New states of quantum matter created in the past decade

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2 New states of quantum matter created in the past decade From: Trapped cold atomic systems: Bose-condensed and BCS fermion superfluid states T ~ nanokelvin (traps are the coldest places in the universe!) To: Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions T ~ 10 2 MeV ~ K (temperature of early universe at 1μ sec) Separated by ~21 decades in characteristic energy scales, yet have intriguing overlaps.

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4 Cold atoms: trapped bosons and fermions Box Potential well (trap) Statistics: Bose condensate: macroscopic occupation of single mode (generally lowest) Degenerate Fermi gas => BCS pairing

5 Trapped atomic experiments in a nutshell Warm atomic vapor T=300K, n /cm Magneto-optical trap Laser cool to T 50μK n /cm 3 Evaporatively cool in magnetic (or optical) trap Bosons condense, Fermions BCS-pair TT c nk n /cm 3 N Experiment, and then measure :

6 To probe system, release from trap, let expand and then image with laser: trap laser

7 Long-Lived Lived Alkali Atoms BOSONS (Spin, lifetime) FERMIONS (Z-N=odd-even nuclei) (Z-N=odd-odd nuclei) 7 Li 3/2-6 Li Na 3/2-22 Na y 39 K 3/2+ 40 K 4-1.3x10 9 y 41 K 3/2+ 85 Rb 5/2-86 Rb d 87 Rb 3/2-4.75x10 10 y 131 Cs 5/2+ 9.7d 132 Cs d 133 Cs 7/ Cs 7/2+ 2.3x10 6 y 134 Cs y 209 Fr 9/2-50.0s 208 Fr s

8 Early days of ultracold trapped atomic gases 1995 = first Bose condensation of 87 Rb, 23 Na and 7 Li *Structure of condensate. *Elementary modes: breathing, quadrupole, short wave sound,. *1, 2 and 3 body correlations => evidence for BEC rather than simply condensation in space. *Interference of condensates. Primarily described in terms of mean field theory Gross-Pitaevskii eq. i~ ψ(r,t) / t = [-~ 2 2 /2m + V(r) + g ψ(r,t) 2 ]ψ(r,t)

9 Newer directions in ultracold atomic systems, I Strongly correlated systems * Rapidly rotating bosons: how do many-particle Bose systems carry extreme amounts of angular momentum? Trapping and cooling clouds of fermionic atoms Degenerate Fermi gases and molecular states BCS pairing => new superfluid Crossover from BEC of molecules to BCS paired state * Physics in the strong interaction limit: scale-free regime where r 0 n -1/3. a r 0 = range of interatomic potential few Å n = particle density a = s-wave scattering length Realize through atomic Feshbach resonances

10 Newer directions in ultracold atomic systems, II Novel systems *Physics in optical lattices: Mott transition from superfluid to insulating states; low dimensional systems; 2D superfluids * Spinor gases: trapped by laser fields. Physics of spin degrees of freedom Fragmented condensates * Mixtures of bosons and fermions * Ultracold molecules: coherent mixtures of atoms and molecules, e.g., 87 Rb atoms and 87 Rb 2 molecules; heteronuclear molecules: 6 Li+ 23 Na, 40 K+ 87 Rb

11 Future applications: Trapped ions for quantum computing Slow light Atom lithography Matter lasers

12 Compress matter to form new states Atoms Plasma Nuclei Nuclear matter ρ~2.5x10 14 gm/cm 3 = ρ nm = 0.17 baryons/fm 3 (1 fm = cm) Nucleons Quark matter

13 Quark degrees of freedom Quarks = fractionally charged spin-1/2 fermions, baryon no. = 1/3, with internal SU(3) color degree of freedom. Flavor Charge/ e Mass(MeV) u 2/3 5 ( ) d -1/3 10 ( ) s -1/3 150 (54-92) c b t 2/3-1/3 2/ Hadrons are composed of quarks: proton = u + u + d neutron = _ u + d + d π + = u + d, etc. Form of baryons in the early universe at t < 1μ sec (T > 100 MeV). Possibly basic degrees of freedom in deep interiors of neutron stars.

14 Temperature Ultrarelativistic heavy-ion collisions Quark-gluon plasma 50 MeV Hadronic matter Color superconductivity 2SC Nuclear liquid-gas Neutron stars? CFL

15 Temperature 50 MeV Ultrarelativistic heavy-ion collisions Hadronic matter Quark-gluon plasma 2SC Color Color superconductivity Neutron stars Nuclear liquid-gas Neutron stars?? 2SC CFL CFL

16 Quark-gluon plasma state Degrees of freedom are deconfined quarks and gluons Many more degrees of freedom than hadronic matter (color, spin, particle-antiparticle, & flavor); much larger entropy at given temperature. <= Large latent heat (or sharp rise at least) At low temperatures form Fermi seas of degenerate u,d, and s quarks: (e.g., in neutron stars?)

