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John E. Thomas Students: Joe Kinast, Bason Clancy,

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Presentation on theme: "John E. Thomas Students: Joe Kinast, Bason Clancy,"— Presentation transcript:

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
Duke, Science 2002 – Quark-gluon plasma of Big Bang 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 MIT JILA Innsbruck Rice ENS Duke

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

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

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

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 Tools for Thermodynamic Measurements
Energy input R I Temperature

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

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

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

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

17 Virial Theorem in a Unitary Gas
Local energy density (interaction and kinetic) Ho, PRL (2004) Pressure: x U Trap potential Force Balance: Virial Theorem: 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
Noninteracting Gas (B=528 G) Ideal Fermi Gas Theory

21 Input Energy vs Measured Temperature
Strongly-Interacting Gas at 840 G Ideal Fermi Gas Theory with scaled Fermi 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
Blue – strongly-int. gas Green – non-int. gas Fit Ideal Fermi gas theory Transition!

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
Image Excitation & observation: Trap ON Trap ON again, oscillation for variable 1 ms Release time

27 Breathing Mode Frequency and Damping
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 in damping: Transition! Transition in heat capacity: Superfluid behavior: Hydrodynamic damping 0 as T 0 S/F transition (theory): Levin: Strinati: Bruun:

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

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 B = 900G Cooper Pairs B = 834 G Resonance Stable molecules B = 710 G B Triplet Diatomic Potential: Electron Spins Parallel

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) Trapped atoms Sound excitation: Observation: hold, release & image thold= 0

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: For (Petrov, Salomon, Shlyapnikov) 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: (Feshbach resonance at 834 G) Rice, cloud size 06 Duke, cloud size 05 Duke, sound velocity 06 Carlson (2003) b = Strinati (2004) b = Theory:

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, u1 in the BEC-BCS crossover
Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

47 Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)

48 Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory Leggett Ground 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 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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