text: At temperatures below the lambda point, helium shows the unique property of superfluidity. The fraction of the liquid that forms the superfluid component is a macroscopic quantum fluid. The helium atom is a neutral particle, so . Furthermore, when considering helium-4, the relevant particle mass is , so Eq. () reduces to
  For an arbitrary loop in the liquid, this gives
  Due to the single-valued nature of the wave function
  with  integer, we have
  The quantity
  is the quantum of circulation. For a circular motion with radius r
  In case of a single quantum ()
  When superfluid helium is put in rotation, Eq. () will not be satisfied for all loops inside the liquid unless the rotation is organized around vortex lines (as depicted in Fig. 2). These lines have a vacuum core with a diameter of about 1 Å (which is smaller than the average particle distance). The superfluid helium rotates around the core with very high speeds. Just outside the core (r = 1 Å), the velocity is as large as 160 m/s. The cores of the vortex lines and the container rotate as a solid body around the rotation axes with the same angular velocity. The number of vortex lines increases with the angular velocity (as shown in the upper half of the figure). Note that the two right figures both contain six vortex lines, but the lines are organized in different stable patterns.