Experiments with an Ultracold Three-Component Fermi Gas

Transcription

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 6 Li 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, (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, (2007) Rapp, Hofstetter & Zaránd, PRB 77, (2008) A Color Superconductor in a 1D Harmonic Trap Liu, Hu, & Drummond, PRA 77, (2008)

6 Universal Three-Body Physics New Physics with 3 State Fermi Gas: Three-body interactions No 3-body interactions in a cold 2-state Fermi gas (if λ db >> r 0 ) λ db 3-body interactions allowed in a 3-state Fermi gas λ db The quantum 3-body problem Difficult problem of fundamental interest (e.g. baryons, atoms, nuclei, molecules) Efimov (1970): Solutions with Universal Properties when a >> r 0

7 Three States of 6 Li Hyperfine States Feshbach Resonances 3 } F = 3/ } F = 1/ 2 m s = +1/ 2 m s =!1/ 2 Interactions at High Field

8 Inelastic Collisions No Spin-Exchange Collisions } F = 3/ 2 Energetically forbidden 3 (in a bias field) 2 1 } F = 1/ 2 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 Rapid, all-optical production of DFGs 1 DFG every 5 seconds Load Magneto-Optical Trap 10 9 atoms T ~ 200 µk Crossed Optical Dipole Trap: Two 80 Watt 1064 nm Beams U max = 1 mk/beam Transfer 5x10 6 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 a 12 = -300 a 0 Lower depth of trap by factor of ~ mm U f = 38 µk/beam ν y = 106 Hz ν z = 965 Hz ν = 732 Hz ν x = 3.84 khz

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

11 Making a 3-State Mixture Populating 3 states 2 RF signals with field gradient High Field Absorption Imaging 3 states imaged separately 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 Inner wall B.C. determined by short-range interactions Vitaly Efimov circa 1970 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 (2006)

17 Efimov Resonances Resonance Resonance Resonant features in 3-body loss rate observed in ultracold Cs T. Kraemer et al. Nature (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: Note: Only two free parameters: κ and η 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: κ *, η * (a eff is known)

22 Efimov Resonances

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

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

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

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

27 Trap for 100 nk cloud N total ~ 3.6 x 10 5 ν x = 26.1 Ηz ν y = 26.6 Hz ν z = 109 Hz ν = 42 Hz y Z Evaporation beams Elliptical beam provides trapping in z direction T F = 180 nk x T = 100 nk y-position [micro-meters] x-position [micro-meters] Quantum Degenerate Gas in SU(3) Regime k F a = 0.25 Helmholtz arrangement provides B z for Feshbach tuning and sufficient radial gradient for atom trapping

28 Prospects for Color Superfluidity Color Superfluidity in a Lattice (increased density of states) T C = 0.2 T F (in a lattice with d = 2 µm, V 0 = 3 E R ) Atom density ~10 11 /cc Atom lifetime ~ 1 s (assuming K 3 ~ cm 6 /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 ~ r 0 Fits yield 3-body parameters for 6 Li 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