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Kubo Formalism for Spin Drag in an Atomic Fermi Gas

V. P. J. Jacobs

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Spin drag, the friction between interacting atoms of opposite spin, is the single relaxation mechanism of spin currents in cold atomic gases. Experiments are ongoing and one of the quantities of interest is the spin drag relaxation rate in a two-component atomic Fermi gas. Motivated by these experiments, we use the Kubo formalism to obtain an expression for the spin drag conductivity. The sunset approximation to the selfenergy is considered and a T 2 dependence of the relaxation rate is found. The effect of the BCS phase transition is studied by taking into account pair correlations with a ladder summation. Preliminary results indicate a sudden increase of the spin drag relaxation rate close to but above the critical temperature.

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Spin drag, the friction between interacting atoms of opposite spin, is the single relaxation mechanism of spin currents in cold atomic gases. Experiments are ongoing and one of the quantities of interest is the spin drag relaxation rate in a two-component atomic Fermi gas. Motivated by these experiments, we use the Kubo formalism to obtain an expression for the spin drag conductivity. The sunset approximation to the selfenergy is considered and a T 2 dependence of the relaxation rate is found. The effect of the BCS phase transition is studied by taking into account pair correlations with a ladder summation. Preliminary results indicate a sudden increase of the spin drag relaxation rate close to but above the critical temperature.
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We calculate the spin-drag relaxation rate for a two-component ultracold atomic Fermi gas with positive scattering length between the two-spin components. In one dimension, we find that it vanishes linearly with temperature. In three dimensions, the spin-drag relaxation rate vanishes quadratically with temperature for sufficiently weak interactions. This quadratic temperature dependence is present, up to logarithmic corrections, in the two-dimensional (2D) case as well. For stronger interaction, the system exhibits a Stoner ferromagnetic phase transition in two and three dimensions. We show that the spin-drag relaxation rate is enhanced by spin fluctuations as the temperature approaches the critical temperature of this transition from above.
Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed ``spin drag'' relaxation time ${\ensuremath{\tau}}_{\mathrm{sd}}$. In this paper we present both numerical and analytical calculations of ${\ensuremath{\tau}}_{\mathrm{sd}}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for ${\ensuremath{\tau}}_{\mathrm{sd}}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in one-dimensional inhomogeneous systems of interacting fermions.
Part of Focus on Bose Condensation Phenomena in Atomic and Solid State Physics We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose–Einstein condensation. In these systems, the spin conductivity is determined by spin drag, i.e. frictional drag between the two spin components due to interactions. We find that in the critical region, the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.
We consider spin transport in a two-component atomic Bose gas in three dimensions, at temperatures just above the critical temperature for Bose-Einstein condensation. In these systems the spin conductivity is determined by spin drag, i.e., frictional drag between the two spin components due to interactions. We find that in the critical region the temperature dependence of the spin conductivity deviates qualitatively from the Boltzmann result and is fully determined by the critical exponents of the phase transition. We discuss the size of the critical region where these results may be observed experimentally.
We consider two parallel layers of two-dimensional spin-polarized dipolar Fermi gas without any tunneling between the layers. The effective interactions describing screening and correlation effects between the dipoles in a single layer (intra-layer) and across the layers (interlayer) are modeled within the Hubbard approximation. We calculate the rate of momentum transfer between the layers when the gas in one layer has a steady flow. The momentum transfer induces a steady flow in the second layer which is assumed initially at rest. This is the drag effect familiar from double-layer semiconductor and graphene structures. Our calculations show that the momentum relaxation time has temperature dependence similar to that in layers with charged particles which we think is related to the contributions from the collective modes of the system.