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 ~ 10 2 MeV ~ 10 12 K (temperature of early universe at ~ 1 m 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 ~ 10 4 – 10 7 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) F qgp ~ const n exc 4/3 E cold atoms ~ const n 2/3 /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, Even at GUT scale, 10 15 GeV, g s (cf. electrodynamics: e 2 /4 p ~ 1/2 = 1/137 => e ~ 1/3) L ~ 150 MeV QGP is always strongly interacting In cold atoms, effective atom-atom interaction is short range and s-wave:

10000 5000

6 Li repulsive a = s-wave atom-atom scattering length. Cross section: s =8 p a 2 Go from weakly repulsive to strongly repulsive to strongly attractive to weakly attractive by dialing external magnetic field through Feshbach resonance

0 -5000 -10000 400

attractive

600 800 1000 Magnetic Field ( G ) 1200

Remarkably similar behavior of ultracold fermionic atoms and low density neutron matter

(a nn = -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

d

v Shear viscosity h : 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, N c : AdS/CFT duality h ~ n t m v 2 t = n p  , s ~ n t n t = no. of degrees of freedom producing viscosity p = mv = mean particle momentum ~  = mean free path / (interparticle spacing) Bound  mean free path > interparticle spacing

Familiar (weakly interacting) systems well obey bound

Classical gas: h~ nmv 2 t ~ T 1/2 ( hard spheres), s ~ log T h /s ~ T 1/2 / log T , growing with T Degenerate Fermi gas: h~ 1/T 2 , s ~ T (Fermi liquid) h /s ~ 1/T 3 , dropping with T Low T Bose gas: h ~ 1/T 5 , s ~ T 3 (phonons) h /s ~ 1/T 8 , dropping with T Have minimum (at T ~ T F 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 T F )

Laurence Yaffe – QCD transport theory

Shear viscosity from radial breathing mode

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

T c

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

Shear viscosity/ entropy density ratio vs. T/T F

G.M.Bruun & H. Smith, PRA 75, 043612 (2007)

Data: J. Thomas et al.

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 v

2

(p

T

)

Elliptic flow => almost vanishing viscosity in quark-gluon plasma

M. Luzum & P. Romatschke, 0804.4015

Derek Teaney -- Viscosity in v 2 and R AA

v2 and RAA

Viscosity issues:

In heavy ion collisions: How to extract viscosity from heavy ion collisions?

Validity of hydro? Dependence on p t ?

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. Nozi è res and S. Schmitt-Rink, J. Low Temp Phys. 59, 195 (1985)

Pairs shrink T c /T f ~ 0.2 T c /T f ~ e -1/kfa 6 Li

Phase diagram of quark-gluon plasma

T. Hatsuda

tricritical point Chiral symmetry breaking QGP (quark-gluon plasma) chirally symmetric (Bose-Einstein decondensation) Neutrons, protons, pions, … CROSSOVER ??

paired quarks (color superconductivity) (density)

Interplay between BCS pairing and chiral condensate

Hadronic phase breaks chiral symmetry, producing chiral (particle antiparticle) bosonic condensate: a,b,c = color i,j,k

=

flavor b C: charge conjugation 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!   d R   ~  3 d L * ~ d L * d R 

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)

Hadronic Normal (as m s increases) Color SC

Phase diagram of cold fermions vs. interaction strength

Temperature T c Free fermions +di-fermion molecules /E F ~0.22

a>0 T c BEC of di-fermion molecules 0 Free fermions BCS a<0 T c ~ E F e p /2kF|a| (magnetic field B) -1/k f 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 g bb >0 K Rb Rb K strong g bb >0 Binding of 40 K + 87 Rb Phases vs g bf (<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

=

E interaction /E kinetic >> 1 Electrons in a metal E int ~ e 2 /r 0 r 0 = interparticle spacing ~ 1 /k f E ke ~ v f k f 2 /m => G ~ ~ e 2 / v f 10 -2 -10 -3 c => a eff = ~ a eff 1-5 Dusty interstellar plasmas Laser-induced plasmas (NIF, GSI) Quark-gluon plasmas E int ~ g 2 /r 0, r 0 ~ 1/T, E ke ~ T => G ~ g 2 > 1 Ultracold trapped atomic plasmas G ~ n 9 1/3 /T K [where n 9 = n/(10 9 Non-degenerate plasma, E ke ~ T => G /cm 3) = E int and T /E ke ~ K = (T/ 1K)] e 2 /r 0 T

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 -...

Ultrarelativistic heavy-ion collisions Quark-gluon plasma 0 Hadronic matter 2SC Nuclear liquid-gas Neutron stars 1 GeV ?

Baryon chemical potential 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 m s 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