Quark matter meets cold atoms 474th International Wilhelm und Else Heraeus Seminar on Strong interactions: from methods to structures, Bad Honnef, Feb 12-16, 2011 Mei Huang IHEP, CAS TPCSF, CAS

2 Content I.Recent progress of QCD phase structure Cold quark matter & cold atoms II.Interplay between chiral and deconfinement phase transitions

3 I. Recent Progress of QCD phase structure

4 QCD phase diagram: For physical quark mass, crossover at zero and small baryon density, and first order phase transition at finite baryon density. CEP is the end point of first order phase transition. HM QGP CEP Heating QCD vacuum: (RHIC, LHC, early universe) 1, Chiral symmetry restoration 2, Deconfinement phase transition

5 QCD phase diagram after 1999 Squeezing QCD matter: Color superconductor HM QGP CSC Pairing with mismatch beta-equilibrium, charge neutrality

6 Imbalanced CSC meets imbalanced cold atoms MH, I.Shovkovy, PRD70:051501,2004; ,2004 Shovkovy, M.H, PLB564:205,2003 M.H., I. Shovkovy, NPA729:835,2003 Interior gap & Breached Pairing Liu,Wilczek, PRL90:047002,2003 Gubankova, Liu, Wilczek, PRL91:032001,2003 Gapless 2SC phase Chromomagnetic instabilitySuperfluid density is negative Wu, Yip, PRA67: , 2003 Other possibilities: LOFF state(1964), phase separation

7 Zwierlein, Schirotzek, Schunck, & Ketterle, Science 2005, cond-mat/ Partridge, Li, Kamar, Liao, & Hulet, Science 2005, cond-mat/ n 1 =n 2 n 1 >>n 2 phase separation Imbalanced pairing in cold atom system

8 M.H. PRD73:045007, 2006; Int.J.Mod.Phys.A21, 910, (2006) I. Giannakis, D.F.Hou, M.H., H.C.Ren, PRD75:011501,2007, PRD75:014015,2007 Group G Subspace: Group H Coset space: M=G/H Instability of NG bosons FF-like state Higgs instability spatial inhomogeneity For gapless superfluidity (BP) state, no charge Coulomb energy competes with Higgs instability, phase separation is more favored.

9 Abuki-Baym-Hatsuda-Yamamoto, arXiv: BCS-BEC crossover Abuki, He, Zhuang, Deng, Pu, Wang Abuki-Baym-Hatsuda-Yamamoto ……

10 Compact Star sQGP QCD phase diagram High T part after 2003 P. Romatschke, U. Romatschke, Phys.Rev.Lett.99:172301,2007 Discovery of sQGP at RHIC

11 Viscosity/entropy density (units of ) He near  point QGP simulations String theory limit Slide from John E. Thomas

12 II. Interplay between chiral and deconfinement phase transitions

: Quarkyonic phase chiral symmetric but confined phase L. McLerran, R. Pisarski 2007 Phase diagram at large Nc Conditions: Large Nc Deconfined quark Fermi surface Particle-particle pairing is suppressed Particle-hole (color singlet) pairing dominant chiral density wave

14 Can “Quarkyonic phase” be realized in real QCD? Fukushima, Hatsuda, arXiv: “Quarkyonic phase” has extended meaning, here indicates chiral symmetric but confined phase. More interests are attracted to the relation between chiral and deconfinement phase transitions

15 Lattice results on chiral and deconfinement phase transitions at zero mu Chiral limit: coincide Physical quark mass (2+1): RBC-Bielefeld: coincide Wuppertal-Budapest: (crossover feature)

16 Relation between chiral and deconfinement phase transitions in PNJL or PLSM model

17 Order parameter of center symmetry: Polyakov loop Confinement: center symmetry Deconfinement: center symmetry breaking

18 Relation between chiral and deconfinement phase transitions in PNJL model Different choices of Polyakov potential: fixed by lattice QCD at finite T

19 Sasaki,Friman,Redlich, hep-ph/ Kenji Fukushima, arXiv: Chiral symmetry broken and deconfined / coincidence

20 Chiral symmetric but confined phase in PLSM model H. Mao, J. Jin, MH, arXiv: , J.Phys.G37:035001,2010

21 In PNJL or PLSM model, at zero baryon density, whether chiral phase transition and deconfinement phase transition coincide or not depends much on parameters used. In these models, there are no real interplay between chiral phase transition and deconfinement phase transition.

22 Dressed Polyakov loop An equivalent order parameter for deconfinement phase transition: Gattringer,PRL97(2006) Bilgici et.al. PRD77(2008) Braun, Hass,Marhauser,Pawlowski, arXiv:

23 Order parameter of center symmetry: Dressed Polyakov loop or dual chiral condensate Gattringer,PRL97(2006) n=1: dressed Polyakov loop Dressed Polyakov on lattice: Bilgici et.al. in DSE: Fischer et.al. Linking confinement to spectral properties of Dirac operator

24 The periodicity property of the quark fields change under the the gauge transformation Uz: Dual observables:

25 Dressed Polyakov loop in NJL model

26 Chiral limit: coincide T.Mukherjee, H.Chen, M.Huang, arXiv: ,PRD82:034015,2010

27 Physical quark mass: crossover region T.Mukherjee, H.Chen, M.Huang, arXiv: ,PRD82:034015,2010 Y.Aoki, Z.Fofor,A.Katz,K.Szabo, hep-lat/ , PLB643:46-54,2006 1st order:

28 Why for 1 st phase transition? T.Mukherjee, H.Chen, M.Huang, arXiv: ,PRD82:034015,2010 for 1 st phase transition is preserved by the singularity. If this is true, there will be no “quarkyonic” phase or chiral symmetric but confined phase at finite density.

29 Nf=2+1 NJL model: sequential (flavor dependent) phase transitions Fukun Xu, T.Mukherjee, M.H., arXiv: CEP related to future RHIC and FAIR Exp. will be the CEP of light u,d quarks

30 Summary 1, Much progress on QCD phase diagram at finite temperature and density has been made in the last 10 years. 2, Quantitative results are still few!