A quantum vortex dipole, comprised of a closely bound pair of
vortices of equal strength with opposite circulation, is a spatially
localized travelling excitation of a planar superfluid that carries
linear momentum, suggesting a possible analogy with ray optics. We
investigate numerically and analytically the motion of a quantum vortex
dipole incident upon a step-change in the background superfluid density
of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to
the conservation of fluid momentum and energy, the incident and
refracted angles of the dipole satisfy a relation analogous to Snell’s
law, when crossing the interface between regions of different density.
The predictions of the analogue Snell’s law relation are confirmed for a
wide range of incident angles by systematic numerical simulations of the
Gross-Piteavskii equation. Near the critical angle for total internal
reflection, we identify a regime of anomalous Snell’s law behaviour
where the finite size of the dipole causes transient capture by the
interface. Remarkably, despite the extra complexity of the interface
interaction, the incoming and outgoing dipole paths obey Snell’s
law.
Magnetization of a half-quantum vortex in a spinor Bose-Einstein condensate
