1. Measuring Entropy and Quantum Viscosity in a Strongly Interacting Atomic Fermi Gas Support: ARO NSF DOE NASA* John E. Thomas Ken O’Hara* Mike Gehm* Stephen Granade* Staci Hemmer* Joe Kinast* Bason Clancy* Le Luo* Andrey Turlapov* Post Docs: Xu Du Jessie Petricka Students: James Joseph Yingyi Zhang Chenglin Cao Ethan Elliot Willie Ong JETLab Group

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

3. Tunable Interactions: Feshbach Resonance *Generated using formula published in Bartenstein, et al, PRL 94 103201 (2005) Scattering length 840 G @ 528 G

4. Quantum Degeneracy in Fermi Gases Trap Fermi Temperature Scale: T F = 2.4  K Optical Trap Parameters: Zero Temperature Harmonic Potential: = =

5. Experimental Apparatus

7. Outline Thermodynamics of strongly-interacting Fermi gases: – Model-independent measurements of entropy and energy – Calibrating the endpoint temperature for adiabatic sweeps Quantum viscosity in strongly-interacting Fermi gases: – Expansion dynamics of rotating Fermi gases – Comparison to the minimum viscosity conjecture Introduction: Fermi gases as a Paradigm for Strong Interactions in Nature

8. Strongly Interacting Fermi Systems in Nature  Ultracold Atomic Fermi Gases  High-Temperature Superconductors  Neutron Matter  Quark-Gluon Plasma  Black Holes in String Theory Quark-gluon plasma T = 10 12 K Duke, Science (2002) O’Hara et al. Strongly Interacting Degenerate 6 Li gas T = 10 -7 K Similar “Elliptic” Flow

9. Universal Regime: Neutron Matter Model (Bertsch’s Challenge) T= 0 Interparticle spacing L is the only length scale. Theory: Carlson (2003)  = - 0.560 Strinati (2004)  = - 0.545 Baker 1999, Heiselberg, 2001 B = 528 G Ideal Fermi Gas B = 840G Strongly Interacting Fermi Gas Fermi Energy

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

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

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

13. Energy E Measurement Virial Theorem in HO potential Thomas, PRL (2005), Castin (2004) Werner and Castin, PRA (2006) Son (2007) Measure energy E from the cloud size Energy per particle Universal Thermodynamics Ho, PRL (2004)

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

15. Entropy S from the Cloud Size at 1200 G

16. Measuring the Energy E versus Entropy S by Adiabatic Sweep of Magnetic Field B Weakly interacting at 1200 G: Entropy S W known from cloud size — Ideal Fermi gas Energy Measurement: Adiabatic: Strongly interacting at 840 G: Energy E S known from cloud size — Universal Fermi gas z B End 1200 G z Start 840 G

17. Energy versus Entropy Ideal gas Data

18. Comparison with Theory Pseudogap—Chen et al. NSR—Hu et al. QMC—Bulgac Haussmann

19. Temperature from Energy versus Entropy Temperature continuous: Below S c Superfluid Energy continuous: Above S c Normal Fluid E 0 = ground state energy Energy units heat capacity jumps heat capacity continuous by matching

20. Temperature from Energy versus Entropy C jump fit Superfluid regime Normal fluid regime

21. Temperature from E(S) Fit C continuous Fit C jump

22. Estimated Critical Parameters What type of transition? Expt: Fit with heat capacity jump Expt: Fit with continuous heat capacity Theory: QMC—Bulgac Theory: Variational—Haussman-Zwerger ScSc EcEc TcTc 2.2(1)0.83(1)0.21(1) 1.6(3)0.7(1)0.19(2) 2.15 0.82 0.27 1.61(5)0.67(1)0.214(7) Can we confirm the transition temperature?

23. Endpoint Temperature Calibration Adiabatic sweep between strongly interacting and ideal gas regimes From fit C jump From fit C continuous JILA group: onset of pair condensation at (T I /T F ) c = 0.18 Calibration shows that (T I /T F ) c = 0.18 corresponds to T c /T F = 0.19

24. Sound wave speed Ground State Energy and  Extrapolation to zero entropy Cloud size ratio: strong/weak

25. Sound propagation

26. New Measurements of b: Independent of density to 1.8% over a factor of 30 in density, exhibiting universal scaling at 834 G. 2) b from the Extrapolated Ground State Energy E(S = 0)* (Hu et al., Nat. Phys. 2007)*Avoids systematic error due to finite T HO trap: 1) b from the Sound Speed at Resonance (Joseph et al., PRL 2007) * v F is Fermi speed for ideal gas at trap center  = - 0.565 (15)

27. New Measurements of b: 3) b from the cloud size ratio: *Corrected for magnetic field dependent axial trapping potential *Avoids systematic error due to finite T and atom number N measurement  = - 0.565 (15) (sound)(energy-entropy) Theory: Carlson (2008)  = - 0.60(1)

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

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

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

31. Low Viscosity Hydrodynamics in Expansion of a Rotating Gas BEC Experiments: O. Hechenblaikner et al., PRL (2002) M. Modugno et al., PRA (2003) BEC Theory: M. Edwards et al., PRL (2002) Superfluid: Irrotational Flow Can a Normal fluid rotate like a Superfluid?

32. Expansion of a rotating gas

33. Measure the aspect ratio and angle Rotating about z-axis Aspect ratio of the widths of principal axes  is the angle of the principal axes with respect to the laboratory axes 

34. Expansion Dynamics: Comparison to theory Theory: Irrotational hydrodynamics, no free parameters E = 0.56 E F,  0 = 178 rad/s E = 2.10 E F,  0 = 178 rad/s

35. Red—normal fluid Moment of inertia Irrotational Condition I min must be quenched! Angular Momentum Conservation Energy Conservation Blue—superfluid I = L/ 

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

37. W 0 = 0.40 w z ; E = 0.56 E F W 0 = 0.40 w z ; E = 1.21 E F How low is the viscosity?

38. Viscosity  in units of Deep trap (20%) Shallow trap (5%)

39. Viscosity/entropy density (units of ) He near  point QGP simulations String theory limit

40. Interior Dynamics of a Rotating Gas

42. Summary Thermodynamics of strongly-interacting Fermi gases: – Model-independent measurements of entropy and energy – Experimental Temperature Calibration and T c Minimum viscosity hydrodynamics: – Nearly perfect irrotational flow in expansion, both superfluid and normal fluid regime – Normal fluid is in quantum viscosity regime – May be close to minimum viscosity conjecture

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

44. Entropy versus mean square size

45. Ideal Gas with Fit (No heat cap jump)

46. Temperature from Fit (No heat cap jump) Exact From E-S fit

47. Temperature Calibrations Fit C continuous Fit C jump Adiabatic sweep Empirical Temp (equal energy)