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Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas

Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas. John E. Thomas. Students: Joe Kinast, Bason Clancy, Le Luo, James Joseph Post Doc: Andrey Turlapov. Theory: Jelena Stajic, Qijin Chen, Kathy Levin. Supported by: DOE, NSF, ARO, NASA.

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Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas

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  1. Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas John E. Thomas Students: Joe Kinast, Bason Clancy, Le Luo, James Joseph Post Doc: Andrey Turlapov Theory: Jelena Stajic, Qijin Chen, Kathy Levin Supported by:DOE, NSF, ARO, NASA

  2. Strongly- Interacting Fermi Gases as a Paradigm – Quark-gluon plasma of Big Bang Duke, Science 2002 Rice Duke ENS MIT JILA Innsbruck • Fermions are the building blocks of matter • Strongly-interacting Fermi gases are stable • Link to other interacting Fermi systems: • High-TC superconductors – Neutron stars – Effective Field Theory, Lattice Field Theory - Elliptic flow – String theory! - Quantum Viscosity

  3. Degeneracy in Fermi Gases Our atom:Fermionic Harmonic Potential: Zero Temperature Optical Trap Parameters: = = Trap Fermi Temperature Scale: TF = 2.4 mK

  4. Tunable Interactions: Feshbach Resonance Scattering length 840 G @ 528 G *generated using formula published in Bartenstein, et al, PRL94 103201 (2005)

  5. Universal Strong Interactions at T = 0 George Bertsch’s problem: (Unitary gas) L Cloud size: Baker, Heiselberg Ground State: Effective mass: Trap Fermi Temperature:

  6. Outline • All-optical trapping and evaporative cooling • Experiments • Virial Theorem (universal energy measurement) • Thermodynamics: Heat capacity (transition energy) • Oscillations and Damping (superfluid hydrodynamics) • Quantum Viscosity • Sound Waves in Bose and Fermi Superfluids

  7. Preparation of Degenerate 6Li gas Atoms precooled in a magneto-optical trap to 150 mK 2 MW/cm2 U0=0.7 mK

  8. Forced Evaporation in an Optical Trap

  9. High-Field Imaging

  10. Experimental Apparatus

  11. Experimental Apparatus

  12. I Energy input R 0 Temperature Tools for Thermodynamic Measurements

  13. Temperature from Thomas-Fermi fit Maxwell- Boltzmann Integrate (T/TF)fit 0 Zero Temp T-F x Shape Parameter: (T/TF)fit From Thomas – Fit: empirical temperature for strongly-interacting gas Fermi Radius:sF “true” temperature for non-interacting gas

  14. Calibrating the Empirical temperature Calibration using theoretical density profiles: Stajic, Chen, Levin PRL (2005) S/F transition predicted Conjecture:

  15. Precision energy input Trap ON Trap ON again, gas rethermalises time Final Energy E(theat) Initial energy E0 Expansion factor:

  16. Virial Theorem (Strongly-interacting Fermi gas obeys the Virial theorem for an Ideal gas!)

  17. Virial Theorem in a Unitary Gas Pressure: Ho, PRL (2004) Local energy density (interaction and kinetic) Trap potential Force Balance: U Virial Theorem: x Test!

  18. Verification of the Virial Theorem Fermi Gas at 840 G Linear Scaling Confirms Virial Theorem Consistent with hydrodynamic expansion over wide range of T! Fixed expansion time E(theat) calculated assuming hydrodynamic expansion

  19. Heat Capacity Energy versus empirical temperature (Superfluid transition)

  20. Input Energy vs Measured Temperature Ideal Fermi Gas Theory Noninteracting Gas (B=528 G)

  21. Input Energy vs Measured Temperature Ideal Fermi Gas Theory with scaled Fermi temperature Strongly-Interacting Gas at 840 G

  22. Low temperature region Power law fit Strongly-Interacting Gas (B=840 G) Ideal Fermi gas theory with scaled temperature

