Is an Ultra-Cold Strongly Interacting Fermi Gas a Perfect Fluid? Support: ARO NSF DOE NASA* John E. Thomas “JETLAB” Group Quark-gluon plasma T = 10 12 K Computer simulation of RHIC collision Ultracold atomic Fermi gas T = 10 - 7 K
Jan 01, 2016
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