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Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas Students: Joe Kinast, Bason Clancy, Le Luo, James Joseph Post Doc: Andrey Turlapov.

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Presentation on theme: "Collective Modes and Sound Velocity in a Strongly Interacting Fermi Gas Students: Joe Kinast, Bason Clancy, Le Luo, James Joseph Post Doc: Andrey Turlapov."— Presentation transcript:

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

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

3 Degeneracy in Fermi Gases Trap Fermi Temperature Scale: T F = 2.4 K Optical Trap Parameters: Zero Temperature Harmonic Potential: Our atom: Fermionic = =

4 Tunable Interactions: Feshbach Resonance *generated using formula published in Bartenstein, et al, PRL (2005) Scattering length G

5 Universal Strong Interactions at T = 0 George Bertschs problem: (Unitary gas) L Ground State: Trap Fermi Temperature: Effective mass: Cloud size: Baker, Heiselberg

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 2 MW/cm 2 U 0 =0.7 mK Preparation of Degenerate 6 Li gas Atoms precooled in a magneto-optical trap to 150 K

8 Forced Evaporation in an Optical Trap

9 High-Field Imaging

10 Experimental Apparatus

11

12 Energy input R I 0 Temperature Tools for Thermodynamic Measurements

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

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

15 Precision energy input Trap ON again, gas rethermalises time Trap ON Final Energy E(t heat ) Initial energy E 0 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: x U Trap potential Test! Force Balance: Virial Theorem: Local energy density (interaction and kinetic) Ho, PRL (2004)

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

19 Heat Capacity Energy versus empirical temperature (Superfluid transition)

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

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

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

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

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

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

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

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

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 temperature for strongly-interacting gas (B=840 G) Hydrodynamic frequency, 1.84 Collisionless gas frequency, 2.10

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

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

33 Wires!

34 Sound Wave Propagation in Bose and Fermi Superfluids

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

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 Trapped atoms Slice of green light (pulsed) Sound excitation: Observation: hold, release & image t hold = 0

38 Sound propagation on resonance (834 G)

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

40 Speed of Sound, u 1 in the BEC-BCS Crossover

41 Sound Velocity in a BEC of Molecules Mean field: Harmonic Trap: Local Sound Speed c: Full trap average: v F0 = Fermi velocity, trap center, noninteracting gas Dalfovo et al, Rev Mod Phys 1999 For (Petrov, Salomon, Shlyapnikov)

42 Speed of Sound, u 1 for a BEC of Molecules

43 Sound Velocity at Resonance Harmonic Trap: Pressure:Local Sound Speed c: v F0 = Fermi velocity, trap center, noninteracting gas

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

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

46 Speed of sound, u 1 in the BEC-BCS crossover Theory: Grigory Astrakharchik (Trento) Monte-Carlo Theory

47 Speed of sound, u 1 in the BEC-BCS crossover Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

48 Speed of sound, u 1 in the BEC-BCS crossover Leggett Ground State Theory Theory: Yan He & Kathy Levin (Chicago) Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

49 Summary 2 Experiments reveal high T c transitions in behavior: - Heat capacity - Breathing mode Strongly-interacting Fermi gases: - Nuclear Matter – High T c Superconductors Sound-wave measurements: - First Sound from BEC to BCS regime - Very good 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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