Quantum theory of a vortex line in an optical lattice

Jani-Petri Martikainen

Jani-Petri Martikainen and H. T. C. Stoof
Nanoscience Center/Department of Physics, University of Jyväskylä, Survontie 9, PO Box 35 (YFL), Finland

We discuss the quantum theory of a vortex line in a stack of weakly-coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We explain how the physics of the vortex line is described by the one-dimensional Bose-Hubbard model and how the interactions can induce squeezing of the vortex. At classical level, the theory of the vortex line in an optical lattice has soliton solutions. We also discuss this novel possibility as well as how the normal modes of the vortex line couple with the quadrupole modes of the Bose-Einstein condensate.