Observation of the Leggett-Rice Effect in a Unitary Fermi Gas

Abstract

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...

Dynamics of Interacting Fermions in Spin-Dependent Potentials

“…1) implemented by a magnetic field gradient [2][3][4], or a spin-dependent harmonic trapping frequency [5][6][7][8] -equivalent to a spatially-varying gradient. Even in the weakly interacting regime, drastic modifications of the single-particle dynamics were reported.…”

“…To model two classes of experiments [2][3][4] and [5][6][7][8], we consider spin-dependent potentials of the form…”

Demagnetization dynamics of noninteracting trapped fermions

“…Recently there has been much experimental progress studying spin diffusion [1][2][3][4][5][6][7][8][9] and spin segregation dynamics (time-dependent separation of the spatial distributions of the spin components) [10][11][12][13][14][15][16] in trapped atomic gases. A typical experimental protocol consists of preparing a transversely spin-polarized gas and then observing the spin relaxation dynamics under the influence of a magnetic field gradient.…”

Crossover from collisionless to collisional spin dynamics of polarized fermions

“…In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two regimes have been studied experimentally and theoretically in cold atoms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], liquid helium [16][17][18][19], and solid state systems [20][21][22].…”

“…At lower temperatures one would need to include the Hartree-Fock mean-field terms which drive the Leggett-Rice effect [3], and demagnetization [8]. Our linearization of the collision integral will break down at large λ, where the dynamics create spin configuration which are far from equilibrium.…”