Collision of two spin-polarized fermionic clouds

Abstract

We study the collision of two spin-polarized Fermi clouds in a harmonic trap using a simulation of the Boltzmann equation. As observed in recent experiments, we find three distinct regimes of behavior. For weak interactions the clouds pass through each other. If interactions are increased they approach each other exponentially and for strong interactions they bounce off each other several times. We thereby demonstrate that all these phenomena can be reproduced using a semiclassical collisional approach and that these changes in behavior are associated with an increasing collision rate. We then show that the oscillation of the clouds in the bounce regime is an example of an unusual case in quantum gases: a nonlinear coupling between collective modes, namely, the spin dipole mode and the axial breathing mode, which is enforced by collisions. We also determine the frequency of the bounce as a function of the final temperature of the equilibrated system. Recently, spin transport has become a much studied field in solid-state systems, for example, in mesoscopic phenomena, where the electronic spin degree of freedom is used to create new devices. Understanding the spin relaxation, diffusion, and other transport properties is of fundamental importance in such fields. In atomic gases it has been studied mainly in spinor Bose gases [1,2]. There has been renewed interest in spin transport in Fermi gases which are a clearer parallel to electronic systems [3][4][5][6][7][8]. An important advantage of cold gases in such studies is the simplification due to the absence of relaxation mechanisms for spin currents apart from direct collisions between atoms of different spin, unlike, e.g., in a solid, where collisions with the ionic lattice can be important. In addition, the atomic interaction and initial temperature of the clouds are easily tunable parameters. Finally, as we shall see, very large spin polarizations can be easily created, leading to large spin currents.Here we study the collision of two clouds with opposite spin polarization following the recent experiments of Sommer et al. [7]. We confine ourselves to the semiclassical regime, using a Boltzmann equation simulation. In contrast, a recent theoretical study has instead used a hydrodynamic approach based on a many-body equation of state [9].One of the most striking experimental observations was the bouncing of the clouds off each other. Here we will demonstrate that this phenomenon can be understood purely in terms of semiclassical collisions, without recourse to, e.g., mean fields or other more complicated effects. For instance, our approach predicts that all quantities considered here depend only on the square of the scattering length and not on its sign. Also, as we will show, the bouncing oscillations can be understood as an example of a nonlinear coupling between * o.goulko@damtp.cam.ac.uk collective modes which, to the best of our knowledge, has not been studied in Fermi gases. , where ω z < ω x = ω y . We assume that the system is in the normal phase and that...

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Numerical solution of the Boltzmann equation for trapped Fermi gases with in-medium effects

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Spin Drag of a Fermi Gas in a Harmonic Trap

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