We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.

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 ...

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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...