Nearly perfect liquids: strongly coupled systems from quark-gluon plasmas to ultracold atoms Gordon Baym University of Illinois 8 April April 2009

Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions T ~ 10 2 MeV ~ 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 ~ 10 4 – 10 7 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:  = (0.2) Green’s Function Monte Carlo, Gezerlis & Carlson (2008) Experiment: -0.61(2) Duke (2008) F qgp ~ const n exc 4/3 E cold atoms ~ const n 2/3 /m ( => CFT)

Strongly coupled systems In quark-gluon plasma, Even at GUT scale, GeV, g s ~ 1/2 (cf. electrodynamics: e 2 /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  a 2 Go from weakly repulsive to strongly repulsive to strongly attractive to weakly attractive by dialing external magnetic field through Feshbach resonance. 6 Li  ~ 150 MeV repulsive attractive Resonance at B= 830 G

Remarkably similar behavior of ultracold fermionic atoms and low density neutron matter (a nn = fm)‏ A. Gezerlis and J. Carlson, Phys. Rev. C 77, (R) (2008)‏ A. Gezerlis and J. Carlson, Phys. Rev. C 77, (R) (2008)‏ nn effective range begins to 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  : F =  A v /d d v Stress tensor

Conjectured lower bound on ratio of first viscosity to entropy density, s: Kovtun, Son, & Starinets, PRL 94 (2005)  ~ n t m v 2  = n p, s ~ n t n t = no. of degrees of freedom producing viscosity p = mv = mean particle momentum ~ / (interparticle spacing) = mean free path = mean free path Bound  mean free path > interparticle spacing Equality exact in N=4 supersymmetric Yang Mills theory in limit of large number of colors, N c : AdS/CFT duality

Familiar (weakly interacting) systems well obey bound Degenerate Fermi gas: Classical gas:  nmv 2    hard spheres), s ~ log T  /s    log T, growing with T   , s ~ T (Fermi liquid)  /s  , dropping with T :    s ~ T 3 (phonons) Low T Bose gas:    s ~ T 3 (phonons)  /s ~ 1/T 8, dropping with T Have minimum (at T ~ T F 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 T F )

Laurence Yaffe – QCD transport theory

Shear viscosity/ entropy density ratio vs. T/T F TcTcTcTc Shear viscosity from radial breathing mode Data: J. Thomas et al. Theory: T. Schaefer, Phys. Rev. A 76, (2007) G. Rupak & T.Schaefer, PRA76, (2007) G.M.Bruun & H. Smith, PRA 75, (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 ) Shear viscosity of Fermi gas at unitarity

Hydrodynamic predictions of v 2 (p T ) Elliptic flow => almost vanishing viscosity in quark-gluon plasma M. Luzum & P. Romatschke,

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. Nozières and S. Schmitt-Rink, J. Low Temp Phys. 59, 195 (1985) T c /T f ~ 0.2 T c /T f ~ e -1/k f a Pairs shrink 6 Li

(color superconductivity) QGP (quark-gluon plasma) Phase diagram of quark-gluon plasma T. 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 Hadronic phase breaks chiral symmetry, producing chiral (particle- antiparticle) bosonic condensate: Color superconducting phase has particle-particle pairing ~ 3~ 3~ 3~ 3 b ~ d L * d R  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! a,b,c = color i,j,k = flavor C: charge conjugation     dRdRdRdR dL*dL*dL*dL*

Hatsuda, Tachibana, Yamamoto & GB, PRL 97, (2006); PRD 76, (2007) New critical point in phase diagram : induced by chiral condensate – diquark pairing coupling via axial anomaly Hadronic Normal Color SC (as m s increases)‏

Phase diagram of cold fermions vs. interaction strength (magnetic field B)‏ Unitary regime (Feshbach resonance) -- crossover No phase transition through crossover BCS BEC of di-fermion molecules Temperature TcTc Free fermions +di-fermion molecules Free fermions -1/k f a0 a>0 a<0 T c /E F ~0.22 T c ~ E F e -  /2k F |a|

Atomic Bose-Fermi mixtures: model diquark-quark to baryon transition GB, K. Maeda, T. Hatsuda, in preparation K Rb K Binding of 40 K + 87 Rb Phases vs g bf (<0) weak g bb >0 strong g bb >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:

Michael Murillo – Strongly coupled plasmas

Strongly coupled plasmas:  = E interaction /E kinetic >> 1 Electrons in a metal E int ~ e 2 /r 0 r 0 = interparticle spacing ~ 1 /k f E ke ~ k f 2 /m =>  ~ e 2 / v f =  eff v f ~ c =>  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 2 > 1 Ultracold trapped atomic plasmas Non-degenerate plasma, E ke ~ T =>  = E int /E ke ~ e 2 /r 0 T  ~ n 9 1/3 /T K [where n 9 = n/(10 9 /cm 3) 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 -...

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  (>0)‏

Phase diagram of trapped imbalanced Fermi gases Trap geometry superfluid core normal envelope MIT Shin, Schnuck, Schirotzek, & Ketterle, Nature 451, 689 (2008)