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

Support:

ARONSFDOENASA*

John E. Thomas

“JETLAB” Group

Quark-gluon plasma T = 1012 K

Computer simulation of RHIC collision

Ultracold atomic Fermi gas

T = 10-7 K

Optically Trapped Fermi Gas

Our atom: Fermionic

1,2

1= 0,

2

1=

znuclear ,electron I S z

agnet coils

Tunable Interactions: Feshbach Resonance

*Generated using formula published in Bartenstein, et al, PRL 94 103201 (2005)

aScattering length

840 G

0a @ 528 G

02000L

:Spacing cleInterparti

a

Uni

vers

al R

egim

e

Quantum Degeneracy in Fermi Gases

Trap Fermi Temperature Scale:

TF = 2.4 K

5102NHz600)( 3/1 zyx

Optical Trap Parameters:

3/1)3( NhTkE FBF

Zero Temperature

FBF TkE

hnnn zyx )( Harmonic Potential:

1,2

1= 0,

2

1=

2 MW/cm2

U0/kB = 700 K

Preparation of Degenerate 6Li gas

Atoms precooled

in a magneto-optical trap

to 150 K

Ultrastable CO2 Laser Trap

K 7000 U20 MW/cm 0.2I

sec103.2 4heat t

• Extremely Low Noise

– Intensity Noise Heating Time

• Ultra-High Vacuum

– Pressure: < 10-11 Torr

– Heating: < 5 nK/sec

– Lifetime: 400 sec

Stable Commercial Laser

• Negligible Optical Heating

– Scatters two photons per hour

– Optical Heating = 18 pK/s

= 10.6 m

Experimental Apparatus

Experimental Apparatus

Outline

• 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

• Introduction: Fermi gases as a Paradigm for Interacting Fermions in Nature

Strongly Interacting Systems in Nature

Duke, Science (2002)

Strongly Interacting 6Li gas T = 10-7 K

Ultracold Atomic 6Li Gas Quark-Gluon Plasma High Tc Superconductors

Neutron Matter Black Holes in String Theory

Similar “Elliptic” Flow Quark-gluon plasma T = 1012 K

The Universal Regime

T= 0

Interparticle spacing L

is the only length scale.

idealgnd )1(E E

Bertsch 1998, Baker 1999, Heiselberg, 2001

22

2ideal

LmE

Fermi Energy

Theory: Carlson (2008) )1(60.0

Experiment: Duke (2008) )2(61.0

Strongly Interacting Fermi Gas

0 a

L

Ideal Fermi Gas

Quantum Viscosity in the Universal Regime

vFd

Ad v

n

Entropy density natural unit: Bkns

2

/

L

Lp

Viscosity natural unit:

B// ks Ratio natural unit:

The Minimum Viscosity Conjecture—String Theory

Kovtun et al., PRL 2005

B4

1

ks

Viscosity—Hydrodynamics

Entropy density—Thermodynamics

Is a Strongly-interacting atomic Fermi gas a

fluid with the minimum shear viscosity?

Thermodynamics of Strongly Interacting Fermi gases

• Ground State Energy

• Finite Temperature Thermodynamics

• Critical Parameters

“Universal” – independent of the microscopic interactions

Energy E Measurement

Universal Gas obeys the Virial Theorem Duke, PRL (2005)

223E zm zEnergy per particle

For a universal quantum gas,the energy E is determined by the cloud size

UE 2In a HO potential:

Entropy S Measurement by Adiabatic Sweep of Magnetic Field B

Start840 G

BEnd1200 G

Weakly interacting:Entropy at 1200 G known from cloud size — Ideal Fermi gas

Entropy S from the Cloud Size at 1200 G

IW SS

Measuring the Energy E versus Entropy Sby Adiabatic Sweep of Magnetic Field B

Weakly interacting at 1200 G:Entropy SW known from cloud size — Ideal Fermi gas (textbook)

Energy Measurement:

GzS zmE840

223

Adiabatic:

WS SS

Strongly interacting at 840 G:Energy ES known from cloud size— Universal Fermi gas

zB

End1200 G

zStart840 G

Energy versus Entropy

Ideal gas

Data: Strongly interacting 6Li gas

Critical temperature for the superfluid transition

Analog of a super-high temperature superconductor that would workat several thousand degrees!

Tc = 0.20 TF !!

S

ET

Minimum Viscosity Hydrodynamics

“Quantum viscosity”— Rotating Fermi gases

Quantum Viscosity

vFd

Ad v

mfp pnKittel Thermal Physics—Viscosity

Gyulassy (1985) xp n

Entropy density Bkns B// ks

Quantum Viscosity

n Shuryak (2005) If “Quantum viscosity”1

How does the viscosity for a strongly interacting Fermi gas compareto the String Theory conjecture for /s ?

BS/k

Bks

Rotating Fermi gas

Entropy per particle

30002

H 6000Air

Low Viscosity Hydrodynamics: Expansion of a Rotating Cloud

Can a Normal fluid rotate like a Superfluid?

Expansion of a rotating gas

Measuring the angle of the cloud

Measure the angle of the long axis of the rotating cloud with respect to the laboratory axis

Measuring the Angular Velocity

Superfluid, 0 = 178 rad/s Normal Fluid, 0 = 178 rad/s

Theory—superfluid flow

Rotates faster as it expands—opposite to the behaviorof an ice-skater!

Quenching of the moment of inertia versus deformation parameter

Normal fluid rotates like a Superfluid!

222

222

2

yx

yx

I

I

rigid

Fundamental prediction for irrotational flow

Red—normal fluid

Blue—superfluid

Very low viscosity!

2y

2x

0 = 178 rad/s ; Superfluid 0 = 178 rad/s ; Normal Fluid

2 1

2

How low is the viscosity ?

n

n

nViscosity in units of

Deep trap (20%)

Shallow trap (5%)

Viscosity/entropy density (units of ) Bk/

He near point

QGP simulations

String theory limit

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

The 2008 Team

1st row:Willie OngChenglin CaoJames JosephYingyi ZhangLe LuoDave Weisberg

2nd row:Ethan ElliotJohn ThomasXu Du

3rd row:Jessie PetrickaBason Clancy