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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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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
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Degeneracy in Fermi Gases
Our atom: Fermionic Trap Fermi Temperature Scale: = Harmonic Potential: Optical Trap Parameters: Zero Temperature TF = 2.4 mK
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Tunable Interactions: Feshbach Resonance
*generated using formula published in Bartenstein, et al, PRL (2005) Scattering length @ 528 G 840 G
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Universal Strong Interactions at T = 0
George Bertsch’s problem: (Unitary gas) Baker, Heiselberg Ground State: Effective mass: Trap Fermi Temperature: L Cloud size:
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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
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Preparation of Degenerate 6Li gas
Atoms precooled in a magneto-optical trap to 150 mK 2 MW/cm2 U0=0.7 mK
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Forced Evaporation in an Optical Trap
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High-Field Imaging
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Experimental Apparatus
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Experimental Apparatus
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Tools for Thermodynamic Measurements
Energy input R I Temperature
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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
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Calibrating the Empirical temperature
Conjecture: Calibration using theoretical density profiles: Stajic, Chen, Levin PRL (2005) S/F transition predicted
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Precision energy input
Initial energy E0 Trap ON again, gas rethermalises time Trap ON Expansion factor: Final Energy E(theat)
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Virial Theorem (Strongly-interacting Fermi gas obeys the
Virial theorem for an Ideal gas!)
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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!
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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
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Heat Capacity Energy versus empirical temperature
(Superfluid transition)
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Input Energy vs Measured Temperature
Noninteracting Gas (B=528 G) Ideal Fermi Gas Theory
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Input Energy vs Measured Temperature
Strongly-Interacting Gas at 840 G Ideal Fermi Gas Theory with scaled Fermi temperature
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Low temperature region
Strongly-Interacting Gas (B=840 G) Ideal Fermi gas theory with scaled temperature Power law fit
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Energy vs on log-log scale
Blue – strongly-int. gas Green – non-int. gas Fit Ideal Fermi gas theory Transition!
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Energy vs Theory for Strongly- interacting gas (Chicago, 2005)
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Oscillation of a trapped Fermi gas
Study same system (strongly-interacting Fermi gas) by different method
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Breathing mode in a trapped Fermi gas
Image Excitation & observation: Trap ON Trap ON again, oscillation for variable 1 ms Release time
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Breathing Mode Frequency and Damping
Noninteracting Gas 840 G Strongly- Interacting Gas w = frequency t = damping time
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Radial Breathing Mode: Frequency vs Magnetic Field
Hu et al.
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Radial Breathing Mode: Damping Rate vs Magnetic Field
Pair Breaking
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Frequency w versus temperature for strongly-interacting gas (B=840 G)
Hydrodynamic frequency, 1.84 Collisionless gas frequency, 2.10
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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:
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Quantum Viscosity? Viscosity: Shuryak (2005) Radial mode: Axial mode:
Innsbruck Axial: a = 0.4 Duke Radial: a = 0.2
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Wires!
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Sound Wave Propagation in Bose and Fermi Superfluids
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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
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Molecular BECs are cold
“Hot” BEC, 710 G (after free expansion) “Cold” BEC, 710 G (after free expansion, from the same trap)
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Sound: Excitation by a pulse of repulsive potential
Slice of green light (pulsed) Trapped atoms Sound excitation: Observation: hold, release & image thold= 0
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Sound propagation on resonance (834 G)
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Sound propagation at 834 G Forward Moving Notch Backward Moving Notch
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Speed of Sound, u1 in the BEC-BCS Crossover
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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
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Speed of Sound, u1 for a BEC of Molecules
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Sound Velocity at Resonance
Pressure: Local Sound Speed c: Harmonic Trap: vF0 = Fermi velocity, trap center, noninteracting gas
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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:
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Transverse Average—I lied!
More rigorous theory with correct c(0) agrees with trap average to 0.2 % (Capuzzi, 2006):
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Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)
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Speed of sound, u1 in the BEC-BCS crossover
Monte-Carlo Theory Theory: Grigory Astrakharchik (Trento)
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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)
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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
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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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