Intersections of nuclear physics and cold atom physics

Transcription

1 Intersections of nuclear physics and cold atom physics Thomas Schaefer North Carolina State University

2 Unitarity limit Consider simple square well potential a < 0 a =, ǫ B = 0 a > 0, ǫ B > 0

3 Unitarity limit Now take the range to zero, keeping ǫ B 0 Universal relations T = 1 ik + 1/a ǫ B = 1 2ma 2 ψ B 1 ar exp( r/a)

4 Feshbach resonances Atomic gas with two spin states: and V closed open r Feshbach resonance a(b) = a 0 ( 1 + B B 0 ) Unitarity limit a σ = 4π k 2

5 Universality Neutron Matter Feshbach Resonance in 6 Li What do these systems have in common? dilute: rρ 1/3 1 a r k 1 F strongly correlated: aρ 1/3 1

6 Dilute Fermi gas: field theory Non-relativistic fermions at low momentum L eff = ψ ( i M ) ψ C 0 2 (ψ ψ) 2 Unitary limit: a, σ 4π/k 2 (C 0 ) This limit is smooth: HS-trafo, Ψ = (ψ, ψ ) [ ] L = Ψ 2 i 0 + σ 3 Ψ + ( Ψ σ + Ψφ + h.c. ) 1 φ φ, 2m C 0 Low T (T < T c µ): Pairing and superfluidity

7 Dilute Fermi gas: BCS-BEC crossover

8 Intersection I: Many body physics/equation of state Free fermi gas at zero temperature E N = 3 5 k 2 F 2m N V = k3 F 3π 2 Consider unitarity limit (a, r 0) E N = ξ 3 5 k 2 F 2m k F (3π 2 N/V ) 1/3 Prize problem (George Bertsch, 1998): Determine ξ Similar problems: = αǫ F, k B T c = βǫ F

9 Analytic work: Epsilon expansion ξ = 1 2 ǫ3/ ǫ5/2 lnǫ ǫ 5/ O(1) O(1) O(ǫ) Green function MC ξ(ǫ=1) = Experiment 20 Pairing gap ( ) = 0.9 E FG E/E FG 10 odd N even N E = 0.44 N E FG N ξ = (Carlson et al.) ξ = 0.38(2) (Luo, Thomas)

10 Neutron matter with realistic interactions LO 3 NLO 3 FP 1981 APR 1998 CMPR v CMPR v SP 2005 GC 2007 GIFPS 2008 free E 0 /E k F (MeV) Results close to unitary limit (for k F a > 10). Corrections tend to cancel (range effects, p-waves, 3-body).

11 Density Functionals Gradient terms (from epsilon expansion) E(x) = n(x)v (x) n(x)5/3 m ( n(x)) mn(x) + O( 4 n) free Fermi gas: ( ) ( ) consider V (x) = 1 2 mω2 x 2 lim N E N E 0 N = ξ 0.63 evidence for large surface effects E N /E O( n) 2 N 1/3 fit ETFT N Blume et al., see also Bulgac (SFLDA), Gandolfi et al.

12 Intersection II: Pairing Numerical results (Carlson & Reddy, Burovsky et al.) = 0.48E F T c = 0.15E F Gap remarkably close to extrapolated BCS+Gorkov result = 8E ( F (4e) 1/3 e exp 2 π ) 2k F a (a ) = 0.49E F = = Gorkov (induced interaction) crucial, reduces gap by 1/2 +

13 Pairing gap with realistic interactions / E F k F [fm -1 ] BCS QMC s-wave QMC AV k F a (MeV) k F [fm -1 ] BCS Chen 93 Wambach 93 Schulze 96 Schwenk 03 Fabrocini 05 Cao 06 dqmc 09 AFDMC 08 QMC AV k F a Range corrections important, smaller than in unitary limit. But: QMC gaps larger than previous estimates.

14 Intersection III: Elliptic flow (QGP) Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy Parameter v Hydro model π K p Λ PHENIX Data π + +π K +K p+p STAR Data 0 K S Λ+Λ b Transverse Momentum p T source: U. Heinz (2005) dn p 0 d 3 p = v 0 (p ) (1 + 2v 2 (p ) cos(2φ) +...) pz =0 (GeV/c)

15 Viscosity and elliptic flow Viscous effects increase with impact parameter and p T. v ideal η/s=0.03 η/s=0.08 η/s=0.16 PHOBOS v 2 (percent) ideal η/s=0.03 η/s=0.08 η/s=0.16 STAR N Part p T [GeV] Romatschke (2007), see also Teaney (2003) Many questions: Dependence on initial conditions, freeze out, etc. conservative bound η s < 0.4

16 Almost ideal fluid dynamics (cold gases) Hydrodynamic expansion converts σ σ µ coordinate space anisotropy σ σ to momentum space anisotropy O Hara et al. (2002)

17 Collective oscillations Radial breathing mode Ideal fluid hydrodynamics (P = 2 3 E) n t + (n v) = 0 v ( t + v ) P v = mn V m 60 (a) (<x 2 >) (1/2) ( µm) (b) (c) Hydro frequency at unitarity 10 ω = 3 ω Damping small, depends on T/T F t hold (ms) 6 8 experiment: Kinast et al. (2005)

18 Viscous hydrodynamics Energy dissipation (η, ζ, κ: shear, bulk viscosity, heat conductivity) Ė = 1 d 3 x η(x) ( i v j + j v i 23 ) 2 2 δ ij k v k d 3 x ζ(x) ( i v i ) 2 1 d 3 x κ(x) ( i T) 2 T Shear viscosity to entropy ratio (assuming ζ =κ=0) η s = (3λN)1 3 Γ E 0 N ω E F S 1.5 η/s T/T F Schaefer (2007), see also Bruun, Smith T T F T T F, τ R η/p

19 Elliptic flow: High T limit Quantum viscosity η = η 0 (mt) 3/ Aspect Ratio η = η 0 (mt) 3/2 τ R = η/p Time After Release (µs) fit: η 0 = 0.33 ± 0.04 theory: η 0 = π = 0.26

20 Summary Unitary Fermi gas has become the benchmark problem for many body methods (equation of state, pairing, DFT) in nuclear physics (at least for pure neutron matter). Interesting (but maybe not quantitative) connections to the physics of quark matter and the quark gluon plasma, in particular nearly perfect fluidity. Many questions: Universality of nearly perfect fluidity? Quasi-particle picture?

21 More intersections Few body physics: Efimov effect, etc. Several species: Three species (quark-hadron transition), four species (nuclear matter, SU(4) symmetry). Finite polarization: critical δµ, LOFF phase (relevant to stressed color superconductivity). Rotating systems: Vortices (formation, pinning, etc.). New ideas: gauge fields, role of dimensionality, AdS/NRCFT.