  23. Energy vs on log-log scale Transition! Blue – strongly-int. gas Green – non-int. gas Fit Ideal Fermi gas theory

  24. Energy vs Theory for Strongly- interacting gas (Chicago, 2005)

  25. Oscillation ofa trapped Fermi gas Study same system (strongly-interacting Fermi gas) by different method

  26. Breathing mode in a trapped Fermi gas Image Trap ON Release Excitation & observation: Trap ON again, oscillation for variable 1 ms time

  27. 528 G Noninteracting Gas 840 G Strongly- Interacting Gas w = frequency t = damping time Breathing Mode Frequency and Damping

  28. Radial Breathing Mode: Frequency vs Magnetic Field Hu et al.

  29. Radial Breathing Mode: Damping Rate vs Magnetic Field Pair Breaking

  30. Frequency w versus temperaturefor strongly-interacting gas (B=840 G) Collisionless gas frequency, 2.10 Hydrodynamic frequency, 1.84

  31. Damping 1/t versus temperaturefor strongly-interacting gas (B=840 G) Transition! Superfluid behavior: Hydrodynamic damping 0 as T 0 Transition in damping: Transition in heat capacity: S/F transition (theory): Levin: Strinati: Bruun:

  32. Quantum Viscosity? Viscosity: Shuryak (2005) Radial mode: Axial mode: Duke Radial: a = 0.2 Innsbruck Axial: a = 0.4

  33. Wires!

  34. Sound Wave Propagationin Bose and Fermi Superfluids

  35. Magnetic tuning between Bose and Fermi Superfluids Singlet Diatomic Potential: Electron Spins Anti-parallel Stable molecules B = 710 G B B = 834 G B = 900G = Triplet Diatomic Potential: Electron Spins Parallel = Cooper Pairs Resonance

  36. Molecular BECs are cold “Hot” BEC, 710 G (after free expansion) “Cold” BEC, 710 G (after free expansion, from the same trap)

  37. Sound:Excitation by a pulse of repulsive potential Slice of green light (pulsed) Observation: hold, release & image thold= 0 Trapped atoms Sound excitation:

  38. Sound propagation on resonance (834 G)

  39. Sound propagation at 834 G Forward Moving Notch Backward Moving Notch

  40. Speed of Sound, u1 in the BEC-BCS Crossover

  41. Sound Velocity in a BEC of Molecules Mean field: Dalfovo et al, Rev Mod Phys 1999 Harmonic Trap: Local Sound Speed c: Full trap average: (Petrov, Salomon, Shlyapnikov) For vF0= Fermi velocity, trap center, noninteracting gas

  42. Speed of Sound, u1 for a BEC of Molecules

  43. Sound Velocity at Resonance Pressure: Local Sound Speed c: Harmonic Trap: vF0 = Fermi velocity, trap center, noninteracting gas

  44. b from the sound velocity at resonance Full trap average: Experiment: Duke, sound velocity 06 (Feshbach resonance at 834 G) Duke, cloud size 05 Rice, cloud size 06 Theory: Carlson (2003)b = - 0.560 Strinati (2004)b = - 0.545

  45. Transverse Average—I lied! More rigorous theory with correct c(0) agrees with trap average to 0.2 % (Capuzzi, 2006):

  46. Speed of sound, u1in the BEC-BCS crossover Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

  47. Speed of sound, u1in the BEC-BCS crossover Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

  48. Speed of sound, u1in the BEC-BCS crossover Leggett Ground Monte-Carlo Theory State Theory Theory: Grigory Astrakharchik (Trento) Theory: Yan He & Kathy Levin (Chicago)

  49. Summary • Strongly-interacting Fermi gases: • -Nuclear Matter – High Tc Superconductors • 2 Experiments reveal high Tc transitions in behavior: • -Heat capacity • -Breathing mode • Sound-wave measurements: • -First Soundfrom BEC to BCS regime • - Verygood agreement with QMC calculations

  50. The Team (2005) Left to Right: Eric Tong, Bason Clancy, Ingrid Kaldre, Andrey Turlapov, John Thomas, Joe Kinast, Le Luo, James Joseph

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