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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