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I've been reading up on Superfluids, and they've fascinated me. I understand why their superfluid component has zero viscosity, but there's one aspect that's bothering me, and that's the formation of so called "vortices". Why is their existence necessary?

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The superfluid can be in a state with zero vortices. But if one imparts angular momentum to the superfluid, then the angular momentum is physically expressed either by the superfluid rotating as a whole, or by the presence of vortices.

In an ordinary fluid vortices can also appear of course, but they get damped away by viscosity. This is not so for the superfluid: the vortices persist and they are quantized in angular momentum (owing to the fact that the phase increment around a loop has to be a multiple of $2\pi$, and with non-zero angular momentum there is a term $\exp(i m \phi)$ in the wavefunction).

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    $\begingroup$ How can we impart angular momentum to the superfluid, if it has zero viscosity? By this I mean, let's say we rotate the superfluid in a rotating container. Since it has zero viscosity it can't "grip" to the walls, right? Unless there's another way? $\endgroup$
    – jambajuice
    Feb 7, 2022 at 11:45
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    $\begingroup$ @jambajuice One way is to put a spoon into the fluid and move the spoon. Or more generally, introduce a bump in the fluid's potential energy as a function of position, and move the bump around in a circular motion. This can sometimes be done by means of tailored magnetic fields. $\endgroup$
    – Andrew Steane
    Feb 7, 2022 at 11:47
  • $\begingroup$ Ah okay, so why can't the angular momentum just be expressed in the rotation of this bump? Is that not enough? $\endgroup$
    – jambajuice
    Feb 7, 2022 at 12:40
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    $\begingroup$ @jambajuice The bump pushes against (i.e. transfers momentum to) the part of the fluid nearest it. Thus momentum gets put into the fluid, in different directions at different locations, so the net result is angular momentum in the fluid. Then one stops any further movement of the bump, and indeed usually one would remove it completely, like removing a spoon after stirring. $\endgroup$
    – Andrew Steane
    Feb 7, 2022 at 15:21

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