Is an Ultra-Cold Strongly Interacting Fermi Gas a Perfect Fluid?

1. Ultracold atomic Fermi gas T = 10-7 K Quark-gluon plasma T = 1012 K Computer simulation of RHIC collision Is an Ultra-Cold Strongly Interacting Fermi Gas a Perfect Fluid? John E. Thomas Support: ARO NSF DOE NASA* “JETLAB” Group

2. Optically Trapped Fermi Gas Our atom:Fermionic = = Magnet coils

3. Tunable Interactions: Feshbach Resonance Scattering length Universal Regime 840 G @ 528 G *Generated using formula published in Bartenstein, et al, PRL94 103201 (2005)

4. Quantum Degeneracy in Fermi Gases Harmonic Potential: Optical Trap Parameters: = Zero Temperature = Trap Fermi Temperature Scale: TF = 2.4 mK

5. Preparation of Degenerate 6Li gas Atoms precooled in a magneto-optical trap to 150 mK 2 MW/cm2 U0/kB = 700 mK

6. Ultrastable CO2 Laser Trap Stable Commercial Laser l = 10.6 mm • Negligible Optical Heating • Scatters two photons per hour • Optical Heating = 18 pK/s • Extremely Low Noise • Intensity Noise Heating Time • Ultra-High Vacuum • Pressure: < 10-11 Torr • Heating: < 5 nK/sec • Lifetime: 400 sec

7. Experimental Apparatus

8. Experimental Apparatus

9. Outline • Introduction: Fermi gases as a Paradigm for Interacting Fermions in Nature • Thermodynamics of strongly-interacting Fermi gases: –Model-independent measurements of entropy and energy • Quantum viscosity in strongly-interacting Fermi gases: – Comparison to the minimum viscosity conjecture

10. Strongly Interacting Systems in Nature Strongly Interacting 6Li gas T = 10-7 K Duke, Science (2002) Similar “Elliptic” Flow Quark-gluon plasma T = 1012 K • Ultracold Atomic 6Li Gas • Quark-Gluon Plasma • High Tc Superconductors • Neutron Matter • Black Holes in String Theory

11. The Universal Regime Strongly Interacting Fermi Gas Ideal Fermi Gas Theory: Carlson (2008) Experiment: Duke (2008) T= 0 Interparticle spacing L is the only length scale. Fermi Energy Bertsch 1998, Baker 1999, Heiselberg, 2001

12. Quantum Viscosity in the Universal Regime Viscosity natural unit: Entropy density natural unit: Ratio natural unit:

13. The Minimum Viscosity Conjecture—String Theory Viscosity—Hydrodynamics Kovtun et al., PRL 2005 Entropy density—Thermodynamics Is a Strongly-interacting atomic Fermi gas a fluid with the minimum shear viscosity?

14. Thermodynamics of Strongly Interacting Fermi gases Ground State Energy Finite Temperature Thermodynamics Critical Parameters “Universal” – independent of the microscopic interactions

15. Energy E Measurement Universal Gas obeys the Virial Theorem Duke, PRL (2005) For a universal quantum gas, theenergy E is determined by the cloud size In a HO potential: Energy per particle

16. Entropy S Measurement by Adiabatic Sweep of Magnetic Field B Start 840 G End 1200 G B Weakly interacting: Entropy at 1200 G known from cloud size — Ideal Fermi gas

17. Entropy S from the Cloud Size at 1200 G

18. Measuring the Energy E versus Entropy Sby Adiabatic Sweep of Magnetic Field B B z z End 1200 G Energy Measurement: Adiabatic: Start 840 G Strongly interacting at 840 G: EnergyES known from cloud size — Universal Fermi gas Weakly interacting at 1200 G: EntropySW known from cloud size — Ideal Fermi gas (textbook)

19. Energy versus Entropy Data: Strongly interacting 6Li gas Ideal gas Critical temperature for the superfluid transition Tc = 0.20 TF !! Analog of a super-high temperature superconductor that would work at severalthousanddegrees!

20. Minimum Viscosity Hydrodynamics “Quantum viscosity”— Rotating Fermi gases

21. Quantum Viscosity Gyulassy (1985) Entropy density Kittel Thermal Physics—Viscosity

22. Quantum Viscosity Shuryak (2005) Rotating Fermi gas Entropy per particle If “Quantum viscosity” How does the viscosity for a strongly interacting Fermi gas compare to the String Theory conjecture for h/s ?

23. Low Viscosity Hydrodynamics: Expansion of a Rotating Cloud Can a Normal fluid rotate like a Superfluid?

24. Expansion of a rotating gas

25. Measuring the angleof the cloud Measure the angle of the long axis of the rotating cloud with respect to the laboratory axis

26. Theory—superfluid flow Superfluid, 0 = 178 rad/s Normal Fluid, 0 = 178 rad/s Measuring the Angular Velocity Rotatesfaster as it expands— opposite to the behavior of an ice-skater!

27. Quenching of the moment of inertia versus deformation parameter d Red—normal fluid Blue—superfluid Fundamental prediction for irrotational flow Very low viscosity! Normal fluid rotates like a Superfluid!

28. W0 = 178 rad/s ; Normal Fluid W0 = 178 rad/s ; Superfluid How low is the viscosity h?

29. Viscosity h in units of Deep trap (20%) Shallow trap (5%)

30. Viscosity/entropy density (units of ) He near l-point QGP simulations String theory limit

31. Summary • Thermodynamics of strongly-interacting Fermi gases: –Model-independent measurements of entropy and energy – Experimental temperature calibration and Tc • Minimum viscosity hydrodynamics: – Nearly perfect irrotational flow in expansion, both superfluid and normal fluid regime – May be close to minimum viscosity conjecture

32. The 2008 Team 1st row: Willie Ong Chenglin Cao James Joseph Yingyi Zhang Le Luo Dave Weisberg 2nd row: Ethan Elliot John Thomas Xu Du 3rd row: Jessie Petricka Bason Clancy