Universal Spin Transport in Strongly Interacting Fermi Gases

Ariel SommerMark Ku, Giacomo Roati, Martin Zwierlein

MIT

INT Experimental SymposiumMay 19, 2011

• Net relative motion of atoms with different spin

• Damped due to collisions

Spin Transport

Spin current

Spin transport parameters

• Spin drag coefficient SD

• Spin diffusivity Ds

FSD = ½ M SD vrel

Motivation

• Learn about the unitary Fermi gas through transport properties

• Understand transport properties of strongly interacting systems

Expectations

• Known power laws at high temperature• For T≈TF, expect Ds ≈ ħ/m

• For T<<TF, correlations may influence transport

See:Riedl et al., PRA 78, 053609 (2008)Bruun and Smith PRA 72 043605 (2005)

Experiment 1

• Use 6Li 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

Collision of Two Fermi Gases

Collision of Two Fermi Gases P

ositi

on (

a.u.

)

Center of Mass Difference

Time (ms)

• Bouncing at early times• Exponential relaxation at late times

Varying Interactions

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

Measuring Spin Drag

Overdamped, use an exponential fit to get SD

Results for Spin Drag: Unitarity

Nature 472, 201 (2011)• Maximum drag near TF

Spin Drag vs Interaction Strength

• Maximum drag on resonance

T/TF = 0.32, 0.16

Nature 472, 201 (2011)

Comparison

• No enhanced spin drag at low T

Riedl et al., PRA 78, 053609 (2008) Sommer et al, Nature 472, 201 (2011)

Measuring Spin Diffusivity

• Ds from spin density gradient and equilibration time

Gradient decays at the same rate as d

Spin Diffusion at Unitarity

Minimum Ds = 6.3(3) ħ/m for T < 0.5 TF

Nature 472, 201 (2011)

Spin Diffusion vs Interaction Strength

• Minimum diffusivity on resonanceNature 472, 201 (2011)

Spin Susceptibility

• Spin conductivity: • Einstein relation:

• Derivation – Magnetization in a spin-dependent potential:

spin-diffusion ↔ spin-conduction

Spin Susceptibility

Nature 472, 201 (2011)

Susceptibility < Compressibilityfor T< TF

Relation to Homogeneous Values

• Non-uniform density and average velocity• Trap average:• Measured values:

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)

• More Pauli blocking in the polaron case

Polaron damping 50/50 Spin drag

Drag reduction from peak down to 0.15 TF:

Polaron : 51(6)% reduction

Balanced Gas: 26(4) % reduction

Conclusion

• Spin drag is strong at unitarity• Maximum spin drag on resonance, near TF

– Contrast to viscosity calculation at low T

• Minimum spin diffusion on res., below TF

• Non-uniform density and average velocity affects the measurement