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The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites

Experiments with an Ultracold Three-Component Fermi Gas. The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites John Huckans. Overview. New Physics with Three Component Fermi Gases Color Superconductivity

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The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites

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  1. Experiments with an Ultracold Three-Component Fermi Gas The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites John Huckans

  2. Overview • New Physics with Three Component Fermi Gases • Color Superconductivity • Universal Three-Body Quantum Physics: Efimov States • A Three-State Mixture of 6Li Atoms • Tunable Interactions • Collisional Stability • Efimov Physics in a Three-State Fermi Gas • Universal Three-Body Physics • Three-Body Recombination • Evidence for Efimov States in a 3-State Fermi Gas • Prospects for Color Superconductivity

  3. Color Superconductivity • BCS Pairing in a 3-State Fermi Gas • Pairing competition (attractive interactions) • Non-trivial Order Parameter • Anomalous number of Goldstone modes • (He, Jin, & Zhuang, PRA 74, 033604 (2006)) • No condensed matter analog • Color Superconducting Phase of Quark Matter • Attractive Interactions via Strong Force • Color Superconducting Phase: High Density “Cold” Quark Matter • Color Superconductivity in Neutron Stars • QCD is a SU(3) Gauge Field Theory • 3-State Fermi Gas with Identical Pairwise Interactions: SU(3) Symmetric Field Theory

  4. QCD Phase Diagram C. Sa de Melo, Physics Today, Oct. 2008

  5. Simulating the QCD Phase Diagram • Color Superconducting-to-“Baryon” Phase Transition • 3-state Fermi gas in an optical lattice • Rapp, Honerkamp, Zaránd & Hofstetter, PRL 98, 160405 (2007) • A Color Superconductor in a 1D Harmonic Trap • Liu, Hu, & Drummond, PRA 77, 013622 (2008) • Rapp, Hofstetter & Zaránd, • PRB 77, 144520 (2008)

  6. Universal Three-Body Physics ldb • New Physics with 3 State Fermi Gas: Three-body interactions • No 3-body interactions in a cold 2-state Fermi gas (if ldb >> r0 ) • 3-body interactions allowed in a 3-state Fermi gas • The quantum 3-body problem • Difficult problem of fundamental interest • (e.g. baryons, atoms, nuclei, molecules) • Efimov (1970): Solutions with Universal Properties when a >> r0 ldb

  7. Three States of 6Li Hyperfine States Feshbach Resonances Interactions at High Field

  8. Inelastic Collisions • No Spin-Exchange Collisions • Energetically forbidden • (in a bias field) • Minimal Dipolar Relaxation • Suppressed at high B-field • Electron spin-flip process irrelevant in electron-spin-polarized gas • Three-Body Recombination • Allowed for a 3-state mixture • (Exclusion principle suppression for 2-state mixture)

  9. Making Degenerate Fermi Gases Crossed Optical Dipole Trap: Two 80 Watt 1064 nm Beams • Rapid, all-optical production of DFGs • 1 DFG every 5 seconds • Load Magneto-Optical Trap • 109 atoms • T ~ 200 mK • Transfer 5x106 atoms to optical trap • Create incoherent 2-state mixture • Optical pumping into F=1/2 ground state • Noisy rf pulse equalizes populations • Forced Evaporative Cooling • Apply 300 G bias field for a12 = -300 a0 • Lower depth of trap by factor of ~100 Umax= 1 mK/beam 1.2 mm Uf= 38 mK/beam ny = 106 Hz nz = 965 Hz nx = 3.84 kHz n = 732 Hz

  10. DFG and BEC BEC of Li2 Molecules 2-State Degenerate Fermi Gas Absorption Image after Expansion Absorption Image after Expansion 1.5 mm 1.5 mm 1 mm

  11. Making a 3-State Mixture • High Field Absorption Imaging • 3 states imaged separately Populating 3 states • 2 RF signals with field gradient 0 200 400 600 800 1000 B (Gauss)

  12. Stability of 3-State Fermi Gas • Fraction Remaining • in 3-State Fermi Gas • after 200 ms • Fraction Remaining • in 2-State Fermi Gases • after 200 ms

  13. Resonant Loss Features Resonance Resonance Resonances in the 3-Body Recombination Rate!

  14. Universality in 3-body systems 3-Body Problem in QM: Notoriously Difficult 6 coordinates in COM! Hyper-radius: , + 5 hyper-angles (1970) Efimov: pairwise interactions in resonant limit Vitaly Efimov circa 1970 Hyper-radial wavefunction obeys a 1D Schrodinger eqn. with an effective potential!

  15. Universal Scaling (1970) Efimov: An infinite number of bound 3-body states Vitaly Efimov circa 1970 Inner wall B.C. determined by short-range interactions Infinitely many 3-body bound states (universal scaling): A single 3-body parameter:

  16. Universality with Large “a” (1971) Efimov: extended treatment to large scattering lengths Vitaly Efimov circa 1970 Trimer binding energies are universal functions of Diagram from T. Kraemer et al. Nature 440 315 (2006)

  17. Efimov Resonances Resonance Resonance Resonant features in 3-body loss rate observed in ultracold Cs T. Kraemer et al. Nature 440 315 (2006)

  18. Universal Predictions • Efimov’s theory provides universal predictions • for low-energy three-body observables • Three-body recombination rate for identical bosons E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv:0811.3578 • Note: Only two free parameters: • k* and h* • Log-periodic scaling

  19. Measuring 3-Body Rate Constants Loss of atoms due to recombination: Evolution assuming a thermal gas at temperature T: “Anti-evaporation” and recombination heating:

  20. Recombination Rate Constants (to appear in PRL) (Penn State) (Heidelberg)

  21. Recombination Rate Constants Fit with 2 free parameters: k*, h* (aeff is known)

  22. Efimov Resonances

  23. 3-Body Params. in SU(3) Regime Unitarity Limit at 2 mK

  24. 3-Body Params. in SU(3) Regime Unitarity Limit at 2 mK

  25. 3-Body Params. in SU(3) Regime Unitarity Limit at 2 mK

  26. 3-Body Params. in SU(3) Regime Unitarity Limit at 100 nK

  27. Trap for 100 nK cloud Evaporation beams Ntotal ~ 3.6 x 105 y nx = 26.1 Hz Elliptical beam provides trapping in z direction ny = 26.6 Hz n = 42 Hz Z nz = 109 Hz x TF = 180 nK T = 100 nK Quantum Degenerate Gas in SU(3) Regime Helmholtz arrangement provides Bz for Feshbach tuning and sufficient radial gradient for atom trapping kF a= 0.25

  28. Prospects for Color Superfluidity • Color Superfluidity in a Lattice (increased density of states) • TC= 0.2 TF(in a lattice with d= 2 mm, V0= 3ER ) • Atom density ~1011 /cc • Atom lifetime ~ 1 s (assuming K3 ~ 10-22 cm6/s) • Timescale for Cooper pair formation

  29. Summary • Degenerate 3-State Fermi gas • Observed “Efimov” resonances • Two resonances with moderate scattering lengths • Measured three-body recombination rates • Reasonable agreement with Efimov theory for a ~ r0 • Fits yield 3-body parameters for 6Li at low field • Measured recombination rate at high field • Color superconductivity may be possible in a low-density gas

  30. Thanks to Ken O’Hara John Huckans Ron Stites Eric Hazlett Jason Williams

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