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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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