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

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 Overview

Color Superconductivity 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 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

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

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

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 db >> r 0 ) –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 >> r 0 db

Three States of 6 Li Hyperfine StatesFeshbach Resonances Interactions at High Field

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) Inelastic Collisions

Making Degenerate Fermi Gases Rapid, all-optical production of DFGs –1 DFG every 5 seconds Load Magneto-Optical Trap –10 9 atoms –T ~ 200  K 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 ~100 Crossed Optical Dipole Trap: Two 80 Watt 1064 nm Beams y = 106 Hz z = 965 Hz x = 3.84 kHz 1.2 mm U max = 1 mK/beam U f = 38  K/beam = 732 Hz

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

Making a 3-State Mixture Populating 3 states –2 RF signals with field gradient B (Gauss) High Field Absorption Imaging –3 states imaged separately

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

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

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

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

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

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

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:   and   Log-periodic scaling

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

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

Recombination Rate Constants Fit with 2 free parameters:  *,  * ( a eff is known)

Efimov Resonances

3-Body Params. in SU(3) Regime Unitarity Limit at 2  K

3-Body Params. in SU(3) Regime Unitarity Limit at 2  K

3-Body Params. in SU(3) Regime Unitarity Limit at 2  K

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

Trap for 100 nK cloud Z y x Helmholtz arrangement provides B z for Feshbach tuning and sufficient radial gradient for atom trapping T = 100 nK T F = 180 nK x =  z y =  Hz z = 109 Hz N total ~ 3.6 x 10 5 Elliptical beam provides trapping in z direction Evaporation beams = 42 Hz k F a = 0.25 Quantum Degenerate Gas in SU(3) Regime

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  m, 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

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

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