We consider a rotating Bose-Einstein condensate in a square optical lattice in the regime in which the Hamiltonian of the system can be mapped onto a Josephson junction array. In an approximate scheme where the couplings are assumed uniform, the ground state energy is formulated in terms of the vortex configuration. The results are compared with experimental results and also previously reported results for frustrated XY model. We also show that vortex configuration is robust with respect to change of couplings and therefore the results remain valid when we consider more realistic model with non-uniform couplings.
We derive a uniformly frustrated
XY model that describes two-dimensional Josephson-junction arrays consisting of rotating Bose-Einstein condensates trapped by both a harmonic trap and a corotating deep optical lattice. The harmonic trap makes the coupling constant of the model have a nonuniform parabolic dependence. We study the ground state through Monte Carlo simulations in a wide range of the frustration parameter
f, revealing a rich variety of vortex patterns.