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

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 spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k −1 F , we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6) /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. At unitarity, the contact rises to 0.28(3)k 2 F per particle, measuring the breaking of scaling symmetry. Our observations support the conjecture that in systems with strong scattering, the local relaxation rate is bounded from above by kBT / .Conjectured quantum bounds on transport appear to be respected and nearly saturated by quark-gluon plasmas [1, 2], unitary Fermi gases [3][4][5][6][7][8][9][10][11], and bad metals [12,13]. For many modalities of transport these bounds can be recast as an upper bound on the rate of local relaxation to equilibrium 1/τ r k B T / , where k B is the Boltzmann constant and T is temperature [14,15]. Systems that saturate this "Planckian" bound do not have well defined quasiparticles promoting transport [1,[12][13][14][15]. A canonical example is the quantum critical regime, where one expects diffusivity D ∼ /m, a ratio of shear viscosity to entropy density η/s ∼ /k B , and a conductivity that is linear in T [4, 12, 13]. These limiting behaviors can be understood by combining τ r with a propagation speed v ∼ k B T /m, for example D ∼ v 2 τ r . This argument applies to ultracold three-dimensional (3D) Fermi gases, whose behavior in the strongly interacting regime is controlled by the quantum critical point at divergent scattering length, zero temperature, and zero density [4,16,17]. In such systems, one observes D 2 /m [6-8] and η/s 0.4 /k B [3], compatible with conjectured quantum bounds.However in attractive two-dimensional (2D) Fermi gases, scale invariance is broken by the finite bound-state pair size, so the strongly interacting regime is no longer controlled by a quantum critical point [16,[18][19][20][21][22][23]. Strikingly, an extreme violation of the conjectured D /m bound has been observed in an ultracold 2D Fermi gas: a spin diffusivity of 6.3(8) × 10 −3 /m near ln(k F a 2D ) = 0 [24], where k F is the Fermi momentum and a 2D is the 2D s-wave scattering length. No similarly dramatic effect of dimensionality is observed in charge conductivity [12] or bulk viscosity [25], and such a low spin diffusivity is unexplained by theory [11,19].In this work, we recreate the conditions of Ref. [24], and study the demagnetization dynamics of ultracold 2D Fermi gases using both a coherent spin-echo sequence [8] and time-resolved spectroscopy [7]. We find a modification of th...

Collective excitations in two-dimensional SU( N ) Fermi gases with tunable spin

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Spin transport in a one-dimensional quantum wire

“…The sign of the interaction is encoded in the value of K σ : K σ < 1 corresponds to attractive and K σ > 1 to repulsive interactions. (6). On the side of Kσ > 1, below the separatrix line y 1⊥ ≈ 2Kσ − 2, the coupling y 1⊥ (l) approaches zero at l → ∞ and the cosine term H σ is irrelevant.…”

“…The parameters have been evolved according to Eqs. (6) up to the length scale l * at which either α(l * ) ≈ L or y 1⊥ (l * ) ≈ 1. The white lines show the separatrix y 1⊥ (0) = 2 K 2 σ (0) − 1 / K 2 σ (0) + 1 which corresponds to spin-rotation invariant interactions.…”

“…We have used here L = 5.5µm, α(l = 0) = ρ −1 0 = (0.8µm) −1 and the discretization δl = 0.1µm in Eq. (6). The same values are used in Fig.…”

Fermions in Two Dimensions: Scattering and Many-Body Properties

“…A rich area of study subject to ongoing investigation is that of low dimensionality [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. These dilute cold atomic gases have been trapped using anisotropic potentials, resulting in a quasi-2D pancake-shape gas cloud.…”