Nearly perfect liquids: Nearly perfect liquids: strongly coupled systems strongly coupled systems

from quark-gluon plasmas to from quark-gluon plasmas to ultracold atomsultracold atoms

Gordon BaymGordon Baym

University of IllinoisUniversity of Illinois

8 April 20098 April 2009

Deconfined quark-gluon plasmas

made in ultrarelativistic heavy ion collisions

T ~ 102 MeV ~ 1012 K (temperature of early universe at ~1 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.

Viscosity: heavy-ion elliptic flow Fermi gases near unitarity

Ultracold ionized atomic plasma physics

Crossover: BEC BCS and hadron quark-gluon plasma

Connections:

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

In cold atoms near resonance only length-scale is density. No microscopic parameters enter equation of state:

is a universal parameter. No systematic expansion

Theory: = -0.60 (0.2) Green’s Function Monte Carlo, Gezerlis & Carlson (2008)

Experiment: -0.61(2) Duke (2008)

Fqgp ~ const nexc4/3 Ecold atoms ~ const n2/3/m

( => CFT)

Strongly coupled systems

In quark-gluon plasma,

Even at GUT scale, 1015GeV, gs ~ 1/2 (cf. electrodynamics: e2/4 = 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: =8 a2

Go from weakly repulsive to strongly repulsive to strongly attractive to weakly attractive by dialing external magnetic field through Feshbach resonance .

6Li

~ 150 MeV

repulsive

attractive

Resonance at B= 830 G

Remarkably similar behavior of ultracold fermionic atoms

and low density neutron matter (ann= -18.5 fm)

A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801(R) (2008)A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801(R) (2008)

nn effectiverange beginsto play role

Strong coupling leads to low first viscosity seen in expansion in both systems

= scattering time

Viscosity in elliptic flow in heavy ion collisions and in Fermi gases near unitarity

First viscosity

Strong interactions => small

Shear viscosity Shear viscosity ::

F = F = A v /d A v /ddd vv

Stress tensorStress tensor

Conjectured lower bound on ratio of first viscosity to entropy density, s: Kovtun, Son, & Starinets, PRL 94 (2005)

~ n~ ntt m v m v22 = n p = n p , s ~ n, s ~ ntt

nntt = no. of degrees of freedom producing viscosity = no. of degrees of freedom producing viscosity

p = mv = mean particle momentum ~ p = mv = mean particle momentum ~ / (interparticle spacing) / (interparticle spacing) = mean free path= mean free path

Bound Bound mean free path > interparticle spacing mean free path > interparticle spacing

Equality exact in N=4supersymmetric Yang Mills theoryin limit of large number of colors, Nc: AdS/CFT duality

Familiar (weakly interacting) systems well obey bound

Degenerate Fermi gas:

Classical gas: nmv2hard spheres), s ~ log T /slog T , growing with T

, s ~ T (Fermi liquid) /s , dropping with T

Low T Bose gas: : s ~ Ts ~ T3 3 (phonons) (phonons)

/s ~ 1/T/s ~ 1/T88, dropping with T, dropping with T

Have minimum (at T ~ TF in the absence of other scales)

In He-II, /s ~0.7~ at minimum (T ~ 2K)

cf. unitary Fermi gas, /s ~0.2~ at minimum (T ~ 0.2 TF)

Laurence Yaffe – QCD transport theory

Shear viscosity/ entropy density ratio vs. T/TShear viscosity/ entropy density ratio vs. T/TFF

TTcc

Shear viscosity from radial breathing modeShear viscosity from radial breathing mode

Data:J. Thomas et al.

Theory: T. Schaefer, Phys. Rev. A 76, 063618 (2007)

G. Rupak & T .Schaefer, PRA76, 053607 (2007)

G.M.Bruun &H. Smith, PRA75, 043612 (2007)

Expt: 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 ) Ratio of shear viscosity to entropy density (in units of )

Shear viscosity of Fermi gas at unitarityShear viscosity of Fermi gas at unitarity

Hydrodynamic predictions of v2(pT)

Elliptic flow => almost vanishing viscosity in quark-gluon plasmaElliptic 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 systemsBEC-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)

Tc/Tf ~ 0.2 Tc /Tf ~ e-1/kfa

Pairs shrink

6Li

(color superconductivity)

QGP (quark-gluon plasma)

Phase diagram of quark-gluon plasmaT. Hatsuda

Chiral symmetry breaking chirally symmetric (Bose-Einstein decondensation)

CROSSOVER ??

Neutrons, protons, pions, … paired quarks

(density)

tricritical point

Interplay between BCS pairing and chiral condensate Interplay between BCS pairing and chiral condensate

Hadronic phase breaks chiral symmetry, producing chiral (particle-Hadronic phase breaks chiral symmetry, producing chiral (particle-antiparticle) bosonic condensate: antiparticle) bosonic condensate:

Color superconducting phase has particle-particle pairing Color superconducting phase has particle-particle pairing

~~ 33

b

~ d~ dLL** d dRR

Spontaneous breaking of the axial U(1)Spontaneous breaking of the axial U(1)AA symmetry of QCD (axial symmetry of QCD (axial

anomaly) leads to attractive (‘t Hooft anomaly) leads to attractive (‘t Hooft 6-quark6-quark interaction) between interaction) between the chiral condensate and pairing fields. Each encourages the other! the chiral condensate and pairing fields. Each encourages the other!

a,b,c = colori,j,k = flavorC: charge conjugation

ddRR

ddLL**

Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006); PRD 76, 074001 (2007)

New critical point in phase diagram: induced by chiral condensate – diquark pairing coupling

via axial anomaly

Hadronic

Normal

Color SC

(as ms increases)

Phase diagram of cold fermionsvs. interaction strength

(magnetic field B)

Unitary regime (Feshbach resonance) -- crossoverNo phase transition through crossover

BCS

BEC of di-fermionmolecules

Temperature

Tc

Free fermions +di-fermion molecules

Free fermions

-1/kf a0

a>0a<0

Tc/EF ~0.22

Tc~ EFe-/2kF|a|

Atomic Bose-Fermi mixtures: model diquark-quark to baryon transition

GB, K. Maeda, T. Hatsuda, in preparation

KRb

RbK

Binding of 40K + 87RbPhases vs gbf (<0)

weak gbb>0

strong gbb>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: = Einteraction /Ekinetic >> 1

Electrons in a metal

Eint ~ e2/r0 r0 = interparticle spacing ~ 1/kf

Eke ~ kf2/m => ~ e2/ vf = eff

vf ~ 10-2-10-3c => eff ~ 1-5

Dusty interstellar plasmas

Laser-induced plasmas (NIF, GSI)

Quark-gluon plasmas

Eint ~ g2/r0, r0 ~ 1/T, Eke ~ T => ~ g2 > 1

Ultracold trapped atomic plasmas

Non-degenerate plasma, Eke~ T => = Eint/Eke ~ e2/r0T

~ n91/3/TK [where n9 = n/(109 /cm3) and T

K = (T/ 1K)]

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-...

Quark-gluon plasma

Hadronic matter2SC

CFL

1 GeV

150 MeV

0

Temp

eratur

e

Baryon chemical potential

Neutron stars

?

Ultrarelativistic heavy-ion collisions

Nuclear liquid-gas

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 (>0)

Phase diagram of trapped imbalanced Fermi gases

Trap geometryTrap geometry

superfluid core

normal normal envelopeenvelope

MIT

Shin, Schnuck, Schirotzek, & Ketterle, Nature 451, 689 (2008)