction control!!! all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

11 two classes Bosons Fermions integer spin universal!!! half-integer spin interaction control!!! all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

12 two classes Bosons Fermions integer spin half-integer spin crossover gas as a high-tc superfluid all in ground state: Bose-Einstein condensate only one particle per state: degenerate Fermi gas

13 expt. milestones : is the crossover gas superfluid? Duke, 2002 JILA, MIT 2004 pair condensation Innsbruck, 2004 Duke, Innsbruck, 2004 hydrodynamic expansion pairing gap collective modes Duke 2005 yes! heat capacity MIT, 2005 vortices

14 Cs collective oscillations radial breathing mode Innsbruck experiments Duke Univ. Bartenstein et al., PRL 92, (2004) see also Altmeyer et al., cond-mat/ Kinast et al., PRL 92, (2004) Kinast et al. PRA 70, (R) (2004) Altmeyer et al., PRL 98, (2007) Kinast et al., PRL 94, (2005) and many, many theory papers

15 radial breathing mode frequency (normalized to sloshing mode) damping Ω r /ω / r Γ r /ω r 22 2,2 2,0 18 1,8 1,6 1,4 0,8 0,6 0,4 0,2 BEC limit hydrodynamic plausible explanation: coupling of coll. osc. to pairing gap C. Chin et al., Science 305, 1128 (2004) 2004 collisionless limit Bartenstein et al., PRL 92, (2004) collisionless 0, magnetic field (G)

16 radial breathing mode 2004 exp. data from John Thomas group at Duke Kinast et al, PRA 70, (2004) LHY BEC BCS theory: mean field BCS à la Leggett, Nozières & Schmitt-Rink Hu et al., PRL 93, (2004) quantum Monte Carlo, Astrakharchik et al., PRL 95, (2005) see also Manini and Salasnich, PRA 71, (2005)

17 beyond mean field Phys. Rev. 105, 1119 (1957) Lee-Huang-Yang correction leading correction is positive upshift of collective-mode frequency in mbec regime!

18 precision measurements sloshing modes horizontal beat reveals trap ellipticity of ~6% vertical can be measured with ~10-3 uncertainty compression mode accurate determination of frequency needs very low damping optimized cooling! anharmonicity effects in Gaussian trap potential ~2% suppressed to few 10-3 by normalization to sloshing mode

19 precision measurements Altmeyer et al., PRL 98, (2007) LHY BEC BCS example for test of many-body theories with ultracold atoms!

20 slowly rotating Fermi gas how to detect superfluidity? MIT vortices the only way?

21 slowly rotating Fermi gas how to detect superfluidity? classical gas can carry angular momentum both components hydrodynamic idea: introduce slow rotation under conditions where no vortices are formed superfluid angular momentum only with vortices observe quenching of the moment of inertia!

22 how to measure angular momentum observe precession of quadrupole mode (BEC work: ENS Paris, JILA, MIT) angular momentum per atom L z = 2 Ω m r 2 rms precession frequency atom mass radial rms cloud size ϕ 2ϕ works for any hydrodynamic system (superfluid or normal)

23 what the precession tells us effective MOI (L = θω) Ω trap Ω MOI for rigid rotation introduce dim.less precession parameter,, just for convenience P = 1 for fully rotating non-superfluid cloud superfluid quenching incomplete class. rotation if P<1 we have to separate these two effects!

24 evidence for quenching of the moment of inertia P = 1 T>T c quenched MOI! T<T c

25 superfluid transition temperature P = 1 T c /T F 0.2 general note: we do have a thermometry problem! incomplete classical rotation MOI quenching full classical rotation (no superlfuid)

26 creating a double-well potential

27 interference between two mbecs 700G: mbec regime

28 second-sound modes? out-of-phase oscillation of superfluid and non-superfluid part how to excite? how to detect?

29 join the teams the fermion team 6 Li RG Leonid Sidorenkov Christoph Kohstall Edmundo Sanchez Stefan Riedl (Johannes Denschlag)

30 join the teams the fermion team 6 Li- 40 K RG Frederik (Eric Spiegelhalder Wille) Andreas Florian Trenkwalder Schreck Devang Naik

31 fermion + fermion = boson tunable s-wave interaction fermionic pairing, many-body physics

32 two new twists I. mass imbalance very rich phases Petrov et al., PRL 99, (2007) crystalline phase novel few-body phenomena Iskin & Sá de Melo, PRL 97, (2006) mediated interactions three-body states

33 two new twists II. trap imbalance different resonance lines: species-specific optical potentials selective manipulation of one component!

34 species-specific optical lattice optical potential seen by 40 K, but not by 6 Li 6 Li trapped by interaction with 40 K

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36 interaction properties of Li-K mixtures completely l unknown until 2007 do we have knobs (Feshbach resonances) for - interaction tuning? - molecule formation - crossover physics

37 Feshbach spectroscopy Wille et al., PRL 100, (2008) interspecies i K 2> only

38 interspecies Feshbach resonances B [G] i j channel position [G] width [G] Li 2> + K 1> Li 1> + K 1> Li 1> + K 1> Li 1> + K 1> Li 1> + K 2> Li 1> + K 2> Li 1> + K 2> Li 1> + K 2> Li 1> + K 2> Li 1> + K 3> Li 1> + K 3> Li 1> + K 3> Li 1> + K 3> theory: T. Tiecke, J. Walraven, S. Kokkelmans & E. Tiesinga, P. Julienne system essentially understood, but.

39 they are all narrow! i j B (G) closed-channel dominated Feshbach h resonances! 1000 x wider : entrance-channel dominated (ideal for crossover physics)

40 Fermi-Fermi ( 6 Li 40 K) molecules association via 168G Feshbach resonance 40 K line expansion light heavy molecules free atoms 6 Li line molecules free atoms N~2000 N Li = N K = important milestone for future experiments epe ets!

41 temperature measurement

42 a thermometer!

43 a thermometer!

44 thermalisation of K by Li 1190 G Li K

45 thermalization at unitarity 40 K good probe for strongly interacting Li!

46 fermion + fermion = boson tunable s-wave interaction fermionic pairing, many-body physics

47 ultracold expts. in Innsbruck (four PIs) experiments in full operation single species ( 6 Li) fermions mixtures ( 6 Li & 40 K) few-body physics (Cs 2,Cs 3,Cs 4 ) RG tunable BEC (Cs) &homonucl. mols. (Cs 2 ) two new adventures heteronucl. mols. (RbCs) Hanns-Christoph Nägerl quantum gases of Sr Florian Schreck strongly dipolar systems (Er) Francesca Ferlaino

48 thanks for your attention