To make a superfluid rotate in an annulus shaped container, we start with a normal fluid, rotate the container, then cool it to below critical temperature to get a rotating superfluid.
The allowed values of circulation in a superfluid rotating with non-zero velocity are n*h/m where n could be 1,2,3.. or -1,-2,-3.... If we impart an angular velocity less than 0.5*h/m to the normal fluid, it goes to rest when converted to the superfluid state. If we impart 0.8*h/m, it goes to quantized circulation of h/m when converted to superfluid state. The explanation I got for this from my Professor's notes is that due to the high free energy barrier between the 2 nearest quantized circulations for the superfluid, it goes to the closest one. Is this correct ? Should the circulation not always fall to the nearest lower value of quantized circulation when converted to superfluid state ? How does free energy come into role for this ?