Quantized Vortices

In an ordinary classical fluid the liquid can rotate at any speed. In superfluid helium-4 the velocity of the superfluid component is quantized by the condition

where h is Planck's constant, m is the mass of one helium atom, and n is an integer. Consistent with this equation, the flow satisfies the condition curl is zero everywhere except along vortex lines where the velocity is singular. In the vicinity of a vortex line the liquid velocity is very large. An electron bubble is attracted to a vortex line because the bubble, which is empty apart from the electron, displaces liquid with a high kinetic energy.