Bose-condensed and BCS fermion superfluid states T ~ nano to microkelvin (coldest in the universe)

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2 Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions T ~ 10 2 MeV ~ K (temperature of early universe at ~1µ sec) Bose-condensed and BCS fermion superfluid states T ~ nano to microkelvin (coldest in the universe)

3 Both lab systems are small clouds with many degrees of freedom ~ Strongly interacting systems (QGP always, atoms by choice) Have unprecedented control of cold atom systems: atomic types: bosons, fermions in different hyperfine states molecules, mixtures interaction strengths: controlled by magnetic fields using Feshbach resonances variable particle densities choice of background arenas optical lattices from 1 to 3 D, or none atoms with large magnetic dipole moments optical lattice

4 Dense nuclear matter and cold atom systems QCD phase diagram: hadron quark-gluon plasma and BEC BCS crossover Cold atom analogs of QCD and nuclear systems Artificial magnetic (gauge) fields for neutral systems Ultracold ionized atomic plasma physics: study strongly interacting plasma dynamics in lab Viscosity: heavy-ion elliptic flow Fermi gases near unitarity Superfluidity and pairing in unbalanced systems: trapped fermions color superconductivity (neutron stars)

5 In quark-gluon plasma, QGP strongly interacting Λ ~ 150 MeV Even at Grand Unified (GUT) scale, GeV, g s ~ 1/2 (cf. electrodynamics: e 2 /4π = 1/137 => e~ 1/3) QGP non-perturbative in general

6 Strong interactions in cold atoms In cold atoms, effective atom-atom interaction is short range and s-wave: V(r-r ) = [4π h 2 a/m] δ(r-r ) a = s-wave atom-atom scattering length. Cross section: σ=4π 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 attractive repulsive Resonance at B= 830 G

7 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:

8 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)

9 Confinement of three atomic fermions on lattice; formation of nucleons A, Rapp, G. Zarand, C. Honerkamp, & W. Hofstetter, PRL 98 (2007), PRB 77 (2008) Hubbard model with 3 internal degrees of freedom Red, Green, Blue 3 lowest hyperfine states of 6 Li Small U : (U < 0) Superfluid of two species ( color superfluid ) Large U : Three particles bind together (formation of trions = baryons )

10 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

11 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

12 Phase diagram of cold fermions vs. interaction strength Unitary regime (Feshbach resonance) -- crossover. No phase transition through crossover

13 Interplay between BCS pairing and chiral condensate Hadronic phase breaks chiral symmetry, producing chiral (particleantiparticle) bosonic condensate: Analogous to polarization in two component Fermi gases Color superconducting phase has particle-particle pairings

14 New critical point in phase diagram: induced by chiral condensate diquark pairing coupling via axial anomaly Hadronic Normal QGP (as m s increases) Color SC

15 BEC-BCS crossover in QCD phase diagram GB, T. Hatsuda, M. Tachibana, N. Yamamoto, J. Phys.G: Nucl. Part. Phys. 35 (2008) Normal Hadronic (as m s increases) Color SC Hadrons BCS-BEC crossover BCS paired quark matter Small quark pairs are diquarks

16 Low temperature critical point in Nambu Jona-Lasinio model with the axial anomaly H. Abuki, GB, T. Hatsuda, and N. Yamamoto (PRD 2010) Couple quark fields together with effective 4 and 6 quark interactions: At mean field level, have effective couplings of chiral field φ and pairing field d: K and K from axial anomaly

17 Have low temperature critical point with BCS-BEC crossover

18 Characterizing BEC vs BCS: excitation spectra BEC BCS Δ = gap, µ = chemical potential BEC: µ < 0, Δ << µ BCS: µ > 0, Δ < µ µ => molecule binding energy/ 2 gap at Fermi surface

19 Boson-fermion mixtures of ultracold atoms -- and dense QCD -- forming superfluid of composite fermions K. Maeda, G.B, T. Hatsuda, PRL 103, (2009) Bosons ( 87 Rb) diquarks, fermions ( 40 K) unpaired quarks Formation of b-f molecules transition to nucleons 40 K 87 Rb nucleon unpaired quark diquark n = b & f densities, a bf = b-f scattering length Experiments in optical lattices: Bloch group, Mainz

20 Three species of atomic fermions in continuum Continuum: R.W. Cherng, G. Refael, & E. Demler PRL 99, (2007) T. Ozawa & GB (in progress) Three component system with Hamiltonian U < 0 Order Parameters: Pairing: Polarization: Φ ij = ψ i ψ j N 3 δ ij analogous to chiral condensate of quarks and anti-quarks Same structure as in axial anomaly induced coupling of chiral and pairing fields in dense QCD. Calculations in progress.

