1. Universal Spin Transport in Strongly Interacting Fermi Gases Ariel Sommer Mark Ku, Giacomo Roati, Martin Zwierlein MIT INT Experimental Symposium May 19, 2011

2. Net relative motion of atoms with different spin Damped due to collisions Spin Transport Spin current

3. Spin transport parameters Spin drag coefficient  SD Spin diffusivity D s F SD = ½ M  SD v rel

4. Motivation Learn about the unitary Fermi gas through transport properties Understand transport properties of strongly interacting systems

5. Expectations Known power laws at high temperature For T≈T F, expect D s ≈ ħ/m For T<<T F, correlations may influence transport See: Riedl et al., PRA 78, 053609 (2008) Bruun and Smith PRA 72 043605 (2005)

6. Experiment 1 Use 6 Li in the two lowest hyperfine states Prepare a 50/50 spin mixture at 300G Ramp to 50G, separate the spin states via magnetic gradient pulses Jump to the final field near the Feshbach resonance Observe the evolution

7. Collision of Two Fermi Gases

8. Position (a.u.)

9. Center of Mass Difference Time (ms) Bouncing at early times Exponential relaxation at late times

10. Varying Interactions

11. Experiment 2 Prepare a 50/50 spin mixture at 300G Cool or heat at 300G Ramp to 50G, separate the spin states Jump to the final field Cool again, or heat and wait, until separation is small Observe the evolution to equilibrium

12. Measuring Spin Drag Overdamped, use an exponential fit to get  SD

13. Results for Spin Drag: Unitarity Nature 472, 201 (2011) Maximum drag near T F

14. Spin Drag vs Interaction Strength Maximum drag on resonance T/T F = 0.32, 0.16 Nature 472, 201 (2011)

15. Comparison No enhanced spin drag at low T Riedl et al., PRA 78, 053609 (2008) Sommer et al, Nature 472, 201 (2011)

16. Measuring Spin Diffusivity D s from spin density gradient and equilibration time Gradient decays at the same rate as d

17. Spin Diffusion at Unitarity Minimum D s = 6.3(3) ħ/m for T < 0.5 T F Nature 472, 201 (2011)

18. Spin Diffusion vs Interaction Strength Minimum diffusivity on resonance Nature 472, 201 (2011)

19. Spin Susceptibility Spin conductivity: Einstein relation: Derivation – Magnetization in a spin-dependent potential: spin-diffusion ↔ spin-conduction

20. Spin Susceptibility Nature 472, 201 (2011) Susceptibility < Compressibility for T< T F

21. Relation to Homogeneous Values Non-uniform density and average velocity Trap average: Measured values:

22. Highly Polarized Gas Same procedure, but with a 90/10 mixture arXiv: 1103.2337 (NJP, in production) Solid line: Bruun et al., PRL 100, 240406 (2008)

23. More Pauli blocking in the polaron case Polaron damping 50/50 Spin drag Drag reduction from peak down to 0.15 T F : Polaron : 51(6)% reduction Balanced Gas: 26(4) % reduction

24. Conclusion Spin drag is strong at unitarity Maximum spin drag on resonance, near T F – Contrast to viscosity calculation at low T Minimum spin diffusion on res., below T F Non-uniform density and average velocity affects the measurement