Spontaneous squeezing of a vortex in an optical lattice

We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum-mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.