Quantum theory of vortex lattice state in a rotating Bose-Einstein condensate

We study system of large number of singly quantized vortices in a rotating Bose-Einstein condensate. Analogous to the Meissner effect in superconductors, we show that the vector potential due to the external rotational field can be tuned to cancel the vector potential due to the Magnus field, resulting in a zero average angular momentum and a shear modulus of the vortex lattice. The vortex lattice state exhibits two states, namely, an elastic state and a plastic state. A clear distinction between these states is controlled by the filling fraction, which is the ratio of the number of bosons to the average number of vortices.