Pinning of Hidden Vortices in Bose-Einstein Condensate

We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensate in a rotating double-well trap potential and co-rotating optical lattice. We show that, in agreement with the experiment, the vortex number do not diverge when the rotational frequency $\mathrm{\Omega }\to 1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value $\sqrt l/l$for$l=4$ which supports the conjecture that surface modes with angular momentum $l=4$ are excited when the rotating condensate is trapped in double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning shows very interesting features. We show the existence and pinning of a new type of hidden vortices whose phase profile is similar to that of the visible vortices.