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Massachusetts Institute of Technology Center for Ultracold Atoms at MIT and Harvard

RPMBT-15, Columbus, Ohio, July 31 st , 2009. Fermi Polarons - Building a Fermi Liquid from the Bottom Up -. Martin Zwierlein. Massachusetts Institute of Technology Center for Ultracold Atoms at MIT and Harvard $$$: NSF, AFOSR- MURI, Sloan Foundation. Swimming in the Fermi sea.

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Massachusetts Institute of Technology Center for Ultracold Atoms at MIT and Harvard

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  1. RPMBT-15, Columbus, Ohio, July 31st, 2009 Fermi Polarons- Building a Fermi Liquid from the Bottom Up - Martin Zwierlein Massachusetts Institute of Technology Center for Ultracold Atoms at MIT and Harvard $$$: NSF, AFOSR- MURI, Sloan Foundation

  2. Swimming in the Fermi sea What is the fate of a singleimpurity in a Fermi sea? • Crucial question for • electron transport in lattices • Kondo problem(single magnetic impurity) • mobility of 3He in 4He… • determines the properties ofmany condensed matter systems at low temperature

  3. Polarons: The “N+1”-body problem Polarons • Historically:e- interacting with lattice distortions (phonons) L. D. Landau, Phys. Z. Sowjetunion 3 664 (1933). • Quasi-particle:Electron and its polarization cloud • “Dressed” energy • Weight Z – probability of free propagation • Effective mass m* • Found “everywhere”, important for colossal magnetoresistance, affects spectral function of High-TC materials, applied to fullerenes, polymers, etc… Theory: Landau, Froehlich, Feynman, Anderson

  4. Impurities interacting with a Fermi sea • Example: Kondo effectA spin impurity interacting with Fermi sea of electronsleads to increase in resistance at low temperatures • Our cold atom system: • Mobile impurity interacting with Fermi sea of atoms • Highly imbalanced mixture of two hyperfine states • Highly controllable • Tunable, resonant interactions • All relevant parameters known: Allows quantitative test of many-body theories • Polaron properties determine phase diagram of imbalanced Fermi mixtures

  5. Tunable Interactions Vary interaction strength between spin up and spin down Example: tunable square well (with ): strong attractiondeep bound state Resonancebound state appears weak attractionno bound state scattering length

  6. At high fields, states |1> and |2> havelarge and negative scattering length a12 = −2100 a0 Preparation of an interacting Fermi system in Lithium-6 Electronic spin: S = ½, Nuclear Spin: I = 1  (2I+1)(2S+1) = 6 hyperfine states Optical trapping @ 1064 nm naxial = 10-20 Hznradial= 50–200 Hz Etrap = 0.5 - 5 mK

  7. Feshbach Resonances Scattering Length a0 ] [ [MHz] Energy bound state Atoms form stable molecules Isolated atom pairs are unstable [G] Magnetic Field

  8. The BEC-BCS Crossover

  9. Vortices in the BEC-BCS Crossover Vortex lattices in the BEC-BCS crossover Establishes superfluidityandphase coherence in gases of fermionic atom pairs M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 435, 1047-1051 (2005)

  10. Fermionic Superfluidity withImbalanced Spin Populations What if there are more boys then girls…?

  11. Fermionic Superfluidity with Imbalanced Spin Populations |1> |2> 0% 6% 12% 22% 30% 56% 90% 94% M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)

  12. Phase Diagram for Unequal Mixtures Normal P Superfluid BEC BCS Breakdown: Critical polarization Pc Gap D M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)

  13. Swimming in the Fermi Sea Molecule Polaron Mean Field ? strong attraction weak attraction Energy Theory: Chevy, Forbes, Bulgac, Lobo, Giorgini, Stringari, Prokof’ev, Svistunov,Sachdev, Sheehy, Radzihovsky, Lamacraft, Combescot, Sa de Melo

  14.      Swimming in the Fermi sea A single atom immersed in a cloudwith unitarity limited interactions Binding energy must be universal E = -AEF A = 0.6 F. Chevy PRA 74, 063628 (2006), Variational Cooper pair AnsatzC. Lobo, A. Recati, S. Giorgini, S. Stringari, PRL97, 200403 (2006), Monte-Carlo

  15. Swimming in the Fermi sea Polaron: F. Chevy PRA 74, 063628 (2006), Variational Cooper pair AnsatzC. Lobo, A. Recati, S. Giorgini, S. Stringari, PRL97, 200403 (2006), Monte-Carlo

  16. Swimming in the Fermi sea Polaron: F. Chevy PRA 74, 063628 (2006), Variational Cooper pair AnsatzC. Lobo, A. Recati, S. Giorgini, S. Stringari, PRL97, 200403 (2006), Monte-Carlo

  17. Polaron Energy 1/kF a Meanfield bareMolecule Polaron E/EF Mean-field limit Molecular limit Variational approach/T-Matrix: F. Chevy PRA 74, 063628 (2006), R. Combescot and S. Giraud, PRL 101, 050404 (2008), R. Combescot et al.,PRL 98, 180402 (2007) Diagrammatic Monte-Carlo: N. V. Prokof'ev and B. V. Svistunov, PRB 77, 125101 (2008) T-matrix/ladder approximation: P. Massignan, G. Bruun and H. Stoof, PRA 78, 031602 (2008)

  18. Polaron Quasi-particle weight = Probability of free propagation Weakly interacting limit: Scattering cross section ~ interparticle distance 1/kF -1/kF a

  19. Can we measure thebinding energy?

  20. Radiofrequency spectroscopy       S. Gupta, Z. Hadzibabic, M.W. Zwierlein, C.A. Stan, K. Dieckmann, C.H. Schunck, E.G.M. van Kempen, B.J. Verhaar, and W. Ketterle, Science 300, 1723 (2003)

