Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with s-wave symmetry, i.e., without relative angular momentum.We report measurements of two new physical quantities, the "p-wave contacts", and present evidence that they encode the universal aspects of p-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of 40 K, in which s-wave interactions are suppressed by polarising the sample, while p-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive p-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant p-wave quantum gas. 1 arXiv:1505.08151v4 [cond-mat.quant-gas] 13 Apr 2016 A fundamental question provoked by observation of natural systems is how macroscopic and collective properties depend on microscopic few-body interactions. Ultracold neutral atoms provide a model system in which to explore this question, since in certain conditions,few-body interactions can be tuned and characterised precisely. Over the last decade, a direct link has been made in these systems between thermodynamic properties and the underlying isotropic (s-wave) interactions. At the centre stage is a quantity called the "contact" [1][2][3][4][5][6], which describes how the energy of a system changes when the interaction strength is changed. Surprisingly, the contact is also the pivot of a set of universal relations, that constrain numerous microscopic properties, including the two-particle correlation function at short range. These relations apply regardless of temperature, density, or interaction strength [1-3, 5], to fermions and bosons [7][8][9], and in one-, two-, and three-dimensional systems [7,[10][11][12]. Contact relations have also been extended to Coulomb gases [13] and neutron-proton interactions [14]. Despite the breadth of this discussion, measurements of the contact have so far been restricted to systems with s-wave interactions.In general, the relative wave function of any pair of particles can be decomposed into components with angular momentum equal to an integer multiple of quanta. In a spinpolarised Fermi gas, quantum statistics forbids short-range interactions with even values of . Therefore, the first allowed scattering channel has = 1 (p-wave), which is typically weak due to the centrifugal barrier (see Fig. 1): the scattering cross section decreases with the square of...

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 /m, where m is the particle mass. The development of pair correlations, indicating the transformation of the initially non-interacting gas towards a unitary spin mixture, is observed by measuring Tan's contact parameter.Short-range interactions reach their quantum-mechanical limit when the scattering length that characterizes interparticle collisions diverges. A well controlled model system that realizes this unitary regime is provided by ultracold fermionic alkali atoms tuned to a Fano-Feshbach resonance [1]. These scale-invariant gases are characterized by universal parameters relevant to diverse systems such as the crust of neutron stars at twenty-five orders of magnitude higher density [2,3]. Experiments with ultracold atoms have already greatly contributed to the understanding of equilibrium properties of unitary gases [4][5][6]. Progress has also been made in the study of unitary dynamics [7][8][9][10][11], including observations of suppressed momentum transport [7] and spin transport [8][9][10] due to strong scattering.Spin diffusion is the transport phenomenon that relaxes magnetic inhomogeneities in a many-body system. At low temperature, where Pauli blocking suppresses collision rates, one must distinguish between diffusion driven by gradients in either the magnitude or the direction of magnetization, and quantified by longitudinal spin diffusivity D . This is consistent with a dimensional argument, in which diffusivity is a typical velocity ( k F /m for a cold Fermi gas, where k F is the Fermi momentum) times the mean free path between collisions. In the absence of localization, the mean-free path in a gas cannot be smaller than the interparticle spacing ∼ 1/k F , which translates into a quantum lower bound of roughly /m [9, 14, 15]. However, D ⊥ s as low as 0.0063(8) /m was recently observed in a strongly interacting two-dimensional Fermi gas [10]. This thousand-fold range in transport coefficients remains unexplained by theory.We measure the transverse demagnetization dynamics of a three-dimensional Fermi gas that is initially fully spinpolarized. All of our measurements are carried out with samples of ultracold 40 K atoms in a harmonic trap. Each atom is prepared in an equal superposition of two resonantly interacting internal states, labeled |↑ and |↓ [16], which corresponds to a gas with full transverse magnetization M y = 1 (Fig. 1). Initially, interactions between these identical ultracold fermions is inhibited ...

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) /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 non-zero γ. Tuning the scattering length a, we find that a sign change in γ occurs in the range 0 < (kF a) −1 1.3, where kF 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.Transport properties of unitary Fermi gases have been studied extensively in the past few years. Due to strong inter-particle interactions at unitarity, various transport coefficients like viscosity and spin diffusivity are bounded [1-3] by a conjectured quantum minimum [4][5][6], in three dimensions. On the other hand, transport in twodimensional unitary Fermi gases shows anomalous behavior, apparently violating a quantum limit [7]. This remains to be understood.In the case of spin diffusion, experiments so far [2, 3, 7] have been interpreted with a spin current proportional to the magnetization gradient, J j = −D∇ j M , where D is the diffusion constant [8], and M = M x , M y , M z is the local magnetization. Bold letters indicate vectors in Bloch space and the subscript j ∈ {1, 2, 3} denotes spatial direction. In general, J j has both a longitudinal component J j M and a transverse component J ⊥ j ⊥ M . Longitudinal spin currents are purely dissipative, and the standard diffusion equation applies [5,6,9,10]. However, as Leggett and Rice pointed out [11], the transverse spin current followswhereis the effective transverse diffusivity and γ is the Leggett-Rice (LR) parameter [12] (see Fig. 1a). Physically, the second term describes a reactive component of the spin current that precesses around the local magnetization. This precession has been observed in weakly interacting Fermi gases [7,13,14] and is a manifestation of the so-called identical spinrotation effect [15], which is intimately related to the LR effect [16]. In a unitary Fermi gas, however, neither the existence of the LR effect nor the value of γ has been measured. In this Letter, we provide the first evidence for LR effects in a unitary Fermi gas, and measure γ using a spin-echo technique. Our experiments are carried out in a trapped cloud of 40 K atoms using the two lowest-energy Zeeman states |± z of the electronic ground-state manifold [17]. Interaction...

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...