Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases

Conjectured quantum bounds on transport appear to be respected in many strongly interacting many-body systems. Since transport occurs as a system relaxes to equilibrium, many such bounds can be recast as an upper bound on the local relaxation rate $k_BT/\hbar$. Systems saturating this ``Planckian'' bound lack well defined quasiparticles promoting transport. We measure the transport properties of 2D ultracold Fermi gases of $^{40}$K during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of spin current around the local magnetization. When the 2D scattering length is tuned near an $s$-wave Feshbach resonance to be comparable to the inverse Fermi wave vector $k_F^{-1}$, we find that the bare transverse spin diffusivity reaches a minimum of $1.7(6)\hbar/m$. Demagnetization is also reflected in the growth rate of the $s$-wave contact, observed using time-resolved rf spectroscopy. At unitarity, the contact rises to $0.28(3)k_F^2$ per particle, measuring the breaking of scaling symmetry. Our observations support the conjecture that under strong scattering, the local relaxation rate is bounded from above by $k_BT/\hbar$.