  21. Molecular Pairing  3              Radiofrequency spectroscopy No interactions  3  Photon energy = Zeeman + Binding + Kinetic energy

  22. Molecular Pairing  3        Radiofrequency spectroscopy Loss in |2> C.Chin et al. Science, 305, 1128 (2004) Photon energy = Zeeman + Binding + Kinetic energy

  23. Experimental Realization RF spectroscopy 6Li - Atom: 6 hyperfine states |h> |i> |free> • Spatially resolved • 3D reconstructed Feshbach Resonance at 690G

  24. RF Spectroscopy with in situ Images In situ phase contrast images provide a local probe Signal (a.u.) Radio-frequency offset (kHz) Y. Shin et al, PRL 99, 090403 (2007)

  25. 3d Density Reconstruction Tomographic RF spectroscopy: 3D reconstruction Cylindrical symmetry, Inverse Abel transformation:

  26. Emergence of the Fermi Polaron towards Unitarity Molecular limit A. Schirotzek, C. Wu, A. Sommer, MWZ, PRL, to be published, arXiv/0902.3021

  27. RF Spectroscopy on Polarons Polaron = Free particle + scattered states + Energy Final states afterRF Pulse: OR: Energy Energy RF Spectrum from Fermi’s Golden Rule: i.e.:

  28. RF Spectroscopy on Polarons Polaron = Free particle + scattered states RF Spectrum: Polaron weight: Z Narrow peak long lifetime Scattered states(particle-hole excitations) High energy High momentum Short range physics Spectrum @ 690 G

  29. Quasiparticle residue vs interaction strength S. Pilati, S. Giorgini, PRL 100, 030401 Polaron weight 40% on resonance Molecular limit Mean Field limit |1> majority |3> majority Interaction Strength 1/kFa • Polarons transition to molecules for a critical interaction strength: 0.76 • Transition between Spin ½-Polarons and Spin 0-Polarons • Breakdown of a Fermi liquid • Coincides with critical strength for always having a BEC

  30. Polaron Energy vs Interaction Strength BareMolecule No final state interactionsIncluding final state interactions Mean Field Peak position |1> majority |3> majority Interaction Strength 1/kFa Molecular limit Mean Field limit Diagrammatic Monte-Carlo: N. Prokof'ev and B.V. Svistunov, PRL 99, 250201 (2007)N. V. Prokof'ev and B. V. Svistunov, PRB 77, 125101 (2008)Variational approach/T-Matrix: F. Chevy PRA 74, 063628 (2006), R. Combescot et al.,PRL 98, 180402 (2007), R. Combescot and S. Giraud, PRL 101, 050404 (2008)

  31. Building a Fermi liquid from the bottom up • Polarons are weakly interacting despite resonant interactions: •  Represent the quasi-particles in Landau’s Fermi liquid descriptionBuild a Fermi liquid from the bottom up by adding polarons Peak positoin (EF) Normal P C. Lobo et al.,PRL 97, 200403 (2006) Energy of the polaron liquid: Superfluid Energy of the superfluid at x = 1: BEC BCS Critical imbalance for transition: xc = 0.44 Critical trap population imbalance: P = 0.7

  32. Measuring the Polaron Effective Mass Majority Fermi energy in LDA: Minority potential: For harmonic trapping: On resonance: m*/m ~ 1.2 A. Recati, C. Lobo, and S. Stringari, PRA 78, 023633 (2008)

  33. Measuring the Polaron Effective Mass Trick: Excite Quadrupole Oscillation by jumping interactions from molecular side • Majority mostly unaffected, Minority needs to adjust to new environment • Out-of-phase quadrupole oscillations • Requires T/TF<0.1 for sufficient Polaron lifetime see Bruun et al., PRL 100, 240406 (2008) Hint: Far from the single polaron limit

  34. Measuring the Polaron Effective Mass Measurements from the ENS-group, Nascimbene et al., cond-mat 0907.3032 (2009): MIT • Strong dependence on polarization • Need to extrapolate to P = 100% • ENS finds

  35. Back-Action of Minority on Majority Fermi energies in LDA: Minority potential: Majority potential (“poor man’s guess”) for  Possible explanation for the observed frequency

  36. Conclusion & Outlook • Observation of Fermi Polarons in a Fermi liquid with tunable interactions • Benchmark test for many-body theories • The hydrogen atom of diagrammatic Monte-Carlo calculations – B. Svistunov • Next: Measure m*, collisional properties, Bruun et al., PRL 100, 240406 (2008) • Outlines a new strategy to study strongly interacting systems: • Explore the limit of few impuritiesWavefunction, effective parameters, renormalized interactions • First understand the N+1 limit before addressing N+M-body physics • Related problems: impurity with mass (40K in 6Li + optical lattice)immobile impurity: Anderson’s orthogonality catastrophe

  37. The team BEC 1: Andre Schirotzek Ariel Sommer Fermi 1: Cheng-Hsun Wu Ibon SantiagoDr. Peyman Ahmadi Undergraduates: Sara CampbellCaroline Figgatt Jacob Sharpe Kevin Fischer

  38. Ideal Spectra for this Fermi Liquid Initial state: Fermi sea of polarons with effective mass m* Final state: Free Fermi gas with bare mass m Shape of the spectrum: Jump of the spectrum at Size of the jump: W. Schneider, V. B. Shenoy, M. Randeria, preprint cond-mat 0903:3006 also suppl. Info. in: A. Schirotzek, C. Wu, A. Sommer, MWZ, PRL, to be published, arXiv/0902.3021

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