21 Strong attractive coupling => polarization in 3 component system Nonzero Magnetization, or Polarization Kine+c energy pair pair pair strong interac+on weak interac+on

22 Simulating pion condensed phases of nuclear matter with dipolar fermionic atoms ( 161 Dy, 163 Dy) Color Color superconductivity

23 Fermi seas of neutrons and protons in neutron star matter π - Neutron Fermi energy > proton Fermi energy plus pion rest mass (m π c 2 ) neutrons protons => BEC of pi mesons pion condensate. Technically, have a soft collective spin-isospin instability driven by nuclear tensor interaction, between spins σ: favors similar, except for sign to magnetic dipolar interaction favors

24 Above critical density have transition to new state with nucleons rotated in isospin space: with formation of macroscopic pion field Atomic dysprosium has magnetic moment = 10µ B. Trapped in Urbana (Lev) Populate 11/2 state n At high density get spontaneous excitation of 13/2 p with macroscopic magnetic field pion field. 163 Dy angular mom = 21/2 GB, T. Hatsuda, K. Maeda

25 World s first Dysprosium MOT 164 Dy, 163 Dy, 162 Dy, 161 Dy, 160 Dy ~ 2 X10 8 atoms density ~ /cm 3 Ben Lev s lab, Urbana

26 Simulating gauge fields in neutral cold atoms: 1) Rotation acts as magnetic field Rotate (Bose) atomic cloud in harmonic trap. Energy in rotating frame: Like a magnetic field As Ω approaches trap frequency, system flattens out, becomes effectively 2D. Centrifugal potential balances transverse trapping potential. Vortices

27 Artificial magnetic fields for neutral atoms, II Y.-J. Lin, R. L. Compton, A. R. Perry, W.D. Phillips, J.V. Porto, & I. B. Spielman, PRL 102, (2009) 87 Rb BEC in optical trap: F=1 ground state, T ~ 100nK, N ~ 2.5x10 5 synthetic B field real B field lasers No magnetic field Abrikosov vortices in magnetic field

28 Artificial magnetic fields for neutral atoms, III K. J. Günter, M. Cheneau, T. Yefsah, S. P. Rath, & J. Dalibard, PRA 79, (R) (2009) Two level system Effective Hamiltonian Schematic setup of lasers Artificial B field in z direction: Induced scalar potential

29 Ultracold neutral atomic plasmas T. Killian & S. Rolston, Physics Today, March 2010 T. Killian et al., Physics Reports 449, 77 (2007) Produce by photoionizing trapped cold atomic gas., e.g., Xe, Sr. electron temperatures T e ~ K, ion temperatures T ion - mk, densities n ~ /cm 3, total particle number N~ 10 5 Expand plasma; measure densities, velocities (Doppler) by laser absorption: Optical depth of Sr plasma N = 7X10 7, n~2 X /cm -3

30 Strongly coupled plasmas: Γ = 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 f2 /m => Γ ~ e 2 /~ v f = α eff v f ~ c => α eff ~1-5 Dusty interstellar plasmas ( GSI Laser-induced plasmas (NIF, Quark-gluon plasmas E int ~g 2 /r 0, r 0 ~ 1/T, E ke ~T => Γ ~ g 2 M16: Pillars of Creation Ultracold trapped atomic plasmas Non-degenerate plasma, E ke ~T => Γ = E int /E ke ~e 2 /r 0 T Γ ~ n 1/3 9 /T K ~ [where n 9 = n/10 9 /cm3 and T K = (T/ 1K)]

31 Ion kinetic energy oscillations responding to onset of spatial correlations T. Killian, Science 2007 C Simien, YC Chen, P Gupta, S Laha, Y Martinez, P Mickelson, S Nagel, & T Killian PRL (2004)

32 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, hydrodynamics -thermalization times -correlations -interaction with fast particles -viscosity -...

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