# Why does superfluid helium in a spinning bucket have angular momentum?

Suppose you have a bucket filled with superfluid Helium-4 and you spin it with a large angular velocity Ω, the bucket obviously has angular momentum.

Spinning fast enough, the fluid develops irrotational vortex lines which carry quanta of angular momentum, while leaving the curl of the ∇xv 0, as it should be (with v the microscopic velocity field).

My question is, supposing you start with the bucket at rest, it's obvious that the fluid has no angular momentum, but considering the fact there is no friction between the bucket and the fluid, how does the superfluid get the angular momentum needed to produce vortex lines?

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SteamKing
Staff Emeritus
Homework Helper
I may be missing something, but since when has the presence of friction been necessary for angular momentum to be present in a body, even one composed of a superfluid?

He's asking how does spinning the bucket impart angular momentum to the fluid. If you spin a bucket containing water it is the prescence of viscous /frictional forces that result in the water gaining angular momentum. Is there an analogous situation between the events in the water filled bucket and the superfluid filled bucket?

The superfluid consists of a superfluid component as well as a normal component. The normal component starts to rotate because it has nonzero viscocity and nonzero friction against the bucket wall. Then the interaction between the normal component and the superfluid component causes the vortices to appear.

I'm an undergrad in physics so don't think I'm a surprised expert. Could you show me the evidence for this phenomenon? It seems pretty interesting...

When you calculate the circulation of the momentum around a closed loop, you can show that it is equal to the variation of the phase of the wave function along the loop. Moreover, only the coherent part of the fluid can contribute to this circulation. Since the loop is closed, this implies that this variation is a multiple of 2π. As a result, the circulation of the coherent part of the fluid is quantized. This is by definition the superfluid. The superfluid can totally decouple from the normal fluid.

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