Chirality-Induced Spin Currents in a Fermi Gas

Abstract

We observe and model spin currents arising from chirality and effective spin-exchange interactions in a weakly interacting $^6$Li Fermi gas. Chirality is introduced by a static displacement between the center of the trapped atoms and the center of an applied magnetic bowl, which produces spatially varying spin rotation. Spin-selective spin current is observed via oscillations in the centers of mass of the spin-up and spin-down components, which appear to bounce off of or pass through one another, depending on the relative size of the chirality and s-wave spin scattering interactions. We show that this behavior obeys a driven oscillator equation with an effective spin-dependent driving force.

Figures (7)

• Figure 1: Controlling spin twist in an atomic Fermi gas. A cigar-shaped cloud of $^6$Li (light blue), prepared in a superposition of spin-up and spin-down states, is confined by a focused CO$_2$ laser beam (orange) and a magnetic bowl (red). $x$-dependent spin twist about the chiral $z$-axis is controlled by the offset $x_{os}$ between the centers of the spin-dependent magnetic bowl potential and the trapped cloud (blue) at $x\equiv 0$.
• Figure 2: Spatial profiles for spin-up and spin-down states. Spin-up (blue), spin-down (red). The total density $n_\uparrow+n_\downarrow$ (orange) is conserved. Chirality is controlled by the offset parameter $x_{os}$, see Fig. \ref{['fig:trap']}. a) $x_{os}=1.0\,\sigma_x$ at $t=21$ ms with an s-wave scattering length $a_s=-53.1\,a_0$ G; b) $x_{os}=-0.9\,\sigma_x$ at $t=37$ ms for $a_s=-213.1\,a_0$. Predictions (solid curves).
• Figure 3: Oscillating spin current versus chirality. $\langle x\rangle_{\uparrow\downarrow}$ denotes the center-of-mass of each spin state (blue and red). The s-wave scattering length is fixed at $a_s=-53.1a_0$. Chirality is controlled by the offset $x_{os}$, see Fig. \ref{['fig:trap']}. (a) $x_{os}= 0.8\,\sigma_x$; (b) $x_{os}= 0.0$; (c) $x_{os}=- 0.8\,\sigma_x$; (d) $x_{os}=-3.0\,\sigma_x$, where $\sigma_x\simeq 200\,\mu$m. Time is measured from the end of the $\pi/2$ RF pulse. Each point is the average of $5$ shots. The peak total density (a-c) is $\bar{n}_0=0.9/\mu m^3$, $\nu_x=25.9$ Hz; (d) $\bar{n}_0=0.42/\mu m^3$, $\nu_x=21.8$ Hz. The spin components reverse roles with the sign of $x_{os}$. Solid curves show predictions.
• Figure 4: Oscillating spin current for an s-wave scattering length $a_s=-84.6\,a_0$ ($B=500$ G). The chirality parameter, see Fig. \ref{['fig:trap']}, $x_{os} = 1.15\,\sigma_x$ with $\sigma_x=197\,\mu$m and $\bar{n}_0=0.99/\mu m^3$ with $\nu_x=22.4$ Hz.
• Figure 5: Oscillating spin current for an s-wave scattering length $a_s=-213.1\,a_0$ ($B=437$ G). The chirality parameter, see Fig. \ref{['fig:trap']}, $x_{os} =-0.8\,\sigma_x$ with $\sigma_x=195\,\mu$m and $\bar{n}_0=0.52/\mu m^3$ with $\nu_x=24.3$ Hz.