17 T.D. Lee

18 Tsinghua University Science Park, Beijing

19 Creating high energy density matter in the lab Relativistic Heavy Ion Collider (Brookhaven) since Beams 100 GeV/A Large Hadron Collider (CERN) in GeV/A FAIR (GSI) ca to 45 GeV/A T. Hirano Au( GeV)+Au( GeV)

20 Schematic collision: Two Lorentz contracted nuclei collide, pass through each other, leaving highly excited state of vacuum in between. What collisions actually look like in the lab.. STAR detector

21 ALICE detector at LHC Two major detectors at RHIC PHENIX STAR Two smaller detectors BRAHMS PHOBOS

22 Tabletop trapped atom experiments J. Thomas Lab, Duke

23 A few crucial observations at RHIC: Produce matter with energy densities 5 GeV/fm energy density of ordinary nuclei 0.15 GeV/fm 3 Certainly produce quark-gluon plasma. Fast quarks traversing medium lose energy rapidly. Opaque medium Very rapid build-up of pressure in collisions: Large collective flow, fast thermalization, large interaction cross sections. Hydrodynamics => small viscosity

24 Common problems of cold atom physics and RHIC physics: Small clouds with many degrees of freedom Strongly interacting systems Infrared (long wavelength) problems in qcd and condensed bosons. Recent connections: Crossover: BEC BCS and hadron quark-gluon plasma Viscosity: heavy-ion elliptic flow Fermi gases near unitarity Superfluidity and pairing in unbalanced systems: trapped fermions color superconductivity Ultracold ionized atomic plasma physics

25 Strong interactions In quark-gluon plasma, Even at GUT scale, GeV, g s 1/2 (cf. electrodynamics: e 2 /4π = 1/137 => e 1/3) QGP is always strongly interacting Λ 150 MeV In cold atoms, effective atom-atom interaction is short range and s-wave: V(r 1 -r 2 ) = (4π~ a/m) δ (r 1 -r 2 ) 5000 a = s-wave atom-atom scattering length. 6 Li Cross section: σ=8π a 2 0 Go from weakly repulsive to strongly repulsive to strongly attractive to weakly attractive attractive by dialing external magnetic Magnetic Field ( G ) field through Feshbach resonance. Scattering Length ( a O ) repulsive Resonance at B= 830 G

26 Feshbach resonance in atom-atom scattering open channel closed channel open channel s-wave magnetic moment: μ μ + Δ μ Scattering amplitude M 2 E c E o E c -E 0 Δμ B +... Low energy scattering dominated by bound state closest to threshold Adjusting magnetic field, B, causes level crossing and resonance, seen as divergence of s-wave scattering length, a:

27 Degenerate ultracold atomic Fermi gases Produce trapped degenerate Fermi gases: 6 Li, 40 K High T: Boltzmann distribution Observing Statistics 7 Li vs. 6 Li Low T: Degenerate gas Hulet Increase attractive interaction with Feshbach resonance At resonance have unitary regime, Magnetic Field ( G ) force range << interparticle spacing << scattering length, only relevant length scale is the interparticle spacing. At temperatures 0.2 of the degeneracy temperature (T f ), create BCS paired superfluids. Scattering Length ( a O )

28 Both systems scale-free in strongly coupled regime 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: β is a universal parameter. No systematic expansion Theory: β = (0.2) Green s Function Monte Carlo, Gezerlis & Carlson (2008) Experiment: -0.61(2) Duke (2008)

29 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)

30 BEC-BCS 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 T c /T f 0.2 T c /T f e -1/k fa 6 Li

31 Striking relation of Bose-Einstein condensation and BCS pairing The two phenomena developed along quite different paths Our pairs are not localized..., and our transition is not analogous to a Bose-Einstein condensation. BCS paper Oct We believe that there is no relation between actual superconductors and the superconducting properties of a perfect Bose-Einstein gas. The key point in our theory is that the virtual pairs all have the same net momentum. The reason is not Bose-Einstein statistics, but comes from the exclusion principle.... Bardeen to Dyson, 23 July 1957

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

33 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, CROSSOVER?? paired quarks (color superconductivity) (density)

34 Interplay between BCS pairing and chiral condensate Hadronic phase breaks chiral symmetry, producing chiral (particle- antiparticle) bosonic condensate: b Color superconducting phase has particle-particle pairing a,b,c = color i,j,k = flavor C: charge conjugation 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! Φ Φ d R Φ Φ ~ Φ 3 d L * ~ d L* d R Φ

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

36 Similar coupling of magnetization (spin-up particle -- spin-down hole condensation) to pairing in multicomponent cold fermion atom systems for N >2 => pairing drives magnetization, and hence they can coexist.

37 Deconfinement transition vs. BEC-BCS crossover In SU(2) C : Hadrons <=> 2 fermion molecules. Paired deconfined phase <=> BCS paired fermions In SU(3) C Normal Hadronic Color SC T c molecules BCS free fermions Hadrons BCS-BEC crossover BCS paired quark matter Abuki, Itakura & Hatsuda, PRD65, 2002 μ B

38 Viscosity in elliptic flow in heavy ion collisions and in Fermi gases near unitarity Strong coupling leads to low first viscosity η, seen in expansion in both systems d v Shear viscosity η: F = η A v /d Stress tensor First viscosity τ = scattering time Strong interactions => small η

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

40 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); to be published Ratio of shear viscosity to entropy density (in units of ~)

41 Collectivity: Elliptic flow in non-central collisions: anisotropic in φ (= azimuthal angle in x,z plane) Almond shape overlap region in coordinate space momentum space dn/dφ ~ v 2 (p T ) cos (2φ) + where p T = momentum in x,y plane

42 Hydrodynamic predictions of v 2 (p T ) Elliptic flow => almost vanishing viscosity in quark-gluon plasma 20-30% From T. Hirano

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

44 Conjectured lower bound on ratio of first viscosity to entropy density, s: η ~s/4π Kovtun, Son, & Starinets, PRL 94 (2005) (Equality exact result in N =4 supersymmetric Yang-Mills theory in limit of large number of colors, N c ; AdS/ CFT duality) η~ n t m v 2 τ = n p λ,, s ~ n t n t = no. of degrees of freedom producing viscosity p = mv = mean particle momentum > ~ 1 / (interparticle( spacing) λ = mean free path Bound mean free path > interparticle spacing

45 Familiar (weakly interacting) systems well obey bound Classical gas: η nmv 2 τ Τ 1/2 (hard spheres), s ~ log T η/s Τ 1/2 /log T, growing with T Degenerate Fermi gas: η 1/Τ 2, s ~ T (Fermi liquid) η/s 1/Τ 3, dropping with T Low T Bose gas: η 1/Τ 5, s ~ T 3 (phonons) η/s ~ 1/T 8, dropping with T Have minimum (at T ~ T F in the absence of other scales) In He-II, η/ s ~0.7~ at minimum (T ~ 2K) cf. unitary Fermi gas, η/ s ~0.2~ at minimum (T ~ 0.2 T F )

46 Strongly coupled systems approach viscosity lower bound Cold fermions in normal state at unitarity: η ~ n T/T f, s~ n T/T f => η/s ~ 1 G. Bruun and H. Smith, Phys. Rev. A 75, (2007) Lattice calculations of first viscosity in qcd: Nakamura & Sakai, hep-lat/ Perturbative qcd limit: η T 3 /(α s2 ln α s ) η/s 1/α s2 ln α s GB, Monien, Pethick & Ravenhall, PRL 64(1990)

47 But bound is not exact! Imagine gas of bowling balls (radius a ~ 20 cm) filling large volume (Equilibrium state of balls at T ~ 300K for low enough density) η ~ T 1/2 /a 2, s = s cm + s internal While η/s cm well obeys the bound, s internal >>> s cm η/s total can be arbitrarily small (~ ~)

48 Color pairing in quark matter Review: Alford, Rajagopal, Schaefer, & Schmitt, RMP (2008) 0Temperature 150 MeV Ultrarelativistic heavy-ion collisions Hadronic matter Nuclear liquid-gas Quark-gluon plasma 1 GeV Neutron stars? Baryon chemical potential 2SC CFL Superfluidity condensate of paired quarks => superfluid baryon density (n s ) ColorMeissnereffects transverse color fields screened on spatial scale ~ London penetration depth ~ (μ/g 2 n s ) 1/2 Two interesting phases: 2SC (u,d) Color-flavor locked (CFL) (m u =m d =m s )

49 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 μ (>0)

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

51 THE END