Nearly perfect liquids:
strongly coupled systems
from quark-gluon plasmas to
ultracold atoms
Gordon Baym
University of Illinois
Deconfined quark-gluon plasmas
made in ultrarelativistic heavy ion collisions
T ~ 102 MeV ~ 1012 K (temperature of early universe at ~1m sec)
Trapped cold atomic systems:
Bose-condensed and BCS fermion superfluid states
T ~ nanokelvin (traps are the coldest places in the universe!)
Separated by ~21 decades in characteristic energy scales
-- intriguing overlaps.
Small clouds with many degrees of freedom ~ 104 – 107
Strongly interacting systems
Finite size systems w. edge problems (trap edge, hadronic halo)
Infrared miseries in qcd and condensed bosons.
Connections:
Viscosity: heavy-ion elliptic flow  Fermi gases near unitarity
Ultracold ionized atomic plasma physics
Crossover: BEC  BCS and hadron  quark-gluon plasma
Cold atoms as testing ground for qcd:
Bose-fermion mixtures => RG diquarks + B quarks
3 Fermi systems => simulate formation of baryons from 3 quarks
Non-Abelian atomic systems => simulate lattice gauge theory
with atoms in optical lattices.
Superfluidity and pairing in unbalanced systems:
trapped fermions  color superconductivity
Test relativistic plasma codes in ultracold atom dynamics (hydro
to collisionless)
Both systems scale-free in strongly coupled regime
( => CFT)
Fqgp ~ const nexc4/3
Ecold atoms ~ const n2/3/m
In cold atoms near resonance only length-scale is density.
No microscopic parameters enter equation of state:
b is a universal parameter. No systematic expansion
Theory: b = -0.60 (0.2) Green’s Function Monte Carlo, Gezerlis & Carlson (2008)
Experiment: -0.61(2) Duke (2008)
Strongly coupled systems
In quark-gluon plasma,
L ~ 150 MeV
Even at GUT scale, 1015GeV, gs ~ 1/2
(cf. electrodynamics: e2/4p = 1/137 => e~ 1/3)
QGP is always strongly interacting
In cold atoms, effective atom-atom interaction is short range and
s-wave:
a = s-wave atom-atom scattering length.
Cross section: s=8p a2
Go from weakly repulsive to strongly
repulsive to strongly attractive to weakly
attractive by dialing external magnetic
field through Feshbach resonance .
Scattering Length ( aO )
10000
5000
repulsive
6Li
0
-5000
-10000
400
attractive
600
800
1000
Magnetic Field ( G )
Resonance at B= 830 G
1200
Remarkably similar behavior of ultracold fermionic atoms
and low density neutron matter (ann= -18.5 fm)
nn effective
range begins
to play role
A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801(R) (2008)
Viscosity in elliptic flow in heavy ion collisions
and in Fermi gases near unitarity
Strong coupling leads to low first viscosity h,
seen in expansion in both systems
Shear viscosity h:
v
d
F = h A v /d
Stress tensor
First viscosity
t = scattering time
Strong interactions => small h
Conjectured lower bound
on ratio of first viscosity to
entropy density, s:
Kovtun, Son, & Starinets, PRL 94 (2005)
Equality exact in N=4
supersymmetric Yang Mills theory
in limit of large number of colors, Nc:
AdS/CFT duality
h~ nt m v2t = n p ,
s ~ nt
nt = no. of degrees of freedom producing viscosity
p = mv = mean particle momentum ~
/ (interparticle spacing)
 = mean free path
Bound  mean free path > interparticle spacing
Familiar (weakly interacting) systems well obey bound
Classical gas:
h~ nmv2 t ~ T1/2 (hard spheres), s ~ log T
h/s ~ T1/2 /log T , growing with T
Degenerate Fermi gas:
h~ 1/T2 ,
s ~ T (Fermi liquid)
h/s ~ 1/T3, dropping with T
Low T Bose gas: h ~ 1/T5,
s ~ T3 (phonons)
h/s ~ 1/T8, dropping with T
Have minimum (at T ~ TF in the absence of other scales)
In He-II,
h/ s ~0.7~ at minimum (T ~ 2K)
cf. unitary Fermi gas,
h/ s ~0.2~ at minimum (T ~ 0.2 TF)
Laurence Yaffe – QCD transport theory
Shear viscosity from radial breathing mode
Theory: T. Schaefer, Phys. Rev. A 76, 063618 (2007)
G. Rupak &
T .Schaefer,
PRA76, 053607
(2007)
Tc
G.M.Bruun &
H. Smith, PRA
75, 043612
(2007)
Data:
J. Thomas et al.
Shear viscosity/ entropy density ratio vs. T/TF
Shear viscosity of Fermi gas at unitarity
Expt: A. Turlapov, J. Kinast, B. Clancy, L. Luo, J. Joseph, and J.E. Thomas,
J. Low Temp. Phys. (2007)
Ratio of shear viscosity to entropy density (in units of
)
Hydrodynamic predictions of v2(pT)
Elliptic flow => almost vanishing viscosity in quark-gluon plasma
M. Luzum & P. Romatschke, 0804.4015
Derek Teaney -- Viscosity in v2 and RAA v2 and RAA
Viscosity issues:
In heavy ion collisions:
How to extract viscosity from heavy ion collisions?
Validity of hydro? Dependence on pt?
Higher order terms in gradients? Second viscosity effects?
Edge of collision volume: mfp ~ gradients
In cold atoms:
Transport: Boltzmann eqn with medium effects at unitarity?
Effective range corrections – away from unitarity
Breakdown of strong interactions as denity -> 0 at edge of trap
Dam Son
Chris Herzog
BEC transition
John McGreevy: Non-relativistic CFT – applications to cold atoms
not unitary fermions (yet)
BEC-BCS crossover in Fermi systems
Continuously transform from molecules to Cooper pairs:
D.M. Eagles (1969)
A.J. Leggett, J. Phys. (Paris) C7, 19 (1980)
P. Nozières and S. Schmitt-Rink, J. Low Temp Phys. 59, 195 (1985)
Pairs shrink
6Li
Tc/Tf ~ 0.2
Tc /Tf ~ e-1/kfa
Phase diagram of quark-gluon plasma
T. Hatsuda
tricritical point
QGP (quark-gluon plasma)
Chiral symmetry breaking
chirally symmetric
(Bose-Einstein decondensation)
Neutrons, protons, pions, …
paired quarks
(color superconductivity)
CROSSOVER ??
(density)
Interplay between BCS pairing and chiral condensate
Hadronic phase breaks chiral symmetry, producing chiral (particleantiparticle) bosonic condensate:
a,b,c = color
i,j,k = flavor
C: charge conjugation
b
Color superconducting phase has particle-particle pairing
Spontaneous breaking of the axial U(1)A symmetry of QCD (axial
anomaly) leads to attractive (‘t Hooft 6-quark interaction) between
the chiral condensate and pairing fields. Each encourages the other!


dR

~ 3
dL*

~ dL* dR
New critical point in phase diagram:
induced by chiral condensate – diquark pairing coupling
via axial anomaly
Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006);
PRD 76, 074001 (2007)
Normal
Hadronic
(as ms increases)
Color SC
Phase diagram of cold fermions
vs. interaction strength
Temperature
Free fermions
+di-fermion
molecules
Tc/EF ~0.22 a>0
Tc
BEC of
di-fermion
molecules
Free fermions
a<0
Tc~ EFe-p/2kF|a|
(magnetic field B)
BCS
0
-1/kf a
Unitary regime (Feshbach resonance) -- crossover
No phase transition through crossover
Atomic Bose-Fermi mixtures:
model diquark-quark to baryon transition
GB, K. Maeda, T. Hatsuda, in preparation
weak
gbb>0
K
Rb
K
Rb
strong
gbb>0
Binding of 40K + 87Rb
Phases vs gbf (<0)
Ken O’Hara – Ultracold three component Fermi gas
Cheng Chin –
Superfluid – Mott insulator transition in Cs in optical lattices
Simulating U(2) non-Abelian gauge theory
D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003)
-arXiv:0902.3228
Michael Murillo – Strongly coupled plasmas
Strongly coupled plasmas:
G = Einteraction /Ekinetic >> 1
Electrons in a metal
Eint ~ e2/r0
r0 = interparticle spacing ~ 1/kf
Eke ~ kf2/m => G ~ e2/ vf = aeff
vf ~ 10-2-10-3c => aeff ~ 1-5
Dusty interstellar plasmas
Laser-induced plasmas (NIF, GSI)
Quark-gluon plasmas
Eint ~ g2/r0, r0 ~ 1/T, Eke ~ T => G ~ g2 > 1
Ultracold trapped atomic plasmas
G ~ n91/3/TK
[where n9 = n/(109 /cm3) and TK = (T/ 1K)]
Non-degenerate plasma, Eke~ T => G = Eint/Eke ~ e2/r0T
Ultracold plasmas analog systems for gaining understanding
of plasma properties relevant to heavy-ion collisions:
-kinetic energy distributions of electrons and ions
-modes of plasmas: plasma oscillations
-screening in plasmas
-nature of expansion – flow, hydrodynamical (?)
-thermalization times
-correlations
-interaction with fast particles
-viscosity
-...
Temperature
Ultrarelativistic
heavy-ioncollisions
Quark-gluonplasma
150MeV
Hadronicmatter
2SC
Nuclear
liquid-gas
0
Neutronstars
1GeV
?
Baryonchemicalpotential
CFL
Superfluidity and pairing for unbalanced systems
Trapped atoms: change relative populations of two states by hand
QGP: balance of strange (s) quarks to light (u,d) depends on
ratio of strange quark mass ms to chemical potential m (>0)
Phase diagram of trapped imbalanced Fermi gases
Shin, Schnuck, Schirotzek, & Ketterle, Nature 451, 689 (2008)
MIT
normal
envelope
superfluid
core
Trap geometry