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arXiv:1612.00815 · Physical Review Letters

Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases

C. Luciuk, Scott Smale, Fabian Böttcher, Haille Sharum, Ben A. Olsen, Stefan Trotzky, Tilman Enss, Joseph H. Thywissen

Published Mar 31, 2017• 68 citations
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Abstract

We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.

DOI
10.1103/physrevlett.118.130405

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We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.
This thesis summarizes experimental work investigating strongly interacting Fermi gases in two and three dimensions. Radio-frequency spin manipulation is used to initialize and probe strongly interacting Fermi gases dynamically to measure relaxation to a steady-state. Time-resolved spectroscopy is used to discover the p-wave contacts by observing how correlations in the system develop after quenching the atoms into an interacting state. By combining quasi-steady state measurements with new contact relations, an attractive p-wave interaction energy as large as half the Fermi energy is inferred. Spin echo measurements of the magnetization dynamics are used to observe spin transport in two and three dimensions in the presence of strong interactions. The bare spin diffusivity is distinguished from the Leggett-Rice effect, in which demagnetization is slowed by precession of a spin current around the local magnetization. Observations of the demagnetization dynamics support the conjecture that a general quantum bound on spin transport is obeyed where the diffusivity D greater than or similar to ħ/m, where m is the particle mass.
We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity ${D}_{\ensuremath{\parallel}}$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity ${D}_{\ensuremath{\perp}}$ has a strong polarization dependence and approaches a finite value for $T\ensuremath{\rightarrow}0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\ensuremath{\hbar}/m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, ${D}_{\ensuremath{\perp}}$ attains a minimum at strong coupling $\ensuremath{-}1\ensuremath{\lesssim}\mathrm{ln}({k}_{F}{a}_{2D})\ensuremath{\lesssim}1$ and reaches ${D}_{\ensuremath{\perp}}\ensuremath{\sim}0.2...\phantom{\rule{0.16em}{0ex}}0.3\phantom{\rule{0.16em}{0ex}}\ensuremath{\hbar}/m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.
We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of (40)K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter γ=1.08(9) and a bare transverse spin diffusivity D(0)(⊥)=2.3(4)ℏ/m for a normal-state gas initialized with full polarization and at one-fifth of the Fermi temperature, where m is the atomic mass. One might expect γ=0 at unitarity, where two-body scattering is purely dissipative. We observe γ→0 as temperature is increased towards the Fermi temperature, consistent with calculations that show the degenerate Fermi sea restores a nonzero γ. Tuning the scattering length a, we find that a sign change in γ occurs in the range 0<(k(F)a)(-1)≲1.3, where k(F) is the Fermi momentum. We discuss how γ reveals the effective interaction strength of the gas, such that the sign change in γ indicates a switching of branch between a repulsive and an attractive Fermi gas.
This thesis investigates the dynamics of a degenerate Fermi gas in the unitary limit of strong interactions, in particular, the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. Short-range interactions between ultracold fermionic potassium atoms are tuned to their quantum mechanical limit by employing a Feshbach resonance. Spin-echo measurements of magnetization dynamics show that demagnetization is caused by diffusive spin transport with a diffusion constant that saturates at low temperatures to the conjectured quantum-mechanical lower bound ~/m, where m is the particle mass. A prediction for the increase in temperature due to demagnetization based on universal thermodynamics is compared to measured momentum distributions. The development of pair correlations is observed by time-resolved radiofrequency spectroscopy of Tan's contact parameter.
Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $\ensuremath{\gamma}$ are obtained; the sign of $\ensuremath{\gamma}$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin-echo time. While the microscopic diffusivity and $\ensuremath{\gamma}$ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.
Understanding the quantum dynamics of strongly interacting fermions is a problem relevant to diverse forms of matter, including high-temperature superconductors, neutron stars, and quark-gluon plasma. An appealing benchmark is offered by cold atomic gases in the unitary limit of strong interactions. Here, we study the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. We observe the demagnetization of the gas, caused by diffusive spin transport. At low temperatures, the diffusion constant saturates to the conjectured quantum-mechanical lower bound ≃ ħ/m, where m is the particle mass. The development of pair correlations, indicating the transformation of the initially noninteracting gas toward a unitary spin mixture, is observed by measuring Tan's contact parameter.