Stability of a Fermi Gas with Three Spin States The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites Yi Zhang John Huckans

Three-Component Fermi Gases Many-body physics in a 3-State Fermi Gas –Mechanical stability with resonant interactions an open question –Novel many-body phases Competition between different Cooper pairs Competition between Cooper pairing and 3-body bound states Analog to Color Superconductivity and Baryon Formation in QCD Polarized 3-state Fermi gases: Imbalanced Fermi surfaces Novel Cooper pairing mechanisms Analogous to mass imbalance of quarks

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 The Efimov Effect in a Fermi system –Three independent scattering lengths –More complex than Efimov’s original scenario –New phenomena (e.g. exchange reactions) Importance to many-body phenomena –Two-body and three-body physics completely described –Three-body recombination rate determines stability of the gas

Three-State 6 Li Fermi Gas Hyperfine States of 6 Li

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 in a 3-state mixture –(Exclusion principle suppression for 2-state mixture) Inelastic Collisions

Making and Probing 3-State Mixtures Magnetic Field (Gauss) Radio-frequency magnetic fields drive transitions Spectroscopically resolved absorption imaging

The Resonant QM 3-Body Problem Vitaly Efimov circa 1970 (1970) Efimov: An infinite number of bound 3-body states for A single 3-body parameter: Inner wall B.C. determined by short-range interactions Infinitely many 3-body bound states (universal scaling): · ·. ·

QM 3-Body Problem for Large a (1970 & 1971) Efimov: Identical Bosons in Universal Regime Note: Only two free parameters: Log-periodic scaling: E. Braaten, et al. PRL 103, & Diagram from: E. Braaten & H.-W. Hammer, Ann. Phys. 322, 120 (2007) Observable for a < 0: Enhanced 3-body recombination rate at

Universal Regions in 6 Li

The Threshold Regime and the Unitarity Limit Universal predictions only valid at threshold –Collision Energy must be small Smallest characteristic energy scale Comparison to theory requires low temperature and low density (for fermions) Recombination rate unitarity limited in a thermal gas

Making Fermi Gases Cold Evaporative Cooling in an Optical Trap Optical Trap Formed from two 1064 nm, 80 Watt laser beams Create incoherent 3-state mixture –Optical pumping into F=1/2 ground state –Apply two RF fields in presence of field gradient

Making Fermi Gases Ultracold Adiabatically Release Gas into a Larger Volume Trap

Low Field Loss Features Resonances in the 3-Body Recombination Rate! Resonance T. B. Ottenstein et al., PRL 101, (2008).J. H. Huckans et al., PRL102, (2009).

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 in Low-Field Region

P. Naidon and M. Ueda, PRL 103, (2008). E. Braaten et al., PRL 103, (2009). S. Floerchinger, R. Schmidt, and C. Wetterich, Phys. Rev. A 79, (2009)

Recombination Rate in Low-Field Region P. Naidon and M. Ueda, PRL 103, (2008). E. Braaten et al., PRL 103, (2009). S. Floerchinger, R. Schmidt, and C. Wetterich, Phys. Rev. A 79, (2009) Better agreement if  * tunes with magnetic field – A. Wenz et al., arXiv: (2009).

Efimov Trimer in Low-Field Region

3-Body Recombination in High Field Region

Determining the Efimov Parameters using calculations from E. Braaten et al., PRL 103, (2009).

Determining the Efimov Parameters using calculations from E. Braaten et al., PRL 103, (2009).

Determining the Efimov Parameters using calculations from E. Braaten et al., PRL 103, (2009).

Efimov Trimers in High-Field Region also predicts 3-body loss resonances at 125(3) and 499(2) G

3-Body Observables in High Field Region from E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv (2009).

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 ~ 200 ms ( K 3 ~ 5 x cm 6 /s) –Timescale for Cooper pair formation

Summary Observed variation of three-body recombination rate by 8 orders of magnitude Experimental evidence for ground and excited state Efimov trimers in a three-component Fermi gas Observation of Efimov resonance near three overlapping Feshbach resonances Determined three-body parameters in the high field regime which is well described by universality The value of  * is nearly identical for the high-field and low-field regions despite crossing non-universal region Three-body recombination rate is large but does not necessarily prohibit future studies of many-body physics

Fermi Gas Group at Penn State Ken O’Hara John Huckans Ron Stites Eric Hazlett Jason Williams Yi Zhang

Future Prospects Efimov Physics in Ultracold Atoms –Direct observation of Efimov Trimers –Efimov Physics (or lack thereof) in lower dimensions Many-body phenomena with 3-Component Fermi Gases