Figure 1

The lowest-energy Kelvin wave of a single vortex corresponds to a rotation of the tilted vortex line in the opposite direction to the rotation of the condensate. The plots show one complete rotation of the vortex going from left to right. In the tilting mode of a vortex array excited in this experiment, each vortex synchronously undergoes a similar motion. The plots show surfaces of constant density $|\Psi {|}^2=9e-4$ of a condensate cloud (wave function normalized to one) from a numerical simulation using the Gross-Pitaevskii equation. The initial state is a single centered vortex (aligned along the vertical axis); this is excited by resonant driving for two vortex precession periods by tilting the confining potential about an axis in the horizontal plane, as in the experiments, with an amplitude of 4°. In this simulation $N=75000$, $f_{\perp }=61\mathrm{H}\mathrm{z}$, $f_z=172.5\mathrm{H}\mathrm{z}$.Reuse & Permissions

Figure 2

Calculation of the mode frequencies predicted by Eq. (1) for a trapping potential with ${\omega }_z/{\omega }_{\perp }=\sqrt{8}$. (a) ${\omega }_u/{\omega }_{\perp }$ (dot-dashed line), ${\omega }_l/{\omega }_{\perp }$ (dotted line), ${\omega }_t/{\omega }_{\perp }$ (solid line). (b) ${\omega }_u/{\omega }_{\perp }-3$ (dot-dashed line), $3-{\omega }_l/{\omega }_{\perp }$ (dotted line), ${\omega }_t/{\omega }_{\perp }$ (solid line). The plot also shows the ratio $({\omega }_u-{\omega }_l)/2{\omega }_t$ (dashed line).Reuse & Permissions

Figure 3

Absorption image of a vortex array, taken along the $z$ axis.Reuse & Permissions

Figure 4

Exciting the normal scissors mode in the presence of vortices produces a precession that can be used to infer the angular momentum of the vortex array.Reuse & Permissions

Figure 5

(Black squares) Off resonant excitation of the scissors mode when no vortices are present. (White circles) Resonant driving of the “tilting mode” in the presence of a vortex array.Reuse & Permissions

Figure 6

Absorption images of the vortex lattice, viewed in a radial direction.Reuse & Permissions

Figure 7

(Black squares) Anomalous mode initially excited perpendicular to probe beam. (White triangles) Anomalous mode initially excited parallel to probe beam.Reuse & Permissions