# Snell's Law for a vortex dipole in a Bose-Einstein condensate. (arXiv:1811.02110v2 [cond-mat.quant-gas] UPDATED)

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 surface interaction, the

incoming and outgoing dipole paths obey Snell's law.