Figure 1

False color plots of the (a) longitudinal and (b) transverse components of the Bloch vectors across the cloud as a function of time for a density of $2\times {10}^{13}{\mathrm{c}\mathrm{m}}^{-3}$ and a temperature of 800 nK (corresponding to a $380\mu \mathrm{m}$ full width, half maximum cloud size). The angles have been interpolated between bins and time steps of (a) 10 ms and (b) 3 ms.Reuse & Permissions

Figure 2

Bloch vector trajectories across the cloud for $T=600\mathrm{n}\mathrm{K}$ and $n=2\times {10}^{13}{\mathrm{c}\mathrm{m}}^{-3}$. Each spatial bin ($\sim 40\mu \mathrm{m}/\mathrm{\text{bin}}$) is shifted by 1 rad from the adjacent bins (see text). In each bin, the path traced by the Bloch vectors is shown starting with the red points near time $t=0$ and spiralling towards the blue points at $t=0.3\mathrm{s}$ as the Bloch vectors precess about the equilibrium position. (a) Spin waves at ${\partial }^2\nu /\partial z^2\approx 90\mathrm{H}\mathrm{z}/{\mathrm{m}\mathrm{m}}^2$. The equilibrium position (center of precession) has a curvature to match the curved potential. (b) Spin waves are excited for 70 ms at the same curvature, and then at $t=0$ the bias magnetic field is ramped quickly so that ${\partial }^2\nu /\partial z^2\approx 0$, giving an approximately flat equilibrium configuration near the $v$ axis for all spatial bins.Reuse & Permissions

Figure 3

(a) Frequency of the transverse spin-wave component as a function of the peak density. Each frequency is an extrapolation to the limit of small amplitude spin waves to remove the dependence on driving amplitude. The solid line is the predicted dispersion relation, and the dotted lines show the weak and strong coupling limits. All data is for $T=600\mathrm{n}\mathrm{K}$ except for the three tightly clustered points at $n=2\times {10}^{19}{\mathrm{m}}^{-3}$ which correspond to $T=350$, 600, and 1000 nK. (b) Damping rate as a function of density, including a numerical calculation (solid line) which includes elastic collisions and Landau damping.Reuse & Permissions