Towards the shear viscosity of a cold unitary fermi gas

Transcription

1 Towards the shear viscosity of a cold unitary fermi gas Jiunn-Wei Chen National Taiwan U.

2 Shear viscosity y V x (y) x Frictional force T ij iv j ( x) V 2 j i ( x) 1 ij V ( x). 3

3 Shear viscosity measures how perfect a fluid is! Smaller shear viscosity implies larger particle interaction!

4 Kovtun, Son, and Starinets ( 05) Conjecture: Shear viscosity / entropy density Motivated by AdS/CFT

5 QGP (quark gluon plasma) almost saturates the just above Tc (Teaney; Romatschke, Romatschke; Song, Heinz; Luzum ) LQCD, gluon pasma (Karsch, Wyld; Nakamura, Sakai; Meyer) QGP near Tc, a perfect fluid, SQGP

6 goes to a local minimum near a phase transition in more than 30 systems with no exception found so far. Cold Unitary Atoms Rupak & Schafer 2007 T0/TF Nuclear liquid-gas Phase transition JWC et al Lacey et al., PRL 98:092301,2007; 2007 US Nuclear Science Long Range Plan

7 QCD Phase Diagram JWC, Li, Liu, Nakano

8 (JWC, M. Huang, Y.H. Li, E. Nakana, D.L. Yang) 2nd-order p.t.: a < 0, b > 0, c = 0 crossover: + No p.t.: a > 0, b > 0, c = 0 1st-order phase transition a > 0, b < 0, c > 0

9 of Water (Lacey et al.)

10 QCD Bulk Viscosity Karsch, Kharzeev, Tuchin; Meyer; JWC, Wang; Fernandez- Fraile, Gomez Nicola

11 Universality? Universal and behaviors? ( reaches local minimum near p.t. reaches local maximum near p.t.)

12 Cold Fermions S-wave, scattering length Feshbach resonance

13 Scattering Length (S-wave) Unitarity limit

14 Tunable Interactions: Feshbach Resonance a 528 G Universal Regime 840 G *Generated using formula published in Bartenstein, et al, PRL (2005) Source: J.E. Thomas

15 Energy E Measurement Universal Gas obeys the Virial Theorem Duke, PRL (2005) In a HO potential: E 2 U Energy per particle E 3 2 m z z 2 For a universal quantum gas, the energy E is determined by the cloud size Source: J.E. Thomas

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

17 Measuring the Energy E versus Entropy S by Adiabatic Sweep of Magnetic Field B z B Start 840 G End 1200 G z Strongly interacting at 840 G: Energy E S known from cloud size Universal Fermi gas Energy Measurement: Weakly interacting at 1200 G: Entropy S W known from cloud size Ideal Fermi gas (textbook) Adiabatic: E S 3 m 2 z z 2 840G SS S W Source: J.E. Thomas

18 Energy versus Entropy Data: Strongly interacting 6 Li gas Ideal gas Critical temperature for the superfluid transition T E S T c = 0.20 T F!! Analog of a super-high temperature superconductor that would work at several thousand degrees! Source: J.E. Thomas

19 N dependence not seen! Source: T. Schafer

20 Expansion of a rotating gas Source: J.E. Thomas

21 Measuring the angle of the cloud Source: J.E. Thomas Measure the angle of the long axis of the rotating cloud with respect to the laboratory axis

22 Measuring the Angular Velocity Theory superfluid flow Rotates faster as it expands opposite to the behavior of an ice-skater! Superfluid, 0 = 178 rad/s Source: J.E. Thomas Normal Fluid, 0 = 178 rad/s

23 How low is the viscosity? n = 178 rad/s ; Superfluid Source: J.E. Thomas 0 = 178 rad/s ; Normal Fluid

24 Viscosity/entropy density (units of / k B ) Source: J.E. Thomas He near point QGP simulations String theory limit

25 Schafer & Chafin, ; Normal fluid

26 normal fluid 80 deg super fluid only t (ms)

27 Outlook Is the two fluid model a good starting point?