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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 Supported by: DOE, NSF, ARO, NASA John E. Thomas Theory: Jelena Stajic, Qijin Chen, Kathy Levin

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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

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

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

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

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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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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

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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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Energy input R I 0 Temperature Tools for Thermodynamic Measurements

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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

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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 Trap ON again, gas rethermalises time Trap ON Final Energy E(t heat ) Initial energy E 0 Expansion factor:

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

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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!

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

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

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Breathing Mode Frequency and Damping 528 G 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! Transition in damping: Transition in heat capacity: S/F transition (theory): Levin: Strinati: Bruun: Superfluid behavior: Hydrodynamic damping 0 as T 0

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

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

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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 Trapped atoms Slice of green light (pulsed) Sound excitation: Observation: hold, release & image t hold = 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, u 1 in the BEC-BCS Crossover

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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)

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Speed of Sound, u 1 for a BEC of Molecules

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

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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)

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

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

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

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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)

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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

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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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