Coexistence of single and double quantum vortex lines

We discuss the configurations in which singly and doubly quantized vortex lines coexist in a rotating superfluid. General principles of energy minimization lead to the conclusion that in equilibrium the two vortex species segregate within a cylindrical vortex cluster in two coaxial domains where the singly quantized lines are in the outer annular region. This is confirmed with simulation calculations on discrete vortex lines. Experimentally the coexistence can be studied in rotating superfluid ${}^{3}\mathrm{He}$-$A.$ With cw NMR techniques we find the radial distribution of the two vortex species to depend on how the cluster is prepared: (i) By cooling through ${T}_{c}$ in rotation, coexistence in the minimum energy configuration is confirmed. (ii) A disordered agglomerate is formed if one starts with an equilibrium cluster of single quantum vortex lines and adds to it sequentially double quantum lines, by increasing the rotation velocity in the superfluid state. This proves that the energy barriers, which separate different cluster configurations, are too high for metastabilities to anneal.