Abstract
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.
Highlights
One of the defining characteristics of superfluids is their ability to support quantized vortices that carry angular momentum
A vortex closely bound with a vortex of opposite circulation in a Bose-Einstein condensate (BEC) forms a vortex dipole that carries linear fluid momentum [14]; these spatially localized excitations propagate with a constant speed which is inversely proportional to the distance between the vortices
They play a central role in the breakdown of superfluidity [18,19,20] and in energy transport mechanisms underpinning 2D quantum turbulence (2DQT) [21,22,23,24,25]
Summary
One of the defining characteristics of superfluids is their ability to support quantized vortices that carry angular momentum. Vortex dipoles have been created in BECs confined by parabolic potentials [15, 16], and could potentially be precisely manipulated using blue and red-detuned laser beams [17]. They play a central role in the breakdown of superfluidity [18,19,20] and in energy transport mechanisms underpinning 2D quantum turbulence (2DQT) [21,22,23,24,